%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG192+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:39:43 EDT 2023 % Result : Unsatisfiable 20.53s 3.48s % Output : Proof 190.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : ALG192+1 : TPTP v8.1.2. Released v2.7.0. % 0.08/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.33 % Computer : n011.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Mon Aug 28 04:58:55 EDT 2023 % 0.12/0.34 % CPUTime : % 0.18/0.59 ________ _____ % 0.18/0.59 ___ __ \_________(_)________________________________ % 0.18/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.18/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.18/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.18/0.59 % 0.18/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.18/0.59 (2023-06-19) % 0.18/0.59 % 0.18/0.59 (c) Philipp Rümmer, 2009-2023 % 0.18/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.18/0.59 Amanda Stjerna. % 0.18/0.59 Free software under BSD-3-Clause. % 0.18/0.59 % 0.18/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.18/0.59 % 0.18/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.18/0.60 Running up to 7 provers in parallel. % 0.18/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.18/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.18/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.18/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.18/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.18/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.18/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 7.62/1.81 Prover 1: Preprocessing ... % 7.62/1.81 Prover 4: Preprocessing ... % 8.88/1.92 Prover 2: Preprocessing ... % 8.88/1.92 Prover 3: Preprocessing ... % 8.88/1.93 Prover 0: Preprocessing ... % 8.88/1.93 Prover 6: Preprocessing ... % 8.88/1.93 Prover 5: Preprocessing ... % 14.93/2.72 Prover 3: Constructing countermodel ... % 14.93/2.73 Prover 2: Constructing countermodel ... % 15.81/2.82 Prover 0: Constructing countermodel ... % 15.81/2.85 Prover 6: Constructing countermodel ... % 15.81/2.86 Prover 1: Constructing countermodel ... % 15.81/2.86 Prover 4: Constructing countermodel ... % 19.51/3.34 Prover 5: Constructing countermodel ... % 20.53/3.48 Prover 6: proved (2861ms) % 20.53/3.48 % 20.53/3.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.53/3.48 % 20.53/3.48 Prover 0: stopped % 20.53/3.48 Prover 5: stopped % 20.53/3.48 Prover 2: stopped % 20.53/3.48 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.53/3.48 Prover 3: stopped % 20.53/3.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.53/3.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.53/3.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.53/3.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 24.38/3.96 Prover 7: Preprocessing ... % 24.38/3.96 Prover 8: Preprocessing ... % 24.38/3.99 Prover 10: Preprocessing ... % 24.38/3.99 Prover 11: Preprocessing ... % 24.38/4.02 Prover 13: Preprocessing ... % 26.73/4.29 Prover 8: Constructing countermodel ... % 26.73/4.34 Prover 7: Constructing countermodel ... % 27.71/4.40 Prover 10: Constructing countermodel ... % 27.97/4.49 Prover 13: Constructing countermodel ... % 29.03/4.57 Prover 11: Constructing countermodel ... % 64.18/9.18 Prover 13: stopped % 64.31/9.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 65.59/9.38 Prover 16: Preprocessing ... % 67.90/9.74 Prover 16: Constructing countermodel ... % 109.85/15.16 Prover 16: stopped % 109.85/15.16 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 111.03/15.40 Prover 19: Preprocessing ... % 114.65/15.76 Prover 19: Constructing countermodel ... % 116.18/15.96 Prover 1: stopped % 136.35/18.77 Prover 19: stopped % 177.92/26.35 Prover 11: Found proof (size 13233437) % 177.92/26.35 Prover 11: proved (22870ms) % 177.92/26.36 Prover 10: stopped % 177.92/26.37 Prover 8: stopped % 177.92/26.37 Prover 4: stopped % 177.92/26.37 Prover 7: stopped % 177.92/26.38 % 177.92/26.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p % 177.92/26.38 % 181.12/28.24 % SZS output start Proof for theBenchmark % 181.22/28.29 Assumptions after simplification: % 181.22/28.29 --------------------------------- % 181.22/28.29 % 181.22/28.29 (ax1) % 181.45/28.35 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.35 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 181.45/28.35 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 181.45/28.35 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 181.45/28.35 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 181.45/28.35 [v23: $i] : ? [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = % 181.45/28.35 v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 181.45/28.35 v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, e4) = % 181.45/28.35 v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = % 181.45/28.35 v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 % 181.45/28.35 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 181.45/28.35 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & % 181.45/28.35 $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & % 181.45/28.35 $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 181.45/28.35 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | % 181.45/28.35 v24 = e2 | v24 = e1 | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = % 181.45/28.35 e1 | v23 = e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & % 181.45/28.35 (v21 = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 = % 181.45/28.35 e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 = e2 | % 181.45/28.35 v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 = e1 | v18 = % 181.45/28.35 e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 = e0) & (v16 = e4 | % 181.45/28.35 v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & (v15 = e4 | v15 = e3 | v15 = % 181.45/28.35 e2 | v15 = e1 | v15 = e0) & (v14 = e4 | v14 = e3 | v14 = e2 | v14 = e1 | % 181.45/28.35 v14 = e0) & (v13 = e4 | v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 % 181.45/28.35 = e4 | v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | % 181.45/28.35 v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = % 181.45/28.35 e1 | v10 = e0) & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = % 181.45/28.35 e4 | v8 = e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 % 181.45/28.35 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = e0) & % 181.45/28.35 (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 | v4 = e3 | v4 % 181.45/28.35 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 = e2 | v3 = e1 | v3 = % 181.45/28.35 e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e4 | v1 = % 181.45/28.35 e3 | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 % 181.45/28.35 | v0 = e0)) % 181.45/28.35 % 181.45/28.36 (ax10) % 181.45/28.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.36 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e4) = v1 & % 181.45/28.36 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e3) & op(e4, e0) = v2 & $i(v2)))))) % 181.45/28.36 % 181.45/28.36 (ax100) % 181.45/28.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.36 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e2) = v1 & % 181.45/28.36 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2)))))) % 181.45/28.36 % 181.45/28.36 (ax101) % 181.45/28.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.36 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e0) = v1 & % 181.45/28.36 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2)))))) % 181.45/28.36 % 181.45/28.36 (ax102) % 181.45/28.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.36 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e1) = v1 & % 181.45/28.36 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2)))))) % 181.45/28.36 % 181.45/28.36 (ax103) % 181.45/28.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.36 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e2) = v1 & % 181.45/28.36 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e1) & op(e2, e4) = v2 & $i(v2)))))) % 181.45/28.36 % 181.45/28.36 (ax104) % 181.45/28.36 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.36 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e3) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e1) & op(e3, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax105) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e1) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e2) & op(e1, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax106) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e3) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e2) & op(e3, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax107) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e1) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e3) & op(e1, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax108) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e2) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e3) & op(e2, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax109) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e2) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e0) & op(e2, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax11) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e2) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e4) & op(e2, e0) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax110) % 181.45/28.37 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.37 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e3) = v1 & % 181.45/28.37 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e0) & op(e3, e4) = v2 & $i(v2)))))) % 181.45/28.37 % 181.45/28.37 (ax111) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e0) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e2) & op(e0, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax112) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e3) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e2) & op(e3, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax113) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e0) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e3) & op(e0, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax114) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e2) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e3) & op(e2, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax115) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e1) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e0) & op(e1, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax116) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e3) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e0) & op(e3, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax117) % 181.45/28.38 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.38 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e0) = v1 & % 181.45/28.38 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e1) & op(e0, e4) = v2 & $i(v2)))))) % 181.45/28.38 % 181.45/28.38 (ax118) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e3) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e1) & op(e3, e4) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax119) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e0) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e3) & op(e0, e4) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax12) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e3) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e4) & op(e3, e0) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax120) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e1) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e3) & op(e1, e4) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax121) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e1) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e0) & op(e1, e4) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax122) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e2) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e0) & op(e2, e4) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax123) % 181.45/28.39 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.39 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e0) = v1 & % 181.45/28.39 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e1) & op(e0, e4) = v2 & $i(v2)))))) % 181.45/28.39 % 181.45/28.39 (ax124) % 181.45/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.40 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e2) = v1 & % 181.45/28.40 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e1) & op(e2, e4) = v2 & $i(v2)))))) % 181.45/28.40 % 181.45/28.40 (ax125) % 181.45/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.40 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e0) = v1 & % 181.45/28.40 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e2) & op(e0, e4) = v2 & $i(v2)))))) % 181.45/28.40 % 181.45/28.40 (ax126) % 181.45/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.40 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e1) = v1 & % 181.45/28.40 $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 = e2) & op(e1, e4) = v2 & $i(v2)))))) % 181.45/28.40 % 181.45/28.40 (ax13) % 181.45/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.45/28.40 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e3) = v1 & % 181.45/28.40 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2)))))) % 181.45/28.40 % 181.45/28.40 (ax14) % 181.76/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.40 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e4) = v1 & % 181.76/28.40 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e1) & op(e4, e0) = v2 & $i(v2)))))) % 181.76/28.40 % 181.76/28.40 (ax15) % 181.76/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.40 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e1) = v1 & % 181.76/28.40 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2)))))) % 181.76/28.40 % 181.76/28.40 (ax16) % 181.76/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.40 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e4) = v1 & % 181.76/28.40 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e3) & op(e4, e0) = v2 & $i(v2)))))) % 181.76/28.40 % 181.76/28.40 (ax17) % 181.76/28.40 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.40 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e1) = v1 & % 181.76/28.40 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e4) & op(e1, e0) = v2 & $i(v2)))))) % 181.76/28.40 % 181.76/28.40 (ax18) % 181.76/28.41 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.41 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e3) = v1 & % 181.76/28.41 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e4) & op(e3, e0) = v2 & $i(v2)))))) % 181.76/28.41 % 181.76/28.41 (ax19) % 181.76/28.41 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.41 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e2) = v1 & % 181.76/28.41 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2)))))) % 181.76/28.41 % 181.76/28.41 (ax2) % 181.76/28.45 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.45 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 181.76/28.45 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 181.76/28.45 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 181.76/28.45 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 181.76/28.45 [v23: $i] : ? [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, % 181.76/28.45 e3) = e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, e1) = % 181.76/28.45 e4) | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, e4) = e4) | % 181.76/28.45 (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, e4) = e4) | (v12 = e4 & % 181.76/28.45 op(e1, e4) = e4) | (v4 = e4 & op(e0, e4) = e4)) & ((v24 = e3 & op(e4, % 181.76/28.45 e4) = e3) | (v23 = e3 & op(e4, e3) = e3) | (v20 = e3 & op(e4, e2) = % 181.76/28.45 e3) | (v15 = e3 & op(e4, e1) = e3) | (v8 = e3 & op(e4, e0) = e3)) & % 181.76/28.45 ((v24 = e3 & op(e4, e4) = e3) | (v22 = e3 & op(e3, e4) = e3) | (v18 = e3 & % 181.76/28.45 op(e2, e4) = e3) | (v12 = e3 & op(e1, e4) = e3) | (v4 = e3 & op(e0, e4) % 181.76/28.45 = e3)) & ((v24 = e2 & op(e4, e4) = e2) | (v23 = e2 & op(e4, e3) = e2) | % 181.76/28.45 (v20 = e2 & op(e4, e2) = e2) | (v15 = e2 & op(e4, e1) = e2) | (v8 = e2 & % 181.76/28.45 op(e4, e0) = e2)) & ((v24 = e2 & op(e4, e4) = e2) | (v22 = e2 & op(e3, % 181.76/28.45 e4) = e2) | (v18 = e2 & op(e2, e4) = e2) | (v12 = e2 & op(e1, e4) = % 181.76/28.45 e2) | (v4 = e2 & op(e0, e4) = e2)) & ((v24 = e1 & op(e4, e4) = e1) | % 181.76/28.45 (v23 = e1 & op(e4, e3) = e1) | (v20 = e1 & op(e4, e2) = e1) | (v15 = e1 & % 181.76/28.45 op(e4, e1) = e1) | (v8 = e1 & op(e4, e0) = e1)) & ((v24 = e1 & op(e4, % 181.76/28.45 e4) = e1) | (v22 = e1 & op(e3, e4) = e1) | (v18 = e1 & op(e2, e4) = % 181.76/28.45 e1) | (v12 = e1 & op(e1, e4) = e1) | (v4 = e1 & op(e0, e4) = e1)) & % 181.76/28.45 ((v24 = e0 & op(e4, e4) = e0) | (v23 = e0 & op(e4, e3) = e0) | (v20 = e0 & % 181.76/28.45 op(e4, e2) = e0) | (v15 = e0 & op(e4, e1) = e0) | (v8 = e0 & op(e4, e0) % 181.76/28.45 = e0)) & ((v24 = e0 & op(e4, e4) = e0) | (v22 = e0 & op(e3, e4) = e0) | % 181.76/28.45 (v18 = e0 & op(e2, e4) = e0) | (v12 = e0 & op(e1, e4) = e0) | (v4 = e0 & % 181.76/28.45 op(e0, e4) = e0)) & ((v23 = e4 & op(e4, e3) = e4) | (v21 = e4 & op(e3, % 181.76/28.45 e3) = e4) | (v17 = e4 & op(e2, e3) = e4) | (v11 = e4 & op(e1, e3) = % 181.76/28.45 e4) | (v3 = e4 & op(e0, e3) = e4)) & ((v23 = e3 & op(e4, e3) = e3) | % 181.76/28.45 (v21 = e3 & op(e3, e3) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v11 = e3 & % 181.76/28.45 op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v23 = e2 & op(e4, % 181.76/28.45 e3) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v17 = e2 & op(e2, e3) = % 181.76/28.45 e2) | (v11 = e2 & op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & % 181.76/28.45 ((v23 = e1 & op(e4, e3) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v17 = e1 & % 181.76/28.45 op(e2, e3) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) % 181.76/28.45 = e1)) & ((v23 = e0 & op(e4, e3) = e0) | (v21 = e0 & op(e3, e3) = e0) | % 181.76/28.45 (v17 = e0 & op(e2, e3) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v3 = e0 & % 181.76/28.45 op(e0, e3) = e0)) & ((v22 = e4 & op(e3, e4) = e4) | (v21 = e4 & op(e3, % 181.76/28.45 e3) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v14 = e4 & op(e3, e1) = % 181.76/28.45 e4) | (v7 = e4 & op(e3, e0) = e4)) & ((v22 = e3 & op(e3, e4) = e3) | % 181.76/28.45 (v21 = e3 & op(e3, e3) = e3) | (v19 = e3 & op(e3, e2) = e3) | (v14 = e3 & % 181.76/28.45 op(e3, e1) = e3) | (v7 = e3 & op(e3, e0) = e3)) & ((v22 = e2 & op(e3, % 181.76/28.45 e4) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v19 = e2 & op(e3, e2) = % 181.76/28.45 e2) | (v14 = e2 & op(e3, e1) = e2) | (v7 = e2 & op(e3, e0) = e2)) & % 181.76/28.45 ((v22 = e1 & op(e3, e4) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v19 = e1 & % 181.76/28.45 op(e3, e2) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v7 = e1 & op(e3, e0) % 181.76/28.45 = e1)) & ((v22 = e0 & op(e3, e4) = e0) | (v21 = e0 & op(e3, e3) = e0) | % 181.76/28.45 (v19 = e0 & op(e3, e2) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v7 = e0 & % 181.76/28.45 op(e3, e0) = e0)) & ((v20 = e4 & op(e4, e2) = e4) | (v19 = e4 & op(e3, % 181.76/28.45 e2) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v10 = e4 & op(e1, e2) = % 181.76/28.45 e4) | (v2 = e4 & op(e0, e2) = e4)) & ((v20 = e3 & op(e4, e2) = e3) | % 181.76/28.45 (v19 = e3 & op(e3, e2) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v10 = e3 & % 181.76/28.45 op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v20 = e2 & op(e4, % 181.76/28.45 e2) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v16 = e2 & op(e2, e2) = % 181.76/28.45 e2) | (v10 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & % 181.76/28.45 ((v20 = e1 & op(e4, e2) = e1) | (v19 = e1 & op(e3, e2) = e1) | (v16 = e1 & % 181.76/28.45 op(e2, e2) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) % 181.76/28.45 = e1)) & ((v20 = e0 & op(e4, e2) = e0) | (v19 = e0 & op(e3, e2) = e0) | % 181.76/28.45 (v16 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 181.76/28.45 op(e0, e2) = e0)) & ((v18 = e4 & op(e2, e4) = e4) | (v17 = e4 & op(e2, % 181.76/28.45 e3) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v13 = e4 & op(e2, e1) = % 181.76/28.45 e4) | (v6 = e4 & op(e2, e0) = e4)) & ((v18 = e3 & op(e2, e4) = e3) | % 181.76/28.45 (v17 = e3 & op(e2, e3) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v13 = e3 & % 181.76/28.45 op(e2, e1) = e3) | (v6 = e3 & op(e2, e0) = e3)) & ((v18 = e2 & op(e2, % 181.76/28.45 e4) = e2) | (v17 = e2 & op(e2, e3) = e2) | (v16 = e2 & op(e2, e2) = % 181.76/28.45 e2) | (v13 = e2 & op(e2, e1) = e2) | (v6 = e2 & op(e2, e0) = e2)) & % 181.76/28.45 ((v18 = e1 & op(e2, e4) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v16 = e1 & % 181.76/28.45 op(e2, e2) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v6 = e1 & op(e2, e0) % 181.76/28.45 = e1)) & ((v18 = e0 & op(e2, e4) = e0) | (v17 = e0 & op(e2, e3) = e0) | % 181.76/28.45 (v16 = e0 & op(e2, e2) = e0) | (v13 = e0 & op(e2, e1) = e0) | (v6 = e0 & % 181.76/28.45 op(e2, e0) = e0)) & ((v15 = e4 & op(e4, e1) = e4) | (v14 = e4 & op(e3, % 181.76/28.45 e1) = e4) | (v13 = e4 & op(e2, e1) = e4) | (v9 = e4 & op(e1, e1) = e4) % 181.76/28.45 | (v1 = e4 & op(e0, e1) = e4)) & ((v15 = e3 & op(e4, e1) = e3) | (v14 = e3 % 181.76/28.45 & op(e3, e1) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v9 = e3 & op(e1, % 181.76/28.45 e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v15 = e2 & op(e4, e1) = % 181.76/28.45 e2) | (v14 = e2 & op(e3, e1) = e2) | (v13 = e2 & op(e2, e1) = e2) | (v9 % 181.76/28.45 = e2 & op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v15 = e1 & % 181.76/28.45 op(e4, e1) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v13 = e1 & op(e2, e1) % 181.76/28.45 = e1) | (v9 = e1 & op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & % 181.76/28.45 ((v15 = e0 & op(e4, e1) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v13 = e0 & % 181.76/28.45 op(e2, e1) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = % 181.76/28.45 e0)) & ((v12 = e4 & op(e1, e4) = e4) | (v11 = e4 & op(e1, e3) = e4) | % 181.76/28.45 (v10 = e4 & op(e1, e2) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v5 = e4 & % 181.76/28.45 op(e1, e0) = e4)) & ((v12 = e3 & op(e1, e4) = e3) | (v11 = e3 & op(e1, % 181.76/28.45 e3) = e3) | (v10 = e3 & op(e1, e2) = e3) | (v9 = e3 & op(e1, e1) = e3) % 181.76/28.45 | (v5 = e3 & op(e1, e0) = e3)) & ((v12 = e2 & op(e1, e4) = e2) | (v11 = e2 % 181.76/28.45 & op(e1, e3) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v9 = e2 & op(e1, % 181.76/28.45 e1) = e2) | (v5 = e2 & op(e1, e0) = e2)) & ((v12 = e1 & op(e1, e4) = % 181.76/28.45 e1) | (v11 = e1 & op(e1, e3) = e1) | (v10 = e1 & op(e1, e2) = e1) | (v9 % 181.76/28.45 = e1 & op(e1, e1) = e1) | (v5 = e1 & op(e1, e0) = e1)) & ((v12 = e0 & % 181.76/28.45 op(e1, e4) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v10 = e0 & op(e1, e2) % 181.76/28.45 = e0) | (v9 = e0 & op(e1, e1) = e0) | (v5 = e0 & op(e1, e0) = e0)) & % 181.76/28.45 ((v8 = e4 & op(e4, e0) = e4) | (v7 = e4 & op(e3, e0) = e4) | (v6 = e4 & % 181.76/28.45 op(e2, e0) = e4) | (v5 = e4 & op(e1, e0) = e4) | (v0 = e4 & op(e0, e0) = % 181.76/28.45 e4)) & ((v8 = e3 & op(e4, e0) = e3) | (v7 = e3 & op(e3, e0) = e3) | (v6 % 181.76/28.45 = e3 & op(e2, e0) = e3) | (v5 = e3 & op(e1, e0) = e3) | (v0 = e3 & % 181.76/28.45 op(e0, e0) = e3)) & ((v8 = e2 & op(e4, e0) = e2) | (v7 = e2 & op(e3, e0) % 181.76/28.45 = e2) | (v6 = e2 & op(e2, e0) = e2) | (v5 = e2 & op(e1, e0) = e2) | (v0 % 181.76/28.45 = e2 & op(e0, e0) = e2)) & ((v8 = e1 & op(e4, e0) = e1) | (v7 = e1 & % 181.76/28.45 op(e3, e0) = e1) | (v6 = e1 & op(e2, e0) = e1) | (v5 = e1 & op(e1, e0) = % 181.76/28.45 e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v4 = e4 & op(e0, e4) = e4) | (v3 % 181.76/28.45 = e4 & op(e0, e3) = e4) | (v2 = e4 & op(e0, e2) = e4) | (v1 = e4 & % 181.76/28.45 op(e0, e1) = e4) | (v0 = e4 & op(e0, e0) = e4)) & ((v4 = e3 & op(e0, e4) % 181.76/28.45 = e3) | (v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 % 181.76/28.45 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v4 = e2 & % 181.76/28.45 op(e0, e4) = e2) | (v3 = e2 & op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = % 181.76/28.45 e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v4 % 181.76/28.45 = e1 & op(e0, e4) = e1) | (v3 = e1 & op(e0, e3) = e1) | (v2 = e1 & % 181.76/28.45 op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = % 181.76/28.45 e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v8 = e0 & op(e4, e0) = e0) | % 181.76/28.45 (v7 = e0 & op(e3, e0) = e0) | (v6 = e0 & op(e2, e0) = e0) | (v5 = e0 & % 181.76/28.45 op(e1, e0) = e0)) & ((v4 = e0 & op(e0, e4) = e0) | (v3 = e0 & op(e0, % 181.76/28.45 e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & op(e0, e1) = % 181.76/28.45 e0))))) % 181.76/28.45 % 181.76/28.45 (ax20) % 181.76/28.45 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.45 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e4) = v1 & % 181.76/28.45 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e1) & op(e4, e0) = v2 & $i(v2)))))) % 181.76/28.45 % 181.76/28.45 (ax21) % 181.76/28.45 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.45 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e1) = v1 & % 181.76/28.45 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2)))))) % 181.76/28.45 % 181.76/28.46 (ax22) % 181.76/28.46 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.46 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e4) = v1 & % 181.76/28.46 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e2) & op(e4, e0) = v2 & $i(v2)))))) % 181.76/28.46 % 181.76/28.46 (ax23) % 181.76/28.46 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.46 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e1) = v1 & % 181.76/28.46 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e4) & op(e1, e0) = v2 & $i(v2)))))) % 181.76/28.46 % 181.76/28.46 (ax24) % 181.76/28.46 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 181.76/28.46 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e2) = v1 & % 181.76/28.46 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e4) & op(e2, e0) = v2 & $i(v2)))))) % 181.76/28.46 % 181.76/28.46 (ax25) % 182.05/28.46 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.46 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e2) = v1 & % 182.05/28.46 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e1) & op(e2, e0) = v2 & $i(v2)))))) % 182.05/28.46 % 182.05/28.46 (ax26) % 182.05/28.46 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.46 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e3) = v1 & % 182.05/28.46 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e1) & op(e3, e0) = v2 & $i(v2)))))) % 182.05/28.46 % 182.05/28.46 (ax27) % 182.05/28.46 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.46 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e1) = v1 & % 182.05/28.46 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e2) & op(e1, e0) = v2 & $i(v2)))))) % 182.05/28.46 % 182.05/28.46 (ax28) % 182.05/28.47 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.47 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e3) = v1 & % 182.05/28.47 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2)))))) % 182.05/28.47 % 182.05/28.47 (ax29) % 182.05/28.47 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.47 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e1) = v1 & % 182.05/28.47 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e3) & op(e1, e0) = v2 & $i(v2)))))) % 182.05/28.47 % 182.05/28.47 (ax3) % 182.05/28.47 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.47 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 182.05/28.47 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 182.05/28.47 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 182.05/28.47 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 182.05/28.47 [v23: $i] : ? [v24: $i] : (op(v24, v24) = e4 & op(v23, v22) = e4 & op(v22, % 182.05/28.47 v23) = e3 & op(v21, v21) = e3 & op(v20, v19) = e4 & op(v19, v20) = e2 & % 182.05/28.47 op(v18, v17) = e3 & op(v17, v18) = e2 & op(v16, v16) = e2 & op(v15, v14) = % 182.05/28.47 e4 & op(v14, v15) = e1 & op(v13, v12) = e3 & op(v12, v13) = e1 & op(v11, % 182.05/28.47 v10) = e2 & op(v10, v11) = e1 & op(v9, v9) = e1 & op(v8, v7) = e4 & op(v7, % 182.05/28.47 v8) = e0 & op(v6, v5) = e3 & op(v5, v6) = e0 & op(v4, v3) = e2 & op(v3, % 182.05/28.47 v4) = e0 & op(v2, v1) = e1 & op(v1, v2) = e0 & op(v0, v0) = e0 & op(e4, % 182.05/28.47 e4) = v24 & op(e4, e3) = v22 & op(e4, e2) = v19 & op(e4, e1) = v14 & % 182.05/28.47 op(e4, e0) = v7 & op(e3, e4) = v23 & op(e3, e3) = v21 & op(e3, e2) = v17 & % 182.05/28.47 op(e3, e1) = v12 & op(e3, e0) = v5 & op(e2, e4) = v20 & op(e2, e3) = v18 & % 182.05/28.47 op(e2, e2) = v16 & op(e2, e1) = v10 & op(e2, e0) = v3 & op(e1, e4) = v15 & % 182.05/28.47 op(e1, e3) = v13 & op(e1, e2) = v11 & op(e1, e1) = v9 & op(e1, e0) = v1 & % 182.05/28.47 op(e0, e4) = v8 & op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & % 182.05/28.47 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 182.05/28.47 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 182.05/28.47 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 182.05/28.47 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 182.05/28.47 % 182.05/28.47 (ax30) % 182.05/28.47 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.47 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e2) = v1 & % 182.05/28.47 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2)))))) % 182.05/28.47 % 182.05/28.47 (ax31) % 182.05/28.47 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.47 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e3) = v1 & % 182.05/28.47 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2)))))) % 182.05/28.47 % 182.05/28.47 (ax32) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e4) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e2) & op(e4, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax33) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e2) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax34) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e4) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e3) & op(e4, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax35) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e2) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e4) & op(e2, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax36) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e3) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e4) & op(e3, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax37) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e3) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax38) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e4) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e0) & op(e4, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax39) % 182.05/28.48 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.48 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e0) = v1 & % 182.05/28.48 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2)))))) % 182.05/28.48 % 182.05/28.48 (ax4) % 182.05/28.49 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.49 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 182.05/28.49 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 182.05/28.49 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 182.05/28.49 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 182.05/28.49 [v23: $i] : ? [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & % 182.05/28.49 ~ (v24 = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 = % 182.05/28.49 v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 = v18) & % 182.05/28.49 ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = v21) & ~ (v22 = % 182.05/28.49 v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = v7) & ~ (v22 = v2) & % 182.05/28.49 ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = v11) & ~ (v21 = v6) & ~ (v21 = % 182.05/28.49 v1) & ~ (v20 = v15) & ~ (v20 = v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ % 182.05/28.49 (v19 = v18) & ~ (v19 = v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = % 182.05/28.49 v14) & ~ (v19 = v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & % 182.05/28.49 ~ (v18 = v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 182.05/28.49 v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = v2) & % 182.05/28.49 ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = v1) & ~ (v15 = % 182.05/28.49 v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = v13) & ~ (v14 = v12) & % 182.05/28.49 ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = v9) & ~ (v14 = v4) & ~ (v13 = % 182.05/28.49 v12) & ~ (v13 = v11) & ~ (v13 = v10) & ~ (v13 = v8) & ~ (v13 = v3) & % 182.05/28.49 ~ (v12 = v11) & ~ (v12 = v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = % 182.05/28.49 v10) & ~ (v11 = v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ % 182.05/28.49 (v9 = v8) & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ % 182.05/28.49 (v8 = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & ~ % 182.05/28.49 (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = v0) & ~ % 182.05/28.49 (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ % 182.05/28.49 (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & % 182.05/28.49 op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, e2) = v14 & op(e4, e1) = v9 & % 182.05/28.49 op(e4, e0) = v4 & op(e3, e4) = v23 & op(e3, e3) = v18 & op(e3, e2) = v13 & % 182.05/28.49 op(e3, e1) = v8 & op(e3, e0) = v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & % 182.05/28.49 op(e2, e2) = v12 & op(e2, e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & % 182.05/28.49 op(e1, e3) = v16 & op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & % 182.05/28.49 op(e0, e4) = v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & % 182.05/28.49 op(e0, e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) % 182.05/28.49 & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 182.05/28.49 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 182.05/28.49 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 182.05/28.49 % 182.05/28.49 (ax40) % 182.05/28.49 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.49 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e4) = v1 & % 182.05/28.49 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e3) & op(e4, e1) = v2 & $i(v2)))))) % 182.05/28.49 % 182.05/28.49 (ax41) % 182.05/28.49 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.49 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e0) = v1 & % 182.05/28.49 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e4) & op(e0, e1) = v2 & $i(v2)))))) % 182.05/28.49 % 182.05/28.49 (ax42) % 182.05/28.49 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.49 [v2: $i] : (op(e3, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e3) = v1 & % 182.05/28.49 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e4) & op(e3, e1) = v2 & $i(v2)))))) % 182.05/28.49 % 182.05/28.49 (ax43) % 182.05/28.49 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.49 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e2) = v1 & % 182.05/28.49 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2)))))) % 182.05/28.49 % 182.05/28.49 (ax44) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e4) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e0) & op(e4, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax45) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e0) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax46) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e4) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e2) & op(e4, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax47) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e0) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e4) & op(e0, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax48) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e2, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e2) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e4) & op(e2, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax49) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e2) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e0) & op(e2, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax5) % 182.05/28.50 ~ (e4 = e3) & ~ (e4 = e2) & ~ (e4 = e1) & ~ (e4 = e0) & ~ (e3 = e2) & ~ % 182.05/28.50 (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~ (e1 = e0) & $i(e4) % 182.05/28.50 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 182.05/28.50 % 182.05/28.50 (ax50) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e3) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e0) & op(e3, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax51) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e0) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e2) & op(e0, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax52) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e3) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e2) & op(e3, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax53) % 182.05/28.50 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.50 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e0) = v1 & % 182.05/28.50 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e3) & op(e0, e1) = v2 & $i(v2)))))) % 182.05/28.50 % 182.05/28.50 (ax54) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e2) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 = e3) & op(e2, e1) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax55) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e3) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax56) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e4) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e1) & op(e4, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax57) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e1) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax58) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e4) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e3) & op(e4, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax59) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e1) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e4) & op(e1, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax6) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] % 182.05/28.51 : ? [v8: $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? % 182.05/28.51 [v13: $i] : ? [v14: $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? % 182.05/28.51 [v18: $i] : ? [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? % 182.05/28.51 [v23: $i] : ? [v24: $i] : (op(e4, v24) = e4 & op(e4, v23) = e3 & op(e4, v22) % 182.05/28.51 = e2 & op(e4, v21) = e1 & op(e4, v20) = e0 & op(e4, e4) = v24 & op(e4, e3) = % 182.05/28.51 v23 & op(e4, e2) = v22 & op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, v19) = % 182.05/28.51 e4 & op(e3, v18) = e3 & op(e3, v17) = e2 & op(e3, v16) = e1 & op(e3, v15) = % 182.05/28.51 e0 & op(e3, e4) = v19 & op(e3, e3) = v18 & op(e3, e2) = v17 & op(e3, e1) = % 182.05/28.51 v16 & op(e3, e0) = v15 & op(e2, v14) = e4 & op(e2, v13) = e3 & op(e2, v12) = % 182.05/28.51 e2 & op(e2, v11) = e1 & op(e2, v10) = e0 & op(e2, e4) = v14 & op(e2, e3) = % 182.05/28.51 v13 & op(e2, e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, v9) = % 182.05/28.51 e4 & op(e1, v8) = e3 & op(e1, v7) = e2 & op(e1, v6) = e1 & op(e1, v5) = e0 & % 182.05/28.51 op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, e1) = v6 & % 182.05/28.51 op(e1, e0) = v5 & op(e0, v4) = e4 & op(e0, v3) = e3 & op(e0, v2) = e2 & % 182.05/28.51 op(e0, v1) = e1 & op(e0, v0) = e0 & op(e0, e4) = v4 & op(e0, e3) = v3 & % 182.05/28.51 op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) & $i(v23) & % 182.05/28.51 $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) & $i(v16) & % 182.05/28.51 $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) % 182.05/28.51 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 182.05/28.51 % 182.05/28.51 (ax60) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e3, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e3) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e4) & op(e3, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax61) % 182.05/28.51 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.51 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e3) = v1 & % 182.05/28.51 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2)))))) % 182.05/28.51 % 182.05/28.51 (ax62) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e4) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e0) & op(e4, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax63) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e0) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax64) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e4) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e3) & op(e4, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax65) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e0) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e4) & op(e0, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax66) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e3) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e4) & op(e3, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax67) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e1) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax68) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e4) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e0) & op(e4, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax69) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e0) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax7) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e3, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e3) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e2) & op(e3, e0) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax70) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e4, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e4) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e1) & op(e4, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax71) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e0, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e0) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e4) & op(e0, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax72) % 182.05/28.52 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.52 [v2: $i] : (op(e1, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e1) = v1 & % 182.05/28.52 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e4) & op(e1, e2) = v2 & $i(v2)))))) % 182.05/28.52 % 182.05/28.52 (ax73) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e1) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e0) & op(e1, e2) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax74) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e3) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e0) & op(e3, e2) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax75) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e0) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e1) & op(e0, e2) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax76) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e3, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e3) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e1) & op(e3, e2) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax77) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e0) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e3) & op(e0, e2) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax78) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e1) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 = e3) & op(e1, e2) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax79) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e2) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e1) & op(e2, e3) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax8) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | (op(e3, e4) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e2) & op(e4, e0) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax80) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e4) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e1) & op(e4, e3) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax81) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e1) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e2) & op(e1, e3) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax82) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e4, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e4) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e2) & op(e4, e3) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax83) % 182.05/28.53 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.53 [v2: $i] : (op(e1, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e1) = v1 & % 182.05/28.53 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e4) & op(e1, e3) = v2 & $i(v2)))))) % 182.05/28.53 % 182.05/28.53 (ax84) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e2, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e2) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e4) & op(e2, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax85) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e2) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax86) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e4) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e0) & op(e4, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax87) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e0) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e2) & op(e0, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax88) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e4, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e4) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e2) & op(e4, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax89) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e0, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e0) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e4) & op(e0, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax9) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e2) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 = e3) & op(e2, e0) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax90) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e2, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e2) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e4) & op(e2, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax91) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e1) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax92) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e4) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e0) & op(e4, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax93) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e4) | (op(e4, e0) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax94) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e4, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e4) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e1) & op(e4, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax95) % 182.05/28.54 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.54 [v2: $i] : (op(e0, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e0) = v1 & % 182.05/28.54 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e4) & op(e0, e3) = v2 & $i(v2)))))) % 182.05/28.54 % 182.05/28.54 (ax96) % 182.05/28.55 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.55 [v2: $i] : (op(e1, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | (op(e0, e1) = v1 & % 182.05/28.55 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e4) & op(e1, e3) = v2 & $i(v2)))))) % 182.05/28.55 % 182.05/28.55 (ax97) % 182.05/28.55 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.55 [v2: $i] : (op(e1, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e1) = v1 & % 182.05/28.55 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e0) & op(e1, e3) = v2 & $i(v2)))))) % 182.05/28.55 % 182.05/28.55 (ax98) % 182.05/28.55 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.55 [v2: $i] : (op(e2, e4) = v0 & $i(v0) & ( ~ (v0 = e1) | (op(e1, e2) = v1 & % 182.05/28.55 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e0) & op(e2, e3) = v2 & $i(v2)))))) % 182.05/28.55 % 182.05/28.55 (ax99) % 182.05/28.55 $i(e4) & $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? % 182.05/28.55 [v2: $i] : (op(e0, e4) = v0 & $i(v0) & ( ~ (v0 = e2) | (op(e2, e0) = v1 & % 182.05/28.55 $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 = e1) & op(e0, e3) = v2 & $i(v2)))))) % 182.05/28.55 % 182.05/28.55 (function-axioms) % 182.05/28.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 182.05/28.55 v2) = v1) | ~ (op(v3, v2) = v0)) % 182.05/28.55 % 182.05/28.55 Those formulas are unsatisfiable: % 182.05/28.55 --------------------------------- % 182.05/28.55 % 182.05/28.55 Begin of proof % 182.05/28.55 | % 182.05/28.55 | ALPHA: (ax1) implies: % 182.50/28.56 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 182.50/28.56 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 182.50/28.56 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 182.50/28.56 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 182.50/28.56 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 182.50/28.56 | [v24: $i] : (op(e4, e4) = v24 & op(e4, e3) = v23 & op(e4, e2) = v22 & % 182.50/28.56 | op(e4, e1) = v21 & op(e4, e0) = v20 & op(e3, e4) = v19 & op(e3, e3) = % 182.50/28.56 | v18 & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 182.50/28.56 | e4) = v14 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) = v11 % 182.50/28.56 | & op(e2, e0) = v10 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = % 182.50/28.56 | v7 & op(e1, e1) = v6 & op(e1, e0) = v5 & op(e0, e4) = v4 & op(e0, e3) % 182.50/28.56 | = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v24) % 182.50/28.56 | & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) & $i(v17) % 182.50/28.56 | & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) & $i(v10) % 182.50/28.56 | & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 182.50/28.56 | $i(v2) & $i(v1) & $i(v0) & (v24 = e4 | v24 = e3 | v24 = e2 | v24 = e1 % 182.50/28.56 | | v24 = e0) & (v23 = e4 | v23 = e3 | v23 = e2 | v23 = e1 | v23 = % 182.50/28.56 | e0) & (v22 = e4 | v22 = e3 | v22 = e2 | v22 = e1 | v22 = e0) & (v21 % 182.50/28.56 | = e4 | v21 = e3 | v21 = e2 | v21 = e1 | v21 = e0) & (v20 = e4 | v20 % 182.50/28.56 | = e3 | v20 = e2 | v20 = e1 | v20 = e0) & (v19 = e4 | v19 = e3 | v19 % 182.50/28.56 | = e2 | v19 = e1 | v19 = e0) & (v18 = e4 | v18 = e3 | v18 = e2 | v18 % 182.50/28.56 | = e1 | v18 = e0) & (v17 = e4 | v17 = e3 | v17 = e2 | v17 = e1 | v17 % 182.50/28.56 | = e0) & (v16 = e4 | v16 = e3 | v16 = e2 | v16 = e1 | v16 = e0) & % 182.50/28.56 | (v15 = e4 | v15 = e3 | v15 = e2 | v15 = e1 | v15 = e0) & (v14 = e4 | % 182.50/28.56 | v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e4 | v13 = e3 | % 182.50/28.56 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e4 | v12 = e3 | v12 = e2 | % 182.50/28.56 | v12 = e1 | v12 = e0) & (v11 = e4 | v11 = e3 | v11 = e2 | v11 = e1 | % 182.50/28.56 | v11 = e0) & (v10 = e4 | v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) % 182.50/28.56 | & (v9 = e4 | v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e4 | v8 = % 182.50/28.56 | e3 | v8 = e2 | v8 = e1 | v8 = e0) & (v7 = e4 | v7 = e3 | v7 = e2 | % 182.50/28.56 | v7 = e1 | v7 = e0) & (v6 = e4 | v6 = e3 | v6 = e2 | v6 = e1 | v6 = % 182.50/28.56 | e0) & (v5 = e4 | v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & (v4 = e4 % 182.50/28.56 | | v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e4 | v3 = e3 | v3 % 182.50/28.56 | = e2 | v3 = e1 | v3 = e0) & (v2 = e4 | v2 = e3 | v2 = e2 | v2 = e1 % 182.50/28.56 | | v2 = e0) & (v1 = e4 | v1 = e3 | v1 = e2 | v1 = e1 | v1 = e0) & % 182.50/28.56 | (v0 = e4 | v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 182.50/28.56 | % 182.50/28.56 | ALPHA: (ax2) implies: % 182.50/28.58 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 182.50/28.58 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 182.50/28.58 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 182.50/28.58 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 182.50/28.58 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 182.50/28.58 | [v24: $i] : (((v24 = e4 & op(e4, e4) = e4) | (v23 = e4 & op(e4, e3) = % 182.50/28.58 | e4) | (v20 = e4 & op(e4, e2) = e4) | (v15 = e4 & op(e4, e1) = e4) % 182.50/28.58 | | (v8 = e4 & op(e4, e0) = e4)) & ((v24 = e4 & op(e4, e4) = e4) | % 182.50/28.58 | (v22 = e4 & op(e3, e4) = e4) | (v18 = e4 & op(e2, e4) = e4) | (v12 % 182.50/28.58 | = e4 & op(e1, e4) = e4) | (v4 = e4 & op(e0, e4) = e4)) & ((v24 = % 182.50/28.58 | e3 & op(e4, e4) = e3) | (v23 = e3 & op(e4, e3) = e3) | (v20 = e3 % 182.50/28.58 | & op(e4, e2) = e3) | (v15 = e3 & op(e4, e1) = e3) | (v8 = e3 & % 182.50/28.58 | op(e4, e0) = e3)) & ((v24 = e3 & op(e4, e4) = e3) | (v22 = e3 & % 182.50/28.58 | op(e3, e4) = e3) | (v18 = e3 & op(e2, e4) = e3) | (v12 = e3 & % 182.50/28.58 | op(e1, e4) = e3) | (v4 = e3 & op(e0, e4) = e3)) & ((v24 = e2 & % 182.50/28.58 | op(e4, e4) = e2) | (v23 = e2 & op(e4, e3) = e2) | (v20 = e2 & % 182.50/28.58 | op(e4, e2) = e2) | (v15 = e2 & op(e4, e1) = e2) | (v8 = e2 & % 182.50/28.58 | op(e4, e0) = e2)) & ((v24 = e2 & op(e4, e4) = e2) | (v22 = e2 & % 182.50/28.58 | op(e3, e4) = e2) | (v18 = e2 & op(e2, e4) = e2) | (v12 = e2 & % 182.50/28.58 | op(e1, e4) = e2) | (v4 = e2 & op(e0, e4) = e2)) & ((v24 = e1 & % 182.50/28.58 | op(e4, e4) = e1) | (v23 = e1 & op(e4, e3) = e1) | (v20 = e1 & % 182.50/28.58 | op(e4, e2) = e1) | (v15 = e1 & op(e4, e1) = e1) | (v8 = e1 & % 182.50/28.58 | op(e4, e0) = e1)) & ((v24 = e1 & op(e4, e4) = e1) | (v22 = e1 & % 182.50/28.58 | op(e3, e4) = e1) | (v18 = e1 & op(e2, e4) = e1) | (v12 = e1 & % 182.50/28.58 | op(e1, e4) = e1) | (v4 = e1 & op(e0, e4) = e1)) & ((v24 = e0 & % 182.50/28.58 | op(e4, e4) = e0) | (v23 = e0 & op(e4, e3) = e0) | (v20 = e0 & % 182.50/28.58 | op(e4, e2) = e0) | (v15 = e0 & op(e4, e1) = e0) | (v8 = e0 & % 182.50/28.58 | op(e4, e0) = e0)) & ((v24 = e0 & op(e4, e4) = e0) | (v22 = e0 & % 182.50/28.58 | op(e3, e4) = e0) | (v18 = e0 & op(e2, e4) = e0) | (v12 = e0 & % 182.50/28.58 | op(e1, e4) = e0) | (v4 = e0 & op(e0, e4) = e0)) & ((v23 = e4 & % 182.50/28.58 | op(e4, e3) = e4) | (v21 = e4 & op(e3, e3) = e4) | (v17 = e4 & % 182.50/28.58 | op(e2, e3) = e4) | (v11 = e4 & op(e1, e3) = e4) | (v3 = e4 & % 182.50/28.58 | op(e0, e3) = e4)) & ((v23 = e3 & op(e4, e3) = e3) | (v21 = e3 & % 182.50/28.58 | op(e3, e3) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v11 = e3 & % 182.50/28.58 | op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v23 = e2 & % 182.50/28.58 | op(e4, e3) = e2) | (v21 = e2 & op(e3, e3) = e2) | (v17 = e2 & % 182.50/28.58 | op(e2, e3) = e2) | (v11 = e2 & op(e1, e3) = e2) | (v3 = e2 & % 182.50/28.58 | op(e0, e3) = e2)) & ((v23 = e1 & op(e4, e3) = e1) | (v21 = e1 & % 182.50/28.58 | op(e3, e3) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v11 = e1 & % 182.50/28.58 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v23 = e0 & % 182.50/28.58 | op(e4, e3) = e0) | (v21 = e0 & op(e3, e3) = e0) | (v17 = e0 & % 182.50/28.58 | op(e2, e3) = e0) | (v11 = e0 & op(e1, e3) = e0) | (v3 = e0 & % 182.50/28.58 | op(e0, e3) = e0)) & ((v22 = e4 & op(e3, e4) = e4) | (v21 = e4 & % 182.50/28.58 | op(e3, e3) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v14 = e4 & % 182.50/28.58 | op(e3, e1) = e4) | (v7 = e4 & op(e3, e0) = e4)) & ((v22 = e3 & % 182.50/28.58 | op(e3, e4) = e3) | (v21 = e3 & op(e3, e3) = e3) | (v19 = e3 & % 182.50/28.58 | op(e3, e2) = e3) | (v14 = e3 & op(e3, e1) = e3) | (v7 = e3 & % 182.50/28.58 | op(e3, e0) = e3)) & ((v22 = e2 & op(e3, e4) = e2) | (v21 = e2 & % 182.50/28.58 | op(e3, e3) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v14 = e2 & % 182.50/28.58 | op(e3, e1) = e2) | (v7 = e2 & op(e3, e0) = e2)) & ((v22 = e1 & % 182.50/28.58 | op(e3, e4) = e1) | (v21 = e1 & op(e3, e3) = e1) | (v19 = e1 & % 182.50/28.58 | op(e3, e2) = e1) | (v14 = e1 & op(e3, e1) = e1) | (v7 = e1 & % 182.50/28.58 | op(e3, e0) = e1)) & ((v22 = e0 & op(e3, e4) = e0) | (v21 = e0 & % 182.50/28.58 | op(e3, e3) = e0) | (v19 = e0 & op(e3, e2) = e0) | (v14 = e0 & % 182.50/28.58 | op(e3, e1) = e0) | (v7 = e0 & op(e3, e0) = e0)) & ((v20 = e4 & % 182.50/28.58 | op(e4, e2) = e4) | (v19 = e4 & op(e3, e2) = e4) | (v16 = e4 & % 182.50/28.58 | op(e2, e2) = e4) | (v10 = e4 & op(e1, e2) = e4) | (v2 = e4 & % 182.50/28.58 | op(e0, e2) = e4)) & ((v20 = e3 & op(e4, e2) = e3) | (v19 = e3 & % 182.50/28.58 | op(e3, e2) = e3) | (v16 = e3 & op(e2, e2) = e3) | (v10 = e3 & % 182.50/28.58 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v20 = e2 & % 182.50/28.58 | op(e4, e2) = e2) | (v19 = e2 & op(e3, e2) = e2) | (v16 = e2 & % 182.50/28.58 | op(e2, e2) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v2 = e2 & % 182.50/28.58 | op(e0, e2) = e2)) & ((v20 = e1 & op(e4, e2) = e1) | (v19 = e1 & % 182.50/28.58 | op(e3, e2) = e1) | (v16 = e1 & op(e2, e2) = e1) | (v10 = e1 & % 182.50/28.58 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v20 = e0 & % 182.50/28.58 | op(e4, e2) = e0) | (v19 = e0 & op(e3, e2) = e0) | (v16 = e0 & % 182.50/28.58 | op(e2, e2) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v2 = e0 & % 182.50/28.58 | op(e0, e2) = e0)) & ((v18 = e4 & op(e2, e4) = e4) | (v17 = e4 & % 182.50/28.58 | op(e2, e3) = e4) | (v16 = e4 & op(e2, e2) = e4) | (v13 = e4 & % 182.50/28.58 | op(e2, e1) = e4) | (v6 = e4 & op(e2, e0) = e4)) & ((v18 = e3 & % 182.50/28.58 | op(e2, e4) = e3) | (v17 = e3 & op(e2, e3) = e3) | (v16 = e3 & % 182.50/28.58 | op(e2, e2) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v6 = e3 & % 182.50/28.58 | op(e2, e0) = e3)) & ((v18 = e2 & op(e2, e4) = e2) | (v17 = e2 & % 182.50/28.58 | op(e2, e3) = e2) | (v16 = e2 & op(e2, e2) = e2) | (v13 = e2 & % 182.50/28.58 | op(e2, e1) = e2) | (v6 = e2 & op(e2, e0) = e2)) & ((v18 = e1 & % 182.50/28.58 | op(e2, e4) = e1) | (v17 = e1 & op(e2, e3) = e1) | (v16 = e1 & % 182.50/28.58 | op(e2, e2) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v6 = e1 & % 182.50/28.58 | op(e2, e0) = e1)) & ((v18 = e0 & op(e2, e4) = e0) | (v17 = e0 & % 182.50/28.58 | op(e2, e3) = e0) | (v16 = e0 & op(e2, e2) = e0) | (v13 = e0 & % 182.50/28.58 | op(e2, e1) = e0) | (v6 = e0 & op(e2, e0) = e0)) & ((v15 = e4 & % 182.50/28.58 | op(e4, e1) = e4) | (v14 = e4 & op(e3, e1) = e4) | (v13 = e4 & % 182.50/28.58 | op(e2, e1) = e4) | (v9 = e4 & op(e1, e1) = e4) | (v1 = e4 & % 182.50/28.58 | op(e0, e1) = e4)) & ((v15 = e3 & op(e4, e1) = e3) | (v14 = e3 & % 182.50/28.58 | op(e3, e1) = e3) | (v13 = e3 & op(e2, e1) = e3) | (v9 = e3 & % 182.50/28.58 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v15 = e2 & % 182.50/28.58 | op(e4, e1) = e2) | (v14 = e2 & op(e3, e1) = e2) | (v13 = e2 & % 182.50/28.58 | op(e2, e1) = e2) | (v9 = e2 & op(e1, e1) = e2) | (v1 = e2 & % 182.50/28.58 | op(e0, e1) = e2)) & ((v15 = e1 & op(e4, e1) = e1) | (v14 = e1 & % 182.50/28.58 | op(e3, e1) = e1) | (v13 = e1 & op(e2, e1) = e1) | (v9 = e1 & % 182.50/28.58 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v15 = e0 & % 182.50/28.58 | op(e4, e1) = e0) | (v14 = e0 & op(e3, e1) = e0) | (v13 = e0 & % 182.50/28.58 | op(e2, e1) = e0) | (v9 = e0 & op(e1, e1) = e0) | (v1 = e0 & % 182.50/28.58 | op(e0, e1) = e0)) & ((v12 = e4 & op(e1, e4) = e4) | (v11 = e4 & % 182.50/28.59 | op(e1, e3) = e4) | (v10 = e4 & op(e1, e2) = e4) | (v9 = e4 & % 182.50/28.59 | op(e1, e1) = e4) | (v5 = e4 & op(e1, e0) = e4)) & ((v12 = e3 & % 182.50/28.59 | op(e1, e4) = e3) | (v11 = e3 & op(e1, e3) = e3) | (v10 = e3 & % 182.50/28.59 | op(e1, e2) = e3) | (v9 = e3 & op(e1, e1) = e3) | (v5 = e3 & % 182.50/28.59 | op(e1, e0) = e3)) & ((v12 = e2 & op(e1, e4) = e2) | (v11 = e2 & % 182.50/28.59 | op(e1, e3) = e2) | (v10 = e2 & op(e1, e2) = e2) | (v9 = e2 & % 182.50/28.59 | op(e1, e1) = e2) | (v5 = e2 & op(e1, e0) = e2)) & ((v12 = e1 & % 182.50/28.59 | op(e1, e4) = e1) | (v11 = e1 & op(e1, e3) = e1) | (v10 = e1 & % 182.50/28.59 | op(e1, e2) = e1) | (v9 = e1 & op(e1, e1) = e1) | (v5 = e1 & % 182.50/28.59 | op(e1, e0) = e1)) & ((v12 = e0 & op(e1, e4) = e0) | (v11 = e0 & % 182.50/28.59 | op(e1, e3) = e0) | (v10 = e0 & op(e1, e2) = e0) | (v9 = e0 & % 182.50/28.59 | op(e1, e1) = e0) | (v5 = e0 & op(e1, e0) = e0)) & ((v8 = e4 & % 182.50/28.59 | op(e4, e0) = e4) | (v7 = e4 & op(e3, e0) = e4) | (v6 = e4 & % 182.50/28.59 | op(e2, e0) = e4) | (v5 = e4 & op(e1, e0) = e4) | (v0 = e4 & % 182.50/28.59 | op(e0, e0) = e4)) & ((v8 = e3 & op(e4, e0) = e3) | (v7 = e3 & % 182.50/28.59 | op(e3, e0) = e3) | (v6 = e3 & op(e2, e0) = e3) | (v5 = e3 & % 182.50/28.59 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v8 = e2 & % 182.50/28.59 | op(e4, e0) = e2) | (v7 = e2 & op(e3, e0) = e2) | (v6 = e2 & % 182.50/28.59 | op(e2, e0) = e2) | (v5 = e2 & op(e1, e0) = e2) | (v0 = e2 & % 182.50/28.59 | op(e0, e0) = e2)) & ((v8 = e1 & op(e4, e0) = e1) | (v7 = e1 & % 182.50/28.59 | op(e3, e0) = e1) | (v6 = e1 & op(e2, e0) = e1) | (v5 = e1 & % 182.50/28.59 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v4 = e4 & % 182.50/28.59 | op(e0, e4) = e4) | (v3 = e4 & op(e0, e3) = e4) | (v2 = e4 & % 182.50/28.59 | op(e0, e2) = e4) | (v1 = e4 & op(e0, e1) = e4) | (v0 = e4 & % 182.50/28.59 | op(e0, e0) = e4)) & ((v4 = e3 & op(e0, e4) = e3) | (v3 = e3 & % 182.50/28.59 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 & % 182.50/28.59 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v4 = e2 & % 182.50/28.59 | op(e0, e4) = e2) | (v3 = e2 & op(e0, e3) = e2) | (v2 = e2 & % 182.50/28.59 | op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) = e2) | (v0 = e2 & % 182.50/28.59 | op(e0, e0) = e2)) & ((v4 = e1 & op(e0, e4) = e1) | (v3 = e1 & % 182.50/28.59 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 & % 182.50/28.59 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 & % 182.50/28.59 | op(e0, e0) = e0) | (((v8 = e0 & op(e4, e0) = e0) | (v7 = e0 & % 182.50/28.59 | op(e3, e0) = e0) | (v6 = e0 & op(e2, e0) = e0) | (v5 = e0 & % 182.50/28.59 | op(e1, e0) = e0)) & ((v4 = e0 & op(e0, e4) = e0) | (v3 = e0 & % 182.50/28.59 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 & % 182.50/28.59 | op(e0, e1) = e0))))) % 182.50/28.59 | % 182.50/28.59 | ALPHA: (ax3) implies: % 182.50/28.59 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 182.50/28.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 182.50/28.59 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 182.50/28.59 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 182.50/28.59 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 182.50/28.59 | [v24: $i] : (op(v24, v24) = e4 & op(v23, v22) = e4 & op(v22, v23) = e3 % 182.50/28.59 | & op(v21, v21) = e3 & op(v20, v19) = e4 & op(v19, v20) = e2 & op(v18, % 182.50/28.59 | v17) = e3 & op(v17, v18) = e2 & op(v16, v16) = e2 & op(v15, v14) = % 182.50/28.59 | e4 & op(v14, v15) = e1 & op(v13, v12) = e3 & op(v12, v13) = e1 & % 182.50/28.59 | op(v11, v10) = e2 & op(v10, v11) = e1 & op(v9, v9) = e1 & op(v8, v7) % 182.50/28.59 | = e4 & op(v7, v8) = e0 & op(v6, v5) = e3 & op(v5, v6) = e0 & op(v4, % 182.50/28.59 | v3) = e2 & op(v3, v4) = e0 & op(v2, v1) = e1 & op(v1, v2) = e0 & % 182.50/28.59 | op(v0, v0) = e0 & op(e4, e4) = v24 & op(e4, e3) = v22 & op(e4, e2) = % 182.50/28.59 | v19 & op(e4, e1) = v14 & op(e4, e0) = v7 & op(e3, e4) = v23 & op(e3, % 182.50/28.59 | e3) = v21 & op(e3, e2) = v17 & op(e3, e1) = v12 & op(e3, e0) = v5 & % 182.50/28.59 | op(e2, e4) = v20 & op(e2, e3) = v18 & op(e2, e2) = v16 & op(e2, e1) = % 182.50/28.59 | v10 & op(e2, e0) = v3 & op(e1, e4) = v15 & op(e1, e3) = v13 & op(e1, % 182.50/28.59 | e2) = v11 & op(e1, e1) = v9 & op(e1, e0) = v1 & op(e0, e4) = v8 & % 182.50/28.59 | op(e0, e3) = v6 & op(e0, e2) = v4 & op(e0, e1) = v2 & op(e0, e0) = v0 % 182.50/28.59 | & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & $i(v19) & $i(v18) % 182.50/28.59 | & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & $i(v12) & $i(v11) % 182.50/28.59 | & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 182.50/28.59 | $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 182.50/28.59 | % 182.50/28.59 | ALPHA: (ax4) implies: % 182.50/28.60 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 182.50/28.60 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 182.50/28.60 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 182.50/28.60 | ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? [v19: % 182.50/28.60 | $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] : ? % 182.50/28.60 | [v24: $i] : ( ~ (v24 = v23) & ~ (v24 = v22) & ~ (v24 = v21) & ~ (v24 % 182.50/28.60 | = v20) & ~ (v24 = v19) & ~ (v24 = v14) & ~ (v24 = v9) & ~ (v24 % 182.50/28.60 | = v4) & ~ (v23 = v22) & ~ (v23 = v21) & ~ (v23 = v20) & ~ (v23 % 182.50/28.60 | = v18) & ~ (v23 = v13) & ~ (v23 = v8) & ~ (v23 = v3) & ~ (v22 = % 182.50/28.60 | v21) & ~ (v22 = v20) & ~ (v22 = v17) & ~ (v22 = v12) & ~ (v22 = % 182.50/28.60 | v7) & ~ (v22 = v2) & ~ (v21 = v20) & ~ (v21 = v16) & ~ (v21 = % 182.50/28.60 | v11) & ~ (v21 = v6) & ~ (v21 = v1) & ~ (v20 = v15) & ~ (v20 = % 182.50/28.60 | v10) & ~ (v20 = v5) & ~ (v20 = v0) & ~ (v19 = v18) & ~ (v19 = % 182.50/28.60 | v17) & ~ (v19 = v16) & ~ (v19 = v15) & ~ (v19 = v14) & ~ (v19 = % 182.50/28.60 | v9) & ~ (v19 = v4) & ~ (v18 = v17) & ~ (v18 = v16) & ~ (v18 = % 182.50/28.60 | v15) & ~ (v18 = v13) & ~ (v18 = v8) & ~ (v18 = v3) & ~ (v17 = % 182.50/28.60 | v16) & ~ (v17 = v15) & ~ (v17 = v12) & ~ (v17 = v7) & ~ (v17 = % 182.50/28.60 | v2) & ~ (v16 = v15) & ~ (v16 = v11) & ~ (v16 = v6) & ~ (v16 = % 182.50/28.60 | v1) & ~ (v15 = v10) & ~ (v15 = v5) & ~ (v15 = v0) & ~ (v14 = % 182.50/28.60 | v13) & ~ (v14 = v12) & ~ (v14 = v11) & ~ (v14 = v10) & ~ (v14 = % 182.50/28.60 | v9) & ~ (v14 = v4) & ~ (v13 = v12) & ~ (v13 = v11) & ~ (v13 = % 182.50/28.60 | v10) & ~ (v13 = v8) & ~ (v13 = v3) & ~ (v12 = v11) & ~ (v12 = % 182.50/28.60 | v10) & ~ (v12 = v7) & ~ (v12 = v2) & ~ (v11 = v10) & ~ (v11 = % 182.50/28.60 | v6) & ~ (v11 = v1) & ~ (v10 = v5) & ~ (v10 = v0) & ~ (v9 = v8) % 182.50/28.60 | & ~ (v9 = v7) & ~ (v9 = v6) & ~ (v9 = v5) & ~ (v9 = v4) & ~ (v8 % 182.50/28.60 | = v7) & ~ (v8 = v6) & ~ (v8 = v5) & ~ (v8 = v3) & ~ (v7 = v6) & % 182.50/28.60 | ~ (v7 = v5) & ~ (v7 = v2) & ~ (v6 = v5) & ~ (v6 = v1) & ~ (v5 = % 182.50/28.60 | v0) & ~ (v4 = v3) & ~ (v4 = v2) & ~ (v4 = v1) & ~ (v4 = v0) & % 182.50/28.60 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 182.50/28.60 | v0) & ~ (v1 = v0) & op(e4, e4) = v24 & op(e4, e3) = v19 & op(e4, % 182.50/28.60 | e2) = v14 & op(e4, e1) = v9 & op(e4, e0) = v4 & op(e3, e4) = v23 & % 182.50/28.60 | op(e3, e3) = v18 & op(e3, e2) = v13 & op(e3, e1) = v8 & op(e3, e0) = % 182.50/28.60 | v3 & op(e2, e4) = v22 & op(e2, e3) = v17 & op(e2, e2) = v12 & op(e2, % 182.50/28.60 | e1) = v7 & op(e2, e0) = v2 & op(e1, e4) = v21 & op(e1, e3) = v16 & % 182.50/28.60 | op(e1, e2) = v11 & op(e1, e1) = v6 & op(e1, e0) = v1 & op(e0, e4) = % 182.50/28.60 | v20 & op(e0, e3) = v15 & op(e0, e2) = v10 & op(e0, e1) = v5 & op(e0, % 182.50/28.60 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 182.50/28.60 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) & % 182.50/28.60 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 182.50/28.60 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax5) implies: % 182.50/28.60 | (5) ~ (e1 = e0) % 182.50/28.60 | (6) ~ (e2 = e0) % 182.50/28.60 | (7) ~ (e2 = e1) % 182.50/28.60 | (8) ~ (e3 = e0) % 182.50/28.60 | (9) ~ (e3 = e1) % 182.50/28.60 | (10) ~ (e3 = e2) % 182.50/28.60 | (11) ~ (e4 = e0) % 182.50/28.60 | (12) ~ (e4 = e1) % 182.50/28.60 | (13) ~ (e4 = e2) % 182.50/28.60 | (14) ~ (e4 = e3) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax6) implies: % 182.50/28.60 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 182.50/28.60 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : % 182.50/28.60 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: % 182.50/28.60 | $i] : ? [v15: $i] : ? [v16: $i] : ? [v17: $i] : ? [v18: $i] : ? % 182.50/28.60 | [v19: $i] : ? [v20: $i] : ? [v21: $i] : ? [v22: $i] : ? [v23: $i] % 182.50/28.60 | : ? [v24: $i] : (op(e4, v24) = e4 & op(e4, v23) = e3 & op(e4, v22) = % 182.50/28.60 | e2 & op(e4, v21) = e1 & op(e4, v20) = e0 & op(e4, e4) = v24 & op(e4, % 182.50/28.60 | e3) = v23 & op(e4, e2) = v22 & op(e4, e1) = v21 & op(e4, e0) = v20 % 182.50/28.60 | & op(e3, v19) = e4 & op(e3, v18) = e3 & op(e3, v17) = e2 & op(e3, % 182.50/28.60 | v16) = e1 & op(e3, v15) = e0 & op(e3, e4) = v19 & op(e3, e3) = v18 % 182.50/28.60 | & op(e3, e2) = v17 & op(e3, e1) = v16 & op(e3, e0) = v15 & op(e2, % 182.50/28.60 | v14) = e4 & op(e2, v13) = e3 & op(e2, v12) = e2 & op(e2, v11) = e1 % 182.50/28.60 | & op(e2, v10) = e0 & op(e2, e4) = v14 & op(e2, e3) = v13 & op(e2, % 182.50/28.60 | e2) = v12 & op(e2, e1) = v11 & op(e2, e0) = v10 & op(e1, v9) = e4 % 182.50/28.60 | & op(e1, v8) = e3 & op(e1, v7) = e2 & op(e1, v6) = e1 & op(e1, v5) = % 182.50/28.60 | e0 & op(e1, e4) = v9 & op(e1, e3) = v8 & op(e1, e2) = v7 & op(e1, % 182.50/28.60 | e1) = v6 & op(e1, e0) = v5 & op(e0, v4) = e4 & op(e0, v3) = e3 & % 182.50/28.60 | op(e0, v2) = e2 & op(e0, v1) = e1 & op(e0, v0) = e0 & op(e0, e4) = % 182.50/28.60 | v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & op(e0, e1) = v1 & op(e0, % 182.50/28.60 | e0) = v0 & $i(v24) & $i(v23) & $i(v22) & $i(v21) & $i(v20) & % 182.50/28.60 | $i(v19) & $i(v18) & $i(v17) & $i(v16) & $i(v15) & $i(v14) & $i(v13) % 182.50/28.60 | & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 182.50/28.60 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax7) implies: % 182.50/28.60 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) & % 182.50/28.60 | ( ~ (v0 = e4) | (op(e4, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.60 | = e2) & op(e3, e0) = v2 & $i(v2)))))) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax8) implies: % 182.50/28.60 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) & % 182.50/28.60 | ( ~ (v0 = e3) | (op(e3, e4) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.60 | = e2) & op(e4, e0) = v2 & $i(v2)))))) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax9) implies: % 182.50/28.60 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) & % 182.50/28.60 | ( ~ (v0 = e4) | (op(e4, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.60 | = e3) & op(e2, e0) = v2 & $i(v2)))))) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax10) implies: % 182.50/28.60 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) & % 182.50/28.60 | ( ~ (v0 = e2) | (op(e2, e4) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.60 | = e3) & op(e4, e0) = v2 & $i(v2)))))) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax11) implies: % 182.50/28.60 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) & % 182.50/28.60 | ( ~ (v0 = e3) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.60 | = e4) & op(e2, e0) = v2 & $i(v2)))))) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax12) implies: % 182.50/28.60 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) & % 182.50/28.60 | ( ~ (v0 = e2) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.60 | = e4) & op(e3, e0) = v2 & $i(v2)))))) % 182.50/28.60 | % 182.50/28.60 | ALPHA: (ax13) implies: % 182.50/28.61 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e4) | (op(e4, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e1) & op(e3, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax14) implies: % 182.50/28.61 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e3) | (op(e3, e4) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e1) & op(e4, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax15) implies: % 182.50/28.61 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e4) | (op(e4, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e3) & op(e1, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax16) implies: % 182.50/28.61 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e1) | (op(e1, e4) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e3) & op(e4, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax17) implies: % 182.50/28.61 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e3) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e4) & op(e1, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax18) implies: % 182.50/28.61 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e1) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e4) & op(e3, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax19) implies: % 182.50/28.61 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e4) | (op(e4, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e1) & op(e2, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax20) implies: % 182.50/28.61 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e2) | (op(e2, e4) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e1) & op(e4, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax21) implies: % 182.50/28.61 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e4) | (op(e4, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e2) & op(e1, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax22) implies: % 182.50/28.61 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e1) | (op(e1, e4) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e2) & op(e4, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax23) implies: % 182.50/28.61 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e2) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e4) & op(e1, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax24) implies: % 182.50/28.61 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e1) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e4) & op(e2, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax25) implies: % 182.50/28.61 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e3) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e1) & op(e2, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax26) implies: % 182.50/28.61 | (35) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e2) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e1) & op(e3, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax27) implies: % 182.50/28.61 | (36) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e3) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e2) & op(e1, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax28) implies: % 182.50/28.61 | (37) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) & % 182.50/28.61 | ( ~ (v0 = e1) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.61 | = e2) & op(e3, e0) = v2 & $i(v2)))))) % 182.50/28.61 | % 182.50/28.61 | ALPHA: (ax29) implies: % 182.50/28.62 | (38) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e2) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.62 | = e3) & op(e1, e0) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax30) implies: % 182.50/28.62 | (39) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e1) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e0) | ( ~ (v2 % 182.50/28.62 | = e3) & op(e2, e0) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax31) implies: % 182.50/28.62 | (40) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e4) | (op(e4, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e2) & op(e3, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax32) implies: % 182.50/28.62 | (41) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e3) | (op(e3, e4) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e2) & op(e4, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax33) implies: % 182.50/28.62 | (42) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e4) | (op(e4, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e3) & op(e2, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax34) implies: % 182.50/28.62 | (43) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e2) | (op(e2, e4) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e3) & op(e4, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax35) implies: % 182.50/28.62 | (44) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e3) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e4) & op(e2, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax36) implies: % 182.50/28.62 | (45) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e2) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e4) & op(e3, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax37) implies: % 182.50/28.62 | (46) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e4) | (op(e4, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e0) & op(e3, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax38) implies: % 182.50/28.62 | (47) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e3) | (op(e3, e4) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e0) & op(e4, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax39) implies: % 182.50/28.62 | (48) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e4) | (op(e4, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e3) & op(e0, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax40) implies: % 182.50/28.62 | (49) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e0) | (op(e0, e4) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e3) & op(e4, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax41) implies: % 182.50/28.62 | (50) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e3) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e4) & op(e0, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax42) implies: % 182.50/28.62 | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e0) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e4) & op(e3, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax43) implies: % 182.50/28.62 | (52) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) & % 182.50/28.62 | ( ~ (v0 = e4) | (op(e4, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.62 | = e0) & op(e2, e1) = v2 & $i(v2)))))) % 182.50/28.62 | % 182.50/28.62 | ALPHA: (ax44) implies: % 182.50/28.63 | (53) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e2) | (op(e2, e4) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e0) & op(e4, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax45) implies: % 182.50/28.63 | (54) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e4) | (op(e4, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e2) & op(e0, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax46) implies: % 182.50/28.63 | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e0) | (op(e0, e4) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e2) & op(e4, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax47) implies: % 182.50/28.63 | (56) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e2) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e4) & op(e0, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax48) implies: % 182.50/28.63 | (57) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e0) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e4) & op(e2, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax49) implies: % 182.50/28.63 | (58) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e3) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e0) & op(e2, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax50) implies: % 182.50/28.63 | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e2) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e0) & op(e3, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax51) implies: % 182.50/28.63 | (60) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e3) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e2) & op(e0, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax52) implies: % 182.50/28.63 | (61) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e0) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e2) & op(e3, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax53) implies: % 182.50/28.63 | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e2) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e3) & op(e0, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax54) implies: % 182.50/28.63 | (63) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e0) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e1) | ( ~ (v2 % 182.50/28.63 | = e3) & op(e2, e1) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax55) implies: % 182.50/28.63 | (64) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e4) | (op(e4, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.63 | = e1) & op(e3, e2) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax56) implies: % 182.50/28.63 | (65) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e3) | (op(e3, e4) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.63 | = e1) & op(e4, e2) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax57) implies: % 182.50/28.63 | (66) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e4) | (op(e4, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.63 | = e3) & op(e1, e2) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.63 | ALPHA: (ax58) implies: % 182.50/28.63 | (67) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) & % 182.50/28.63 | ( ~ (v0 = e1) | (op(e1, e4) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.63 | = e3) & op(e4, e2) = v2 & $i(v2)))))) % 182.50/28.63 | % 182.50/28.64 | ALPHA: (ax59) implies: % 182.50/28.64 | (68) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e3) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e4) & op(e1, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax60) implies: % 182.50/28.64 | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e1) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e4) & op(e3, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax61) implies: % 182.50/28.64 | (70) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e4) | (op(e4, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e0) & op(e3, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax62) implies: % 182.50/28.64 | (71) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e3) | (op(e3, e4) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e0) & op(e4, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax63) implies: % 182.50/28.64 | (72) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e4) | (op(e4, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e3) & op(e0, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax64) implies: % 182.50/28.64 | (73) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e0) | (op(e0, e4) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e3) & op(e4, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax65) implies: % 182.50/28.64 | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e3) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e4) & op(e0, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax66) implies: % 182.50/28.64 | (75) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e0) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e4) & op(e3, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax67) implies: % 182.50/28.64 | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e4) | (op(e4, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e0) & op(e1, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax68) implies: % 182.50/28.64 | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e1) | (op(e1, e4) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e0) & op(e4, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax69) implies: % 182.50/28.64 | (78) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e4) | (op(e4, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e1) & op(e0, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax70) implies: % 182.50/28.64 | (79) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e3) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e0) | (op(e0, e4) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e1) & op(e4, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax71) implies: % 182.50/28.64 | (80) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e1) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e4) & op(e0, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax72) implies: % 182.50/28.64 | (81) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e0) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e4) & op(e1, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax73) implies: % 182.50/28.64 | (82) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) & % 182.50/28.64 | ( ~ (v0 = e3) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.64 | = e0) & op(e1, e2) = v2 & $i(v2)))))) % 182.50/28.64 | % 182.50/28.64 | ALPHA: (ax74) implies: % 182.50/28.65 | (83) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e1) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.65 | = e0) & op(e3, e2) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax75) implies: % 182.50/28.65 | (84) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e3) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.65 | = e1) & op(e0, e2) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax76) implies: % 182.50/28.65 | (85) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e4) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e0) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.65 | = e1) & op(e3, e2) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax77) implies: % 182.50/28.65 | (86) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e1) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.65 | = e3) & op(e0, e2) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax78) implies: % 182.50/28.65 | (87) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e0) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e2) | ( ~ (v2 % 182.50/28.65 | = e3) & op(e1, e2) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax79) implies: % 182.50/28.65 | (88) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e4) | (op(e4, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e1) & op(e2, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax80) implies: % 182.50/28.65 | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e2) | (op(e2, e4) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e1) & op(e4, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax81) implies: % 182.50/28.65 | (90) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e4) | (op(e4, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e2) & op(e1, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax82) implies: % 182.50/28.65 | (91) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e0) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e1) | (op(e1, e4) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e2) & op(e4, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax83) implies: % 182.50/28.65 | (92) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e2) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e4) & op(e1, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax84) implies: % 182.50/28.65 | (93) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e1) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e4) & op(e2, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax85) implies: % 182.50/28.65 | (94) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e4) | (op(e4, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e0) & op(e2, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax86) implies: % 182.50/28.65 | (95) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e2) | (op(e2, e4) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e0) & op(e4, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax87) implies: % 182.50/28.65 | (96) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e4) | (op(e4, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e2) & op(e0, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax88) implies: % 182.50/28.65 | (97) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e1) = v0 & $i(v0) & % 182.50/28.65 | ( ~ (v0 = e0) | (op(e0, e4) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.65 | = e2) & op(e4, e3) = v2 & $i(v2)))))) % 182.50/28.65 | % 182.50/28.65 | ALPHA: (ax89) implies: % 182.50/28.66 | (98) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e2) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e4) & op(e0, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax90) implies: % 182.50/28.66 | (99) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e0) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e4) & op(e2, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax91) implies: % 182.50/28.66 | (100) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e4) | (op(e4, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e0) & op(e1, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax92) implies: % 182.50/28.66 | (101) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e1) | (op(e1, e4) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e0) & op(e4, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax93) implies: % 182.50/28.66 | (102) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e4) | (op(e4, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e1) & op(e0, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax94) implies: % 182.50/28.66 | (103) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e4, e2) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e0) | (op(e0, e4) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e1) & op(e4, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax95) implies: % 182.50/28.66 | (104) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e1) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e4) & op(e0, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax96) implies: % 182.50/28.66 | (105) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e0) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e4) & op(e1, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax97) implies: % 182.50/28.66 | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e2) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e0) & op(e1, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax98) implies: % 182.50/28.66 | (107) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e1) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e0) & op(e2, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax99) implies: % 182.50/28.66 | (108) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e2) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e1) & op(e0, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax100) implies: % 182.50/28.66 | (109) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e4) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e0) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e1) & op(e2, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax101) implies: % 182.50/28.66 | (110) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e4) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e1) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e2) & op(e0, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax102) implies: % 182.50/28.66 | (111) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e4) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e0) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e3) | ( ~ (v2 % 182.50/28.66 | = e2) & op(e1, e3) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax103) implies: % 182.50/28.66 | (112) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) & % 182.50/28.66 | ( ~ (v0 = e3) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.66 | = e1) & op(e2, e4) = v2 & $i(v2)))))) % 182.50/28.66 | % 182.50/28.66 | ALPHA: (ax104) implies: % 182.50/28.67 | (113) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e2) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e1) & op(e3, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax105) implies: % 182.50/28.67 | (114) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e3) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e2) & op(e1, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax106) implies: % 182.50/28.67 | (115) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e0) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e1) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e2) & op(e3, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax107) implies: % 182.50/28.67 | (116) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e0) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e2) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e3) & op(e1, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax108) implies: % 182.50/28.67 | (117) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e0) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e1) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e3) & op(e2, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax109) implies: % 182.50/28.67 | (118) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e3) | (op(e3, e2) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e0) & op(e2, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax110) implies: % 182.50/28.67 | (119) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e2) | (op(e2, e3) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e0) & op(e3, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax111) implies: % 182.50/28.67 | (120) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e3) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e2) & op(e0, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax112) implies: % 182.50/28.67 | (121) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e1) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e0) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e2) & op(e3, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax113) implies: % 182.50/28.67 | (122) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e1) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e2) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e3) & op(e0, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax114) implies: % 182.50/28.67 | (123) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e1) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e0) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e3) & op(e2, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax115) implies: % 182.50/28.67 | (124) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e3) | (op(e3, e1) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e0) & op(e1, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax116) implies: % 182.50/28.67 | (125) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e1) | (op(e1, e3) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e0) & op(e3, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax117) implies: % 182.50/28.67 | (126) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e3) | (op(e3, e0) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e1) & op(e0, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax118) implies: % 182.50/28.67 | (127) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e2) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e0) | (op(e0, e3) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e1) & op(e3, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax119) implies: % 182.50/28.67 | (128) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e2) = v0 & $i(v0) & % 182.50/28.67 | ( ~ (v0 = e1) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.67 | = e3) & op(e0, e4) = v2 & $i(v2)))))) % 182.50/28.67 | % 182.50/28.67 | ALPHA: (ax120) implies: % 182.50/28.68 | (129) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e2) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e0) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e3) & op(e1, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (ax121) implies: % 182.50/28.68 | (130) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e2) | (op(e2, e1) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e0) & op(e1, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (ax122) implies: % 182.50/28.68 | (131) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e1) | (op(e1, e2) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e0) & op(e2, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (ax123) implies: % 182.50/28.68 | (132) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e2) | (op(e2, e0) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e1) & op(e0, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (ax124) implies: % 182.50/28.68 | (133) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e3) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e0) | (op(e0, e2) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e1) & op(e2, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (ax125) implies: % 182.50/28.68 | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e3) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e1) | (op(e1, e0) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e2) & op(e0, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (ax126) implies: % 182.50/28.68 | (135) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e3) = v0 & $i(v0) & % 182.50/28.68 | ( ~ (v0 = e0) | (op(e0, e1) = v1 & $i(v1) & ( ~ (v1 = e4) | ( ~ (v2 % 182.50/28.68 | = e2) & op(e1, e4) = v2 & $i(v2)))))) % 182.50/28.68 | % 182.50/28.68 | DELTA: instantiating (129) with fresh symbols all_4_0, all_4_1, all_4_2 gives: % 182.50/28.68 | (136) op(e1, e2) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e0) | (op(e0, e1) % 182.50/28.68 | = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e4) | ( ~ (all_4_0 = e3) % 182.50/28.68 | & op(e1, e4) = all_4_0 & $i(all_4_0))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (136) implies: % 182.50/28.68 | (137) op(e1, e2) = all_4_2 % 182.50/28.68 | (138) ~ (all_4_2 = e0) | (op(e0, e1) = all_4_1 & $i(all_4_1) & ( ~ % 182.50/28.68 | (all_4_1 = e4) | ( ~ (all_4_0 = e3) & op(e1, e4) = all_4_0 & % 182.50/28.68 | $i(all_4_0)))) % 182.50/28.68 | % 182.50/28.68 | DELTA: instantiating (49) with fresh symbols all_6_0, all_6_1, all_6_2 gives: % 182.50/28.68 | (139) op(e4, e2) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e0) | (op(e0, e4) % 182.50/28.68 | = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e1) | ( ~ (all_6_0 = e3) % 182.50/28.68 | & op(e4, e1) = all_6_0 & $i(all_6_0))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (139) implies: % 182.50/28.68 | (140) op(e4, e2) = all_6_2 % 182.50/28.68 | (141) ~ (all_6_2 = e0) | (op(e0, e4) = all_6_1 & $i(all_6_1) & ( ~ % 182.50/28.68 | (all_6_1 = e1) | ( ~ (all_6_0 = e3) & op(e4, e1) = all_6_0 & % 182.50/28.68 | $i(all_6_0)))) % 182.50/28.68 | % 182.50/28.68 | DELTA: instantiating (51) with fresh symbols all_8_0, all_8_1, all_8_2 gives: % 182.50/28.68 | (142) op(e3, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e0) | (op(e0, e3) % 182.50/28.68 | = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e1) | ( ~ (all_8_0 = e4) % 182.50/28.68 | & op(e3, e1) = all_8_0 & $i(all_8_0))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (142) implies: % 182.50/28.68 | (143) op(e3, e2) = all_8_2 % 182.50/28.68 | (144) ~ (all_8_2 = e0) | (op(e0, e3) = all_8_1 & $i(all_8_1) & ( ~ % 182.50/28.68 | (all_8_1 = e1) | ( ~ (all_8_0 = e4) & op(e3, e1) = all_8_0 & % 182.50/28.68 | $i(all_8_0)))) % 182.50/28.68 | % 182.50/28.68 | DELTA: instantiating (131) with fresh symbols all_10_0, all_10_1, all_10_2 % 182.50/28.68 | gives: % 182.50/28.68 | (145) op(e2, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e1) | (op(e1, % 182.50/28.68 | e2) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e4) | ( ~ % 182.50/28.68 | (all_10_0 = e0) & op(e2, e4) = all_10_0 & $i(all_10_0))))) % 182.50/28.68 | % 182.50/28.68 | ALPHA: (145) implies: % 182.50/28.68 | (146) op(e2, e3) = all_10_2 % 182.50/28.68 | (147) ~ (all_10_2 = e1) | (op(e1, e2) = all_10_1 & $i(all_10_1) & ( ~ % 182.50/28.68 | (all_10_1 = e4) | ( ~ (all_10_0 = e0) & op(e2, e4) = all_10_0 & % 182.50/28.68 | $i(all_10_0)))) % 182.50/28.68 | % 182.50/28.68 | DELTA: instantiating (84) with fresh symbols all_12_0, all_12_1, all_12_2 % 182.50/28.68 | gives: % 182.50/28.69 | (148) op(e0, e4) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e3) | (op(e3, % 182.50/28.69 | e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e2) | ( ~ % 182.50/28.69 | (all_12_0 = e1) & op(e0, e2) = all_12_0 & $i(all_12_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (148) implies: % 182.50/28.69 | (149) op(e0, e4) = all_12_2 % 182.50/28.69 | (150) ~ (all_12_2 = e3) | (op(e3, e0) = all_12_1 & $i(all_12_1) & ( ~ % 182.50/28.69 | (all_12_1 = e2) | ( ~ (all_12_0 = e1) & op(e0, e2) = all_12_0 & % 182.50/28.69 | $i(all_12_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (86) with fresh symbols all_14_0, all_14_1, all_14_2 % 182.50/28.69 | gives: % 182.50/28.69 | (151) op(e0, e4) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e1) | (op(e1, % 182.50/28.69 | e0) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 = e2) | ( ~ % 182.50/28.69 | (all_14_0 = e3) & op(e0, e2) = all_14_0 & $i(all_14_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (151) implies: % 182.50/28.69 | (152) op(e0, e4) = all_14_2 % 182.50/28.69 | (153) ~ (all_14_2 = e1) | (op(e1, e0) = all_14_1 & $i(all_14_1) & ( ~ % 182.50/28.69 | (all_14_1 = e2) | ( ~ (all_14_0 = e3) & op(e0, e2) = all_14_0 & % 182.50/28.69 | $i(all_14_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (82) with fresh symbols all_16_0, all_16_1, all_16_2 % 182.50/28.69 | gives: % 182.50/28.69 | (154) op(e1, e4) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e3) | (op(e3, % 182.50/28.69 | e1) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e2) | ( ~ % 182.50/28.69 | (all_16_0 = e0) & op(e1, e2) = all_16_0 & $i(all_16_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (154) implies: % 182.50/28.69 | (155) op(e1, e4) = all_16_2 % 182.50/28.69 | (156) ~ (all_16_2 = e3) | (op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ % 182.50/28.69 | (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 & % 182.50/28.69 | $i(all_16_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (108) with fresh symbols all_18_0, all_18_1, all_18_2 % 182.50/28.69 | gives: % 182.50/28.69 | (157) op(e0, e4) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e2) | (op(e2, % 182.50/28.69 | e0) = all_18_1 & $i(all_18_1) & ( ~ (all_18_1 = e3) | ( ~ % 182.50/28.69 | (all_18_0 = e1) & op(e0, e3) = all_18_0 & $i(all_18_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (157) implies: % 182.50/28.69 | (158) op(e0, e4) = all_18_2 % 182.50/28.69 | (159) ~ (all_18_2 = e2) | (op(e2, e0) = all_18_1 & $i(all_18_1) & ( ~ % 182.50/28.69 | (all_18_1 = e3) | ( ~ (all_18_0 = e1) & op(e0, e3) = all_18_0 & % 182.50/28.69 | $i(all_18_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (120) with fresh symbols all_20_0, all_20_1, all_20_2 % 182.50/28.69 | gives: % 182.50/28.69 | (160) op(e0, e1) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e3) | (op(e3, % 182.50/28.69 | e0) = all_20_1 & $i(all_20_1) & ( ~ (all_20_1 = e4) | ( ~ % 182.50/28.69 | (all_20_0 = e2) & op(e0, e4) = all_20_0 & $i(all_20_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (160) implies: % 182.50/28.69 | (161) op(e0, e1) = all_20_2 % 182.50/28.69 | (162) ~ (all_20_2 = e3) | (op(e3, e0) = all_20_1 & $i(all_20_1) & ( ~ % 182.50/28.69 | (all_20_1 = e4) | ( ~ (all_20_0 = e2) & op(e0, e4) = all_20_0 & % 182.50/28.69 | $i(all_20_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (56) with fresh symbols all_22_0, all_22_1, all_22_2 % 182.50/28.69 | gives: % 182.50/28.69 | (163) op(e0, e3) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e2) | (op(e2, % 182.50/28.69 | e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 = e1) | ( ~ % 182.50/28.69 | (all_22_0 = e4) & op(e0, e1) = all_22_0 & $i(all_22_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (163) implies: % 182.50/28.69 | (164) op(e0, e3) = all_22_2 % 182.50/28.69 | (165) ~ (all_22_2 = e2) | (op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ % 182.50/28.69 | (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & % 182.50/28.69 | $i(all_22_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (106) with fresh symbols all_24_0, all_24_1, all_24_2 % 182.50/28.69 | gives: % 182.50/28.69 | (166) op(e1, e4) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e2) | (op(e2, % 182.50/28.69 | e1) = all_24_1 & $i(all_24_1) & ( ~ (all_24_1 = e3) | ( ~ % 182.50/28.69 | (all_24_0 = e0) & op(e1, e3) = all_24_0 & $i(all_24_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (166) implies: % 182.50/28.69 | (167) op(e1, e4) = all_24_2 % 182.50/28.69 | (168) ~ (all_24_2 = e2) | (op(e2, e1) = all_24_1 & $i(all_24_1) & ( ~ % 182.50/28.69 | (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e1, e3) = all_24_0 & % 182.50/28.69 | $i(all_24_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (97) with fresh symbols all_26_0, all_26_1, all_26_2 % 182.50/28.69 | gives: % 182.50/28.69 | (169) op(e4, e1) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e0) | (op(e0, % 182.50/28.69 | e4) = all_26_1 & $i(all_26_1) & ( ~ (all_26_1 = e3) | ( ~ % 182.50/28.69 | (all_26_0 = e2) & op(e4, e3) = all_26_0 & $i(all_26_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (169) implies: % 182.50/28.69 | (170) op(e4, e1) = all_26_2 % 182.50/28.69 | (171) ~ (all_26_2 = e0) | (op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 182.50/28.69 | (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, e3) = all_26_0 & % 182.50/28.69 | $i(all_26_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (104) with fresh symbols all_28_0, all_28_1, all_28_2 % 182.50/28.69 | gives: % 182.50/28.69 | (172) op(e0, e2) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e1) | (op(e1, % 182.50/28.69 | e0) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = e3) | ( ~ % 182.50/28.69 | (all_28_0 = e4) & op(e0, e3) = all_28_0 & $i(all_28_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (172) implies: % 182.50/28.69 | (173) op(e0, e2) = all_28_2 % 182.50/28.69 | (174) ~ (all_28_2 = e1) | (op(e1, e0) = all_28_1 & $i(all_28_1) & ( ~ % 182.50/28.69 | (all_28_1 = e3) | ( ~ (all_28_0 = e4) & op(e0, e3) = all_28_0 & % 182.50/28.69 | $i(all_28_0)))) % 182.50/28.69 | % 182.50/28.69 | DELTA: instantiating (65) with fresh symbols all_30_0, all_30_1, all_30_2 % 182.50/28.69 | gives: % 182.50/28.69 | (175) op(e4, e0) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e3) | (op(e3, % 182.50/28.69 | e4) = all_30_1 & $i(all_30_1) & ( ~ (all_30_1 = e2) | ( ~ % 182.50/28.69 | (all_30_0 = e1) & op(e4, e2) = all_30_0 & $i(all_30_0))))) % 182.50/28.69 | % 182.50/28.69 | ALPHA: (175) implies: % 182.50/28.70 | (176) op(e4, e0) = all_30_2 % 182.50/28.70 | (177) ~ (all_30_2 = e3) | (op(e3, e4) = all_30_1 & $i(all_30_1) & ( ~ % 182.50/28.70 | (all_30_1 = e2) | ( ~ (all_30_0 = e1) & op(e4, e2) = all_30_0 & % 182.50/28.70 | $i(all_30_0)))) % 182.50/28.70 | % 182.50/28.70 | DELTA: instantiating (72) with fresh symbols all_32_0, all_32_1, all_32_2 % 182.50/28.70 | gives: % 182.50/28.70 | (178) op(e0, e1) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e4) | (op(e4, % 182.50/28.70 | e0) = all_32_1 & $i(all_32_1) & ( ~ (all_32_1 = e2) | ( ~ % 182.50/28.70 | (all_32_0 = e3) & op(e0, e2) = all_32_0 & $i(all_32_0))))) % 182.50/28.70 | % 182.50/28.70 | ALPHA: (178) implies: % 182.50/28.70 | (179) op(e0, e1) = all_32_2 % 182.50/28.70 | (180) ~ (all_32_2 = e4) | (op(e4, e0) = all_32_1 & $i(all_32_1) & ( ~ % 182.50/28.70 | (all_32_1 = e2) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 & % 182.50/28.70 | $i(all_32_0)))) % 182.50/28.70 | % 182.50/28.70 | DELTA: instantiating (66) with fresh symbols all_34_0, all_34_1, all_34_2 % 182.50/28.70 | gives: % 182.50/28.70 | (181) op(e1, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e4) | (op(e4, % 182.50/28.70 | e1) = all_34_1 & $i(all_34_1) & ( ~ (all_34_1 = e2) | ( ~ % 182.50/28.70 | (all_34_0 = e3) & op(e1, e2) = all_34_0 & $i(all_34_0))))) % 182.50/28.70 | % 182.50/28.70 | ALPHA: (181) implies: % 182.50/28.70 | (182) op(e1, e0) = all_34_2 % 182.50/28.70 | (183) ~ (all_34_2 = e4) | (op(e4, e1) = all_34_1 & $i(all_34_1) & ( ~ % 182.50/28.70 | (all_34_1 = e2) | ( ~ (all_34_0 = e3) & op(e1, e2) = all_34_0 & % 182.50/28.70 | $i(all_34_0)))) % 182.50/28.70 | % 182.50/28.70 | DELTA: instantiating (121) with fresh symbols all_36_0, all_36_1, all_36_2 % 182.50/28.70 | gives: % 182.50/28.70 | (184) op(e3, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e0) | (op(e0, % 182.50/28.70 | e3) = all_36_1 & $i(all_36_1) & ( ~ (all_36_1 = e4) | ( ~ % 182.50/28.70 | (all_36_0 = e2) & op(e3, e4) = all_36_0 & $i(all_36_0))))) % 182.50/28.70 | % 182.50/28.70 | ALPHA: (184) implies: % 182.50/28.70 | (185) op(e3, e1) = all_36_2 % 182.50/28.70 | (186) ~ (all_36_2 = e0) | (op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 182.50/28.70 | (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 182.50/28.70 | $i(all_36_0)))) % 182.50/28.70 | % 182.50/28.70 | DELTA: instantiating (123) with fresh symbols all_38_0, all_38_1, all_38_2 % 182.50/28.70 | gives: % 182.50/28.70 | (187) op(e2, e1) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e0) | (op(e0, % 182.50/28.70 | e2) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e4) | ( ~ % 182.50/28.70 | (all_38_0 = e3) & op(e2, e4) = all_38_0 & $i(all_38_0))))) % 182.50/28.70 | % 182.50/28.70 | ALPHA: (187) implies: % 182.50/28.70 | (188) op(e2, e1) = all_38_2 % 183.08/28.70 | (189) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 183.08/28.70 | (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 183.08/28.70 | $i(all_38_0)))) % 183.08/28.70 | % 183.08/28.70 | DELTA: instantiating (117) with fresh symbols all_40_0, all_40_1, all_40_2 % 183.08/28.70 | gives: % 183.08/28.70 | (190) op(e2, e0) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e1) | (op(e1, % 183.08/28.70 | e2) = all_40_1 & $i(all_40_1) & ( ~ (all_40_1 = e4) | ( ~ % 183.08/28.70 | (all_40_0 = e3) & op(e2, e4) = all_40_0 & $i(all_40_0))))) % 183.08/28.70 | % 183.08/28.70 | ALPHA: (190) implies: % 183.08/28.70 | (191) op(e2, e0) = all_40_2 % 183.08/28.70 | (192) ~ (all_40_2 = e1) | (op(e1, e2) = all_40_1 & $i(all_40_1) & ( ~ % 183.08/28.70 | (all_40_1 = e4) | ( ~ (all_40_0 = e3) & op(e2, e4) = all_40_0 & % 183.08/28.70 | $i(all_40_0)))) % 183.08/28.70 | % 183.08/28.70 | DELTA: instantiating (110) with fresh symbols all_42_0, all_42_1, all_42_2 % 183.08/28.70 | gives: % 183.08/28.70 | (193) op(e0, e4) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e1) | (op(e1, % 183.08/28.70 | e0) = all_42_1 & $i(all_42_1) & ( ~ (all_42_1 = e3) | ( ~ % 183.08/28.70 | (all_42_0 = e2) & op(e0, e3) = all_42_0 & $i(all_42_0))))) % 183.08/28.70 | % 183.08/28.70 | ALPHA: (193) implies: % 183.08/28.70 | (194) op(e0, e4) = all_42_2 % 183.08/28.70 | (195) ~ (all_42_2 = e1) | (op(e1, e0) = all_42_1 & $i(all_42_1) & ( ~ % 183.08/28.70 | (all_42_1 = e3) | ( ~ (all_42_0 = e2) & op(e0, e3) = all_42_0 & % 183.08/28.70 | $i(all_42_0)))) % 183.08/28.70 | % 183.08/28.70 | DELTA: instantiating (73) with fresh symbols all_44_0, all_44_1, all_44_2 % 183.08/28.70 | gives: % 183.08/28.70 | (196) op(e4, e1) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e0) | (op(e0, % 183.08/28.70 | e4) = all_44_1 & $i(all_44_1) & ( ~ (all_44_1 = e2) | ( ~ % 183.08/28.70 | (all_44_0 = e3) & op(e4, e2) = all_44_0 & $i(all_44_0))))) % 183.08/28.70 | % 183.08/28.70 | ALPHA: (196) implies: % 183.08/28.70 | (197) op(e4, e1) = all_44_2 % 183.08/28.70 | (198) ~ (all_44_2 = e0) | (op(e0, e4) = all_44_1 & $i(all_44_1) & ( ~ % 183.08/28.70 | (all_44_1 = e2) | ( ~ (all_44_0 = e3) & op(e4, e2) = all_44_0 & % 183.08/28.70 | $i(all_44_0)))) % 183.08/28.70 | % 183.08/28.70 | DELTA: instantiating (75) with fresh symbols all_46_0, all_46_1, all_46_2 % 183.08/28.70 | gives: % 183.08/28.70 | (199) op(e3, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e0) | (op(e0, % 183.08/28.70 | e3) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e2) | ( ~ % 183.08/28.70 | (all_46_0 = e4) & op(e3, e2) = all_46_0 & $i(all_46_0))))) % 183.08/28.70 | % 183.08/28.70 | ALPHA: (199) implies: % 183.08/28.70 | (200) op(e3, e1) = all_46_2 % 183.08/28.70 | (201) ~ (all_46_2 = e0) | (op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ % 183.08/28.70 | (all_46_1 = e2) | ( ~ (all_46_0 = e4) & op(e3, e2) = all_46_0 & % 183.08/28.70 | $i(all_46_0)))) % 183.08/28.70 | % 183.08/28.70 | DELTA: instantiating (45) with fresh symbols all_48_0, all_48_1, all_48_2 % 183.08/28.70 | gives: % 183.08/28.70 | (202) op(e3, e0) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e2) | (op(e2, % 183.08/28.70 | e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = e1) | ( ~ % 183.08/28.70 | (all_48_0 = e4) & op(e3, e1) = all_48_0 & $i(all_48_0))))) % 183.08/28.70 | % 183.08/28.70 | ALPHA: (202) implies: % 183.08/28.70 | (203) op(e3, e0) = all_48_2 % 183.08/28.70 | (204) ~ (all_48_2 = e2) | (op(e2, e3) = all_48_1 & $i(all_48_1) & ( ~ % 183.08/28.70 | (all_48_1 = e1) | ( ~ (all_48_0 = e4) & op(e3, e1) = all_48_0 & % 183.08/28.70 | $i(all_48_0)))) % 183.08/28.70 | % 183.08/28.70 | DELTA: instantiating (105) with fresh symbols all_50_0, all_50_1, all_50_2 % 183.08/28.70 | gives: % 183.08/28.70 | (205) op(e1, e2) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e0) | (op(e0, % 183.08/28.70 | e1) = all_50_1 & $i(all_50_1) & ( ~ (all_50_1 = e3) | ( ~ % 183.08/28.70 | (all_50_0 = e4) & op(e1, e3) = all_50_0 & $i(all_50_0))))) % 183.08/28.70 | % 183.08/28.70 | ALPHA: (205) implies: % 183.08/28.71 | (206) op(e1, e2) = all_50_2 % 183.08/28.71 | (207) ~ (all_50_2 = e0) | (op(e0, e1) = all_50_1 & $i(all_50_1) & ( ~ % 183.08/28.71 | (all_50_1 = e3) | ( ~ (all_50_0 = e4) & op(e1, e3) = all_50_0 & % 183.08/28.71 | $i(all_50_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (119) with fresh symbols all_52_0, all_52_1, all_52_2 % 183.08/28.71 | gives: % 183.08/28.71 | (208) op(e3, e1) = all_52_2 & $i(all_52_2) & ( ~ (all_52_2 = e2) | (op(e2, % 183.08/28.71 | e3) = all_52_1 & $i(all_52_1) & ( ~ (all_52_1 = e4) | ( ~ % 183.08/28.71 | (all_52_0 = e0) & op(e3, e4) = all_52_0 & $i(all_52_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (208) implies: % 183.08/28.71 | (209) op(e3, e1) = all_52_2 % 183.08/28.71 | (210) ~ (all_52_2 = e2) | (op(e2, e3) = all_52_1 & $i(all_52_1) & ( ~ % 183.08/28.71 | (all_52_1 = e4) | ( ~ (all_52_0 = e0) & op(e3, e4) = all_52_0 & % 183.08/28.71 | $i(all_52_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (67) with fresh symbols all_54_0, all_54_1, all_54_2 % 183.08/28.71 | gives: % 183.08/28.71 | (211) op(e4, e0) = all_54_2 & $i(all_54_2) & ( ~ (all_54_2 = e1) | (op(e1, % 183.08/28.71 | e4) = all_54_1 & $i(all_54_1) & ( ~ (all_54_1 = e2) | ( ~ % 183.08/28.71 | (all_54_0 = e3) & op(e4, e2) = all_54_0 & $i(all_54_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (211) implies: % 183.08/28.71 | (212) op(e4, e0) = all_54_2 % 183.08/28.71 | (213) ~ (all_54_2 = e1) | (op(e1, e4) = all_54_1 & $i(all_54_1) & ( ~ % 183.08/28.71 | (all_54_1 = e2) | ( ~ (all_54_0 = e3) & op(e4, e2) = all_54_0 & % 183.08/28.71 | $i(all_54_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (22) with fresh symbols all_56_0, all_56_1, all_56_2 % 183.08/28.71 | gives: % 183.08/28.71 | (214) op(e3, e2) = all_56_2 & $i(all_56_2) & ( ~ (all_56_2 = e4) | (op(e4, % 183.08/28.71 | e3) = all_56_1 & $i(all_56_1) & ( ~ (all_56_1 = e0) | ( ~ % 183.08/28.71 | (all_56_0 = e1) & op(e3, e0) = all_56_0 & $i(all_56_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (214) implies: % 183.08/28.71 | (215) op(e3, e2) = all_56_2 % 183.08/28.71 | (216) ~ (all_56_2 = e4) | (op(e4, e3) = all_56_1 & $i(all_56_1) & ( ~ % 183.08/28.71 | (all_56_1 = e0) | ( ~ (all_56_0 = e1) & op(e3, e0) = all_56_0 & % 183.08/28.71 | $i(all_56_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (98) with fresh symbols all_58_0, all_58_1, all_58_2 % 183.08/28.71 | gives: % 183.08/28.71 | (217) op(e0, e1) = all_58_2 & $i(all_58_2) & ( ~ (all_58_2 = e2) | (op(e2, % 183.08/28.71 | e0) = all_58_1 & $i(all_58_1) & ( ~ (all_58_1 = e3) | ( ~ % 183.08/28.71 | (all_58_0 = e4) & op(e0, e3) = all_58_0 & $i(all_58_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (217) implies: % 183.08/28.71 | (218) op(e0, e1) = all_58_2 % 183.08/28.71 | (219) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 183.08/28.71 | (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 183.08/28.71 | $i(all_58_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (122) with fresh symbols all_60_0, all_60_1, all_60_2 % 183.08/28.71 | gives: % 183.08/28.71 | (220) op(e0, e1) = all_60_2 & $i(all_60_2) & ( ~ (all_60_2 = e2) | (op(e2, % 183.08/28.71 | e0) = all_60_1 & $i(all_60_1) & ( ~ (all_60_1 = e4) | ( ~ % 183.08/28.71 | (all_60_0 = e3) & op(e0, e4) = all_60_0 & $i(all_60_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (220) implies: % 183.08/28.71 | (221) op(e0, e1) = all_60_2 % 183.08/28.71 | (222) ~ (all_60_2 = e2) | (op(e2, e0) = all_60_1 & $i(all_60_1) & ( ~ % 183.08/28.71 | (all_60_1 = e4) | ( ~ (all_60_0 = e3) & op(e0, e4) = all_60_0 & % 183.08/28.71 | $i(all_60_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (130) with fresh symbols all_62_0, all_62_1, all_62_2 % 183.08/28.71 | gives: % 183.08/28.71 | (223) op(e1, e3) = all_62_2 & $i(all_62_2) & ( ~ (all_62_2 = e2) | (op(e2, % 183.08/28.71 | e1) = all_62_1 & $i(all_62_1) & ( ~ (all_62_1 = e4) | ( ~ % 183.08/28.71 | (all_62_0 = e0) & op(e1, e4) = all_62_0 & $i(all_62_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (223) implies: % 183.08/28.71 | (224) op(e1, e3) = all_62_2 % 183.08/28.71 | (225) ~ (all_62_2 = e2) | (op(e2, e1) = all_62_1 & $i(all_62_1) & ( ~ % 183.08/28.71 | (all_62_1 = e4) | ( ~ (all_62_0 = e0) & op(e1, e4) = all_62_0 & % 183.08/28.71 | $i(all_62_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (109) with fresh symbols all_64_0, all_64_1, all_64_2 % 183.08/28.71 | gives: % 183.08/28.71 | (226) op(e2, e4) = all_64_2 & $i(all_64_2) & ( ~ (all_64_2 = e0) | (op(e0, % 183.08/28.71 | e2) = all_64_1 & $i(all_64_1) & ( ~ (all_64_1 = e3) | ( ~ % 183.08/28.71 | (all_64_0 = e1) & op(e2, e3) = all_64_0 & $i(all_64_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (226) implies: % 183.08/28.71 | (227) op(e2, e4) = all_64_2 % 183.08/28.71 | (228) ~ (all_64_2 = e0) | (op(e0, e2) = all_64_1 & $i(all_64_1) & ( ~ % 183.08/28.71 | (all_64_1 = e3) | ( ~ (all_64_0 = e1) & op(e2, e3) = all_64_0 & % 183.08/28.71 | $i(all_64_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (111) with fresh symbols all_66_0, all_66_1, all_66_2 % 183.08/28.71 | gives: % 183.08/28.71 | (229) op(e1, e4) = all_66_2 & $i(all_66_2) & ( ~ (all_66_2 = e0) | (op(e0, % 183.08/28.71 | e1) = all_66_1 & $i(all_66_1) & ( ~ (all_66_1 = e3) | ( ~ % 183.08/28.71 | (all_66_0 = e2) & op(e1, e3) = all_66_0 & $i(all_66_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (229) implies: % 183.08/28.71 | (230) op(e1, e4) = all_66_2 % 183.08/28.71 | (231) ~ (all_66_2 = e0) | (op(e0, e1) = all_66_1 & $i(all_66_1) & ( ~ % 183.08/28.71 | (all_66_1 = e3) | ( ~ (all_66_0 = e2) & op(e1, e3) = all_66_0 & % 183.08/28.71 | $i(all_66_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (132) with fresh symbols all_68_0, all_68_1, all_68_2 % 183.08/28.71 | gives: % 183.08/28.71 | (232) op(e0, e3) = all_68_2 & $i(all_68_2) & ( ~ (all_68_2 = e2) | (op(e2, % 183.08/28.71 | e0) = all_68_1 & $i(all_68_1) & ( ~ (all_68_1 = e4) | ( ~ % 183.08/28.71 | (all_68_0 = e1) & op(e0, e4) = all_68_0 & $i(all_68_0))))) % 183.08/28.71 | % 183.08/28.71 | ALPHA: (232) implies: % 183.08/28.71 | (233) op(e0, e3) = all_68_2 % 183.08/28.71 | (234) ~ (all_68_2 = e2) | (op(e2, e0) = all_68_1 & $i(all_68_1) & ( ~ % 183.08/28.71 | (all_68_1 = e4) | ( ~ (all_68_0 = e1) & op(e0, e4) = all_68_0 & % 183.08/28.71 | $i(all_68_0)))) % 183.08/28.71 | % 183.08/28.71 | DELTA: instantiating (81) with fresh symbols all_70_0, all_70_1, all_70_2 % 183.08/28.71 | gives: % 183.08/28.72 | (235) op(e1, e3) = all_70_2 & $i(all_70_2) & ( ~ (all_70_2 = e0) | (op(e0, % 183.08/28.72 | e1) = all_70_1 & $i(all_70_1) & ( ~ (all_70_1 = e2) | ( ~ % 183.08/28.72 | (all_70_0 = e4) & op(e1, e2) = all_70_0 & $i(all_70_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (235) implies: % 183.08/28.72 | (236) op(e1, e3) = all_70_2 % 183.08/28.72 | (237) ~ (all_70_2 = e0) | (op(e0, e1) = all_70_1 & $i(all_70_1) & ( ~ % 183.08/28.72 | (all_70_1 = e2) | ( ~ (all_70_0 = e4) & op(e1, e2) = all_70_0 & % 183.08/28.72 | $i(all_70_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (54) with fresh symbols all_72_0, all_72_1, all_72_2 % 183.08/28.72 | gives: % 183.08/28.72 | (238) op(e0, e3) = all_72_2 & $i(all_72_2) & ( ~ (all_72_2 = e4) | (op(e4, % 183.08/28.72 | e0) = all_72_1 & $i(all_72_1) & ( ~ (all_72_1 = e1) | ( ~ % 183.08/28.72 | (all_72_0 = e2) & op(e0, e1) = all_72_0 & $i(all_72_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (238) implies: % 183.08/28.72 | (239) op(e0, e3) = all_72_2 % 183.08/28.72 | (240) ~ (all_72_2 = e4) | (op(e4, e0) = all_72_1 & $i(all_72_1) & ( ~ % 183.08/28.72 | (all_72_1 = e1) | ( ~ (all_72_0 = e2) & op(e0, e1) = all_72_0 & % 183.08/28.72 | $i(all_72_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (21) with fresh symbols all_74_0, all_74_1, all_74_2 % 183.08/28.72 | gives: % 183.08/28.72 | (241) op(e3, e1) = all_74_2 & $i(all_74_2) & ( ~ (all_74_2 = e2) | (op(e2, % 183.08/28.72 | e3) = all_74_1 & $i(all_74_1) & ( ~ (all_74_1 = e0) | ( ~ % 183.08/28.72 | (all_74_0 = e4) & op(e3, e0) = all_74_0 & $i(all_74_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (241) implies: % 183.08/28.72 | (242) op(e3, e1) = all_74_2 % 183.08/28.72 | (243) ~ (all_74_2 = e2) | (op(e2, e3) = all_74_1 & $i(all_74_1) & ( ~ % 183.08/28.72 | (all_74_1 = e0) | ( ~ (all_74_0 = e4) & op(e3, e0) = all_74_0 & % 183.08/28.72 | $i(all_74_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (112) with fresh symbols all_76_0, all_76_1, all_76_2 % 183.08/28.72 | gives: % 183.08/28.72 | (244) op(e2, e0) = all_76_2 & $i(all_76_2) & ( ~ (all_76_2 = e3) | (op(e3, % 183.08/28.72 | e2) = all_76_1 & $i(all_76_1) & ( ~ (all_76_1 = e4) | ( ~ % 183.08/28.72 | (all_76_0 = e1) & op(e2, e4) = all_76_0 & $i(all_76_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (244) implies: % 183.08/28.72 | (245) op(e2, e0) = all_76_2 % 183.08/28.72 | (246) ~ (all_76_2 = e3) | (op(e3, e2) = all_76_1 & $i(all_76_1) & ( ~ % 183.08/28.72 | (all_76_1 = e4) | ( ~ (all_76_0 = e1) & op(e2, e4) = all_76_0 & % 183.08/28.72 | $i(all_76_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (52) with fresh symbols all_78_0, all_78_1, all_78_2 % 183.08/28.72 | gives: % 183.08/28.72 | (247) op(e2, e3) = all_78_2 & $i(all_78_2) & ( ~ (all_78_2 = e4) | (op(e4, % 183.08/28.72 | e2) = all_78_1 & $i(all_78_1) & ( ~ (all_78_1 = e1) | ( ~ % 183.08/28.72 | (all_78_0 = e0) & op(e2, e1) = all_78_0 & $i(all_78_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (247) implies: % 183.08/28.72 | (248) op(e2, e3) = all_78_2 % 183.08/28.72 | (249) ~ (all_78_2 = e4) | (op(e4, e2) = all_78_1 & $i(all_78_1) & ( ~ % 183.08/28.72 | (all_78_1 = e1) | ( ~ (all_78_0 = e0) & op(e2, e1) = all_78_0 & % 183.08/28.72 | $i(all_78_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (23) with fresh symbols all_80_0, all_80_1, all_80_2 % 183.08/28.72 | gives: % 183.08/28.72 | (250) op(e4, e2) = all_80_2 & $i(all_80_2) & ( ~ (all_80_2 = e3) | (op(e3, % 183.08/28.72 | e4) = all_80_1 & $i(all_80_1) & ( ~ (all_80_1 = e0) | ( ~ % 183.08/28.72 | (all_80_0 = e1) & op(e4, e0) = all_80_0 & $i(all_80_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (250) implies: % 183.08/28.72 | (251) op(e4, e2) = all_80_2 % 183.08/28.72 | (252) ~ (all_80_2 = e3) | (op(e3, e4) = all_80_1 & $i(all_80_1) & ( ~ % 183.08/28.72 | (all_80_1 = e0) | ( ~ (all_80_0 = e1) & op(e4, e0) = all_80_0 & % 183.08/28.72 | $i(all_80_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (50) with fresh symbols all_82_0, all_82_1, all_82_2 % 183.08/28.72 | gives: % 183.08/28.72 | (253) op(e0, e2) = all_82_2 & $i(all_82_2) & ( ~ (all_82_2 = e3) | (op(e3, % 183.08/28.72 | e0) = all_82_1 & $i(all_82_1) & ( ~ (all_82_1 = e1) | ( ~ % 183.08/28.72 | (all_82_0 = e4) & op(e0, e1) = all_82_0 & $i(all_82_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (253) implies: % 183.08/28.72 | (254) op(e0, e2) = all_82_2 % 183.08/28.72 | (255) ~ (all_82_2 = e3) | (op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 183.08/28.72 | (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, e1) = all_82_0 & % 183.08/28.72 | $i(all_82_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (53) with fresh symbols all_84_0, all_84_1, all_84_2 % 183.08/28.72 | gives: % 183.08/28.72 | (256) op(e4, e3) = all_84_2 & $i(all_84_2) & ( ~ (all_84_2 = e2) | (op(e2, % 183.08/28.72 | e4) = all_84_1 & $i(all_84_1) & ( ~ (all_84_1 = e1) | ( ~ % 183.08/28.72 | (all_84_0 = e0) & op(e4, e1) = all_84_0 & $i(all_84_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (256) implies: % 183.08/28.72 | (257) op(e4, e3) = all_84_2 % 183.08/28.72 | (258) ~ (all_84_2 = e2) | (op(e2, e4) = all_84_1 & $i(all_84_1) & ( ~ % 183.08/28.72 | (all_84_1 = e1) | ( ~ (all_84_0 = e0) & op(e4, e1) = all_84_0 & % 183.08/28.72 | $i(all_84_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (93) with fresh symbols all_86_0, all_86_1, all_86_2 % 183.08/28.72 | gives: % 183.08/28.72 | (259) op(e2, e0) = all_86_2 & $i(all_86_2) & ( ~ (all_86_2 = e1) | (op(e1, % 183.08/28.72 | e2) = all_86_1 & $i(all_86_1) & ( ~ (all_86_1 = e3) | ( ~ % 183.08/28.72 | (all_86_0 = e4) & op(e2, e3) = all_86_0 & $i(all_86_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (259) implies: % 183.08/28.72 | (260) op(e2, e0) = all_86_2 % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (95) with fresh symbols all_88_0, all_88_1, all_88_2 % 183.08/28.72 | gives: % 183.08/28.72 | (261) op(e4, e1) = all_88_2 & $i(all_88_2) & ( ~ (all_88_2 = e2) | (op(e2, % 183.08/28.72 | e4) = all_88_1 & $i(all_88_1) & ( ~ (all_88_1 = e3) | ( ~ % 183.08/28.72 | (all_88_0 = e0) & op(e4, e3) = all_88_0 & $i(all_88_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (261) implies: % 183.08/28.72 | (262) op(e4, e1) = all_88_2 % 183.08/28.72 | (263) ~ (all_88_2 = e2) | (op(e2, e4) = all_88_1 & $i(all_88_1) & ( ~ % 183.08/28.72 | (all_88_1 = e3) | ( ~ (all_88_0 = e0) & op(e4, e3) = all_88_0 & % 183.08/28.72 | $i(all_88_0)))) % 183.08/28.72 | % 183.08/28.72 | DELTA: instantiating (78) with fresh symbols all_90_0, all_90_1, all_90_2 % 183.08/28.72 | gives: % 183.08/28.72 | (264) op(e0, e3) = all_90_2 & $i(all_90_2) & ( ~ (all_90_2 = e4) | (op(e4, % 183.08/28.72 | e0) = all_90_1 & $i(all_90_1) & ( ~ (all_90_1 = e2) | ( ~ % 183.08/28.72 | (all_90_0 = e1) & op(e0, e2) = all_90_0 & $i(all_90_0))))) % 183.08/28.72 | % 183.08/28.72 | ALPHA: (264) implies: % 183.08/28.73 | (265) op(e0, e3) = all_90_2 % 183.08/28.73 | (266) ~ (all_90_2 = e4) | (op(e4, e0) = all_90_1 & $i(all_90_1) & ( ~ % 183.08/28.73 | (all_90_1 = e2) | ( ~ (all_90_0 = e1) & op(e0, e2) = all_90_0 & % 183.08/28.73 | $i(all_90_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (96) with fresh symbols all_92_0, all_92_1, all_92_2 % 183.08/28.73 | gives: % 183.08/28.73 | (267) op(e0, e1) = all_92_2 & $i(all_92_2) & ( ~ (all_92_2 = e4) | (op(e4, % 183.08/28.73 | e0) = all_92_1 & $i(all_92_1) & ( ~ (all_92_1 = e3) | ( ~ % 183.08/28.73 | (all_92_0 = e2) & op(e0, e3) = all_92_0 & $i(all_92_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (267) implies: % 183.08/28.73 | (268) op(e0, e1) = all_92_2 % 183.08/28.73 | (269) ~ (all_92_2 = e4) | (op(e4, e0) = all_92_1 & $i(all_92_1) & ( ~ % 183.08/28.73 | (all_92_1 = e3) | ( ~ (all_92_0 = e2) & op(e0, e3) = all_92_0 & % 183.08/28.73 | $i(all_92_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (94) with fresh symbols all_94_0, all_94_1, all_94_2 % 183.08/28.73 | gives: % 183.08/28.73 | (270) op(e2, e1) = all_94_2 & $i(all_94_2) & ( ~ (all_94_2 = e4) | (op(e4, % 183.08/28.73 | e2) = all_94_1 & $i(all_94_1) & ( ~ (all_94_1 = e3) | ( ~ % 183.08/28.73 | (all_94_0 = e0) & op(e2, e3) = all_94_0 & $i(all_94_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (270) implies: % 183.08/28.73 | (271) op(e2, e1) = all_94_2 % 183.08/28.73 | (272) ~ (all_94_2 = e4) | (op(e4, e2) = all_94_1 & $i(all_94_1) & ( ~ % 183.08/28.73 | (all_94_1 = e3) | ( ~ (all_94_0 = e0) & op(e2, e3) = all_94_0 & % 183.08/28.73 | $i(all_94_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (92) with fresh symbols all_96_0, all_96_1, all_96_2 % 183.08/28.73 | gives: % 183.08/28.73 | (273) op(e1, e0) = all_96_2 & $i(all_96_2) & ( ~ (all_96_2 = e2) | (op(e2, % 183.08/28.73 | e1) = all_96_1 & $i(all_96_1) & ( ~ (all_96_1 = e3) | ( ~ % 183.08/28.73 | (all_96_0 = e4) & op(e1, e3) = all_96_0 & $i(all_96_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (273) implies: % 183.08/28.73 | (274) op(e1, e0) = all_96_2 % 183.08/28.73 | (275) ~ (all_96_2 = e2) | (op(e2, e1) = all_96_1 & $i(all_96_1) & ( ~ % 183.08/28.73 | (all_96_1 = e3) | ( ~ (all_96_0 = e4) & op(e1, e3) = all_96_0 & % 183.08/28.73 | $i(all_96_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (55) with fresh symbols all_98_0, all_98_1, all_98_2 % 183.08/28.73 | gives: % 183.08/28.73 | (276) op(e4, e3) = all_98_2 & $i(all_98_2) & ( ~ (all_98_2 = e0) | (op(e0, % 183.08/28.73 | e4) = all_98_1 & $i(all_98_1) & ( ~ (all_98_1 = e1) | ( ~ % 183.08/28.73 | (all_98_0 = e2) & op(e4, e1) = all_98_0 & $i(all_98_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (276) implies: % 183.08/28.73 | (277) op(e4, e3) = all_98_2 % 183.08/28.73 | (278) ~ (all_98_2 = e0) | (op(e0, e4) = all_98_1 & $i(all_98_1) & ( ~ % 183.08/28.73 | (all_98_1 = e1) | ( ~ (all_98_0 = e2) & op(e4, e1) = all_98_0 & % 183.08/28.73 | $i(all_98_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (83) with fresh symbols all_100_0, all_100_1, all_100_2 % 183.08/28.73 | gives: % 183.08/28.73 | (279) op(e3, e4) = all_100_2 & $i(all_100_2) & ( ~ (all_100_2 = e1) | % 183.08/28.73 | (op(e1, e3) = all_100_1 & $i(all_100_1) & ( ~ (all_100_1 = e2) | ( % 183.08/28.73 | ~ (all_100_0 = e0) & op(e3, e2) = all_100_0 & % 183.08/28.73 | $i(all_100_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (279) implies: % 183.08/28.73 | (280) op(e3, e4) = all_100_2 % 183.08/28.73 | (281) ~ (all_100_2 = e1) | (op(e1, e3) = all_100_1 & $i(all_100_1) & ( ~ % 183.08/28.73 | (all_100_1 = e2) | ( ~ (all_100_0 = e0) & op(e3, e2) = all_100_0 % 183.08/28.73 | & $i(all_100_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (133) with fresh symbols all_102_0, all_102_1, all_102_2 % 183.08/28.73 | gives: % 183.08/28.73 | (282) op(e2, e3) = all_102_2 & $i(all_102_2) & ( ~ (all_102_2 = e0) | % 183.08/28.73 | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ (all_102_1 = e4) | ( % 183.08/28.73 | ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 183.08/28.73 | $i(all_102_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (282) implies: % 183.08/28.73 | (283) op(e2, e3) = all_102_2 % 183.08/28.73 | (284) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 183.08/28.73 | (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 % 183.08/28.73 | & $i(all_102_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (134) with fresh symbols all_104_0, all_104_1, all_104_2 % 183.08/28.73 | gives: % 183.08/28.73 | (285) op(e0, e3) = all_104_2 & $i(all_104_2) & ( ~ (all_104_2 = e1) | % 183.08/28.73 | (op(e1, e0) = all_104_1 & $i(all_104_1) & ( ~ (all_104_1 = e4) | ( % 183.08/28.73 | ~ (all_104_0 = e2) & op(e0, e4) = all_104_0 & % 183.08/28.73 | $i(all_104_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (285) implies: % 183.08/28.73 | (286) op(e0, e3) = all_104_2 % 183.08/28.73 | (287) ~ (all_104_2 = e1) | (op(e1, e0) = all_104_1 & $i(all_104_1) & ( ~ % 183.08/28.73 | (all_104_1 = e4) | ( ~ (all_104_0 = e2) & op(e0, e4) = all_104_0 % 183.08/28.73 | & $i(all_104_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (18) with fresh symbols all_106_0, all_106_1, all_106_2 % 183.08/28.73 | gives: % 183.08/28.73 | (288) op(e2, e1) = all_106_2 & $i(all_106_2) & ( ~ (all_106_2 = e4) | % 183.08/28.73 | (op(e4, e2) = all_106_1 & $i(all_106_1) & ( ~ (all_106_1 = e0) | ( % 183.08/28.73 | ~ (all_106_0 = e3) & op(e2, e0) = all_106_0 & % 183.08/28.73 | $i(all_106_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (288) implies: % 183.08/28.73 | (289) op(e2, e1) = all_106_2 % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (48) with fresh symbols all_108_0, all_108_1, all_108_2 % 183.08/28.73 | gives: % 183.08/28.73 | (290) op(e0, e2) = all_108_2 & $i(all_108_2) & ( ~ (all_108_2 = e4) | % 183.08/28.73 | (op(e4, e0) = all_108_1 & $i(all_108_1) & ( ~ (all_108_1 = e1) | ( % 183.08/28.73 | ~ (all_108_0 = e3) & op(e0, e1) = all_108_0 & % 183.08/28.73 | $i(all_108_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (290) implies: % 183.08/28.73 | (291) op(e0, e2) = all_108_2 % 183.08/28.73 | (292) ~ (all_108_2 = e4) | (op(e4, e0) = all_108_1 & $i(all_108_1) & ( ~ % 183.08/28.73 | (all_108_1 = e1) | ( ~ (all_108_0 = e3) & op(e0, e1) = all_108_0 % 183.08/28.73 | & $i(all_108_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (116) with fresh symbols all_110_0, all_110_1, all_110_2 % 183.08/28.73 | gives: % 183.08/28.73 | (293) op(e1, e0) = all_110_2 & $i(all_110_2) & ( ~ (all_110_2 = e2) | % 183.08/28.73 | (op(e2, e1) = all_110_1 & $i(all_110_1) & ( ~ (all_110_1 = e4) | ( % 183.08/28.73 | ~ (all_110_0 = e3) & op(e1, e4) = all_110_0 & % 183.08/28.73 | $i(all_110_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (293) implies: % 183.08/28.73 | (294) op(e1, e0) = all_110_2 % 183.08/28.73 | (295) ~ (all_110_2 = e2) | (op(e2, e1) = all_110_1 & $i(all_110_1) & ( ~ % 183.08/28.73 | (all_110_1 = e4) | ( ~ (all_110_0 = e3) & op(e1, e4) = all_110_0 % 183.08/28.73 | & $i(all_110_0)))) % 183.08/28.73 | % 183.08/28.73 | DELTA: instantiating (32) with fresh symbols all_112_0, all_112_1, all_112_2 % 183.08/28.73 | gives: % 183.08/28.73 | (296) op(e1, e3) = all_112_2 & $i(all_112_2) & ( ~ (all_112_2 = e2) | % 183.08/28.73 | (op(e2, e1) = all_112_1 & $i(all_112_1) & ( ~ (all_112_1 = e0) | ( % 183.08/28.73 | ~ (all_112_0 = e4) & op(e1, e0) = all_112_0 & % 183.08/28.73 | $i(all_112_0))))) % 183.08/28.73 | % 183.08/28.73 | ALPHA: (296) implies: % 183.08/28.73 | (297) op(e1, e3) = all_112_2 % 183.08/28.74 | (298) ~ (all_112_2 = e2) | (op(e2, e1) = all_112_1 & $i(all_112_1) & ( ~ % 183.08/28.74 | (all_112_1 = e0) | ( ~ (all_112_0 = e4) & op(e1, e0) = all_112_0 % 183.08/28.74 | & $i(all_112_0)))) % 183.08/28.74 | % 183.08/28.74 | DELTA: instantiating (30) with fresh symbols all_114_0, all_114_1, all_114_2 % 183.08/28.74 | gives: % 183.08/28.74 | (299) op(e1, e3) = all_114_2 & $i(all_114_2) & ( ~ (all_114_2 = e4) | % 183.08/28.74 | (op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ (all_114_1 = e0) | ( % 183.08/28.74 | ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 & % 183.08/28.74 | $i(all_114_0))))) % 183.08/28.74 | % 183.08/28.74 | ALPHA: (299) implies: % 183.08/28.74 | (300) op(e1, e3) = all_114_2 % 183.08/28.74 | (301) ~ (all_114_2 = e4) | (op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ % 183.08/28.74 | (all_114_1 = e0) | ( ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 % 183.08/28.74 | & $i(all_114_0)))) % 183.08/28.74 | % 183.08/28.74 | DELTA: instantiating (42) with fresh symbols all_116_0, all_116_1, all_116_2 % 183.08/28.74 | gives: % 183.08/28.74 | (302) op(e2, e0) = all_116_2 & $i(all_116_2) & ( ~ (all_116_2 = e4) | % 183.08/28.74 | (op(e4, e2) = all_116_1 & $i(all_116_1) & ( ~ (all_116_1 = e1) | ( % 183.08/28.74 | ~ (all_116_0 = e3) & op(e2, e1) = all_116_0 & % 183.08/28.74 | $i(all_116_0))))) % 183.08/28.74 | % 183.08/28.74 | ALPHA: (302) implies: % 183.08/28.74 | (303) op(e2, e0) = all_116_2 % 183.08/28.74 | % 183.08/28.74 | DELTA: instantiating (80) with fresh symbols all_118_0, all_118_1, all_118_2 % 183.08/28.74 | gives: % 183.08/28.74 | (304) op(e0, e3) = all_118_2 & $i(all_118_2) & ( ~ (all_118_2 = e1) | % 183.08/28.74 | (op(e1, e0) = all_118_1 & $i(all_118_1) & ( ~ (all_118_1 = e2) | ( % 183.08/28.74 | ~ (all_118_0 = e4) & op(e0, e2) = all_118_0 & % 183.08/28.74 | $i(all_118_0))))) % 183.08/28.74 | % 183.08/28.74 | ALPHA: (304) implies: % 183.08/28.74 | (305) op(e0, e3) = all_118_2 % 183.08/28.74 | (306) ~ (all_118_2 = e1) | (op(e1, e0) = all_118_1 & $i(all_118_1) & ( ~ % 183.08/28.74 | (all_118_1 = e2) | ( ~ (all_118_0 = e4) & op(e0, e2) = all_118_0 % 183.08/28.74 | & $i(all_118_0)))) % 183.08/28.74 | % 183.08/28.74 | DELTA: instantiating (58) with fresh symbols all_120_0, all_120_1, all_120_2 % 183.08/28.74 | gives: % 183.08/28.74 | (307) op(e2, e4) = all_120_2 & $i(all_120_2) & ( ~ (all_120_2 = e3) | % 183.08/28.74 | (op(e3, e2) = all_120_1 & $i(all_120_1) & ( ~ (all_120_1 = e1) | ( % 183.08/28.74 | ~ (all_120_0 = e0) & op(e2, e1) = all_120_0 & % 183.08/28.74 | $i(all_120_0))))) % 183.08/28.74 | % 183.08/28.74 | ALPHA: (307) implies: % 183.08/28.74 | (308) op(e2, e4) = all_120_2 % 183.08/28.74 | (309) ~ (all_120_2 = e3) | (op(e3, e2) = all_120_1 & $i(all_120_1) & ( ~ % 183.08/28.74 | (all_120_1 = e1) | ( ~ (all_120_0 = e0) & op(e2, e1) = all_120_0 % 183.08/28.74 | & $i(all_120_0)))) % 183.08/28.74 | % 183.08/28.74 | DELTA: instantiating (16) with fresh symbols all_122_0, all_122_1, all_122_2 % 183.08/28.74 | gives: % 183.08/28.74 | (310) op(e3, e1) = all_122_2 & $i(all_122_2) & ( ~ (all_122_2 = e4) | % 183.08/28.74 | (op(e4, e3) = all_122_1 & $i(all_122_1) & ( ~ (all_122_1 = e0) | ( % 183.08/28.74 | ~ (all_122_0 = e2) & op(e3, e0) = all_122_0 & % 183.08/28.74 | $i(all_122_0))))) % 183.08/28.74 | % 183.08/28.74 | ALPHA: (310) implies: % 183.08/28.74 | (311) op(e3, e1) = all_122_2 % 183.08/28.74 | (312) ~ (all_122_2 = e4) | (op(e4, e3) = all_122_1 & $i(all_122_1) & ( ~ % 183.08/28.74 | (all_122_1 = e0) | ( ~ (all_122_0 = e2) & op(e3, e0) = all_122_0 % 183.08/28.74 | & $i(all_122_0)))) % 183.08/28.74 | % 183.08/28.74 | DELTA: instantiating (33) with fresh symbols all_124_0, all_124_1, all_124_2 % 183.08/28.74 | gives: % 183.29/28.74 | (313) op(e2, e3) = all_124_2 & $i(all_124_2) & ( ~ (all_124_2 = e1) | % 183.29/28.74 | (op(e1, e2) = all_124_1 & $i(all_124_1) & ( ~ (all_124_1 = e0) | ( % 183.29/28.74 | ~ (all_124_0 = e4) & op(e2, e0) = all_124_0 & % 183.29/28.74 | $i(all_124_0))))) % 183.29/28.74 | % 183.29/28.74 | ALPHA: (313) implies: % 183.29/28.74 | (314) op(e2, e3) = all_124_2 % 183.29/28.74 | (315) ~ (all_124_2 = e1) | (op(e1, e2) = all_124_1 & $i(all_124_1) & ( ~ % 183.29/28.74 | (all_124_1 = e0) | ( ~ (all_124_0 = e4) & op(e2, e0) = all_124_0 % 183.29/28.74 | & $i(all_124_0)))) % 183.29/28.74 | % 183.29/28.74 | DELTA: instantiating (40) with fresh symbols all_126_0, all_126_1, all_126_2 % 183.29/28.74 | gives: % 183.29/28.74 | (316) op(e3, e0) = all_126_2 & $i(all_126_2) & ( ~ (all_126_2 = e4) | % 183.29/28.74 | (op(e4, e3) = all_126_1 & $i(all_126_1) & ( ~ (all_126_1 = e1) | ( % 183.29/28.74 | ~ (all_126_0 = e2) & op(e3, e1) = all_126_0 & % 183.29/28.74 | $i(all_126_0))))) % 183.29/28.74 | % 183.29/28.74 | ALPHA: (316) implies: % 183.29/28.74 | (317) op(e3, e0) = all_126_2 % 183.29/28.74 | % 183.29/28.74 | DELTA: instantiating (89) with fresh symbols all_128_0, all_128_1, all_128_2 % 183.29/28.74 | gives: % 183.29/28.74 | (318) op(e4, e0) = all_128_2 & $i(all_128_2) & ( ~ (all_128_2 = e2) | % 183.29/28.74 | (op(e2, e4) = all_128_1 & $i(all_128_1) & ( ~ (all_128_1 = e3) | ( % 183.29/28.74 | ~ (all_128_0 = e1) & op(e4, e3) = all_128_0 & % 183.29/28.74 | $i(all_128_0))))) % 183.29/28.74 | % 183.29/28.74 | ALPHA: (318) implies: % 183.29/28.74 | (319) op(e4, e0) = all_128_2 % 183.29/28.74 | (320) ~ (all_128_2 = e2) | (op(e2, e4) = all_128_1 & $i(all_128_1) & ( ~ % 183.29/28.74 | (all_128_1 = e3) | ( ~ (all_128_0 = e1) & op(e4, e3) = all_128_0 % 183.29/28.74 | & $i(all_128_0)))) % 183.29/28.74 | % 183.29/28.74 | DELTA: instantiating (76) with fresh symbols all_130_0, all_130_1, all_130_2 % 183.29/28.74 | gives: % 183.29/28.74 | (321) op(e1, e3) = all_130_2 & $i(all_130_2) & ( ~ (all_130_2 = e4) | % 183.29/28.74 | (op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ (all_130_1 = e2) | ( % 183.29/28.74 | ~ (all_130_0 = e0) & op(e1, e2) = all_130_0 & % 183.29/28.74 | $i(all_130_0))))) % 183.29/28.74 | % 183.29/28.74 | ALPHA: (321) implies: % 183.29/28.74 | (322) op(e1, e3) = all_130_2 % 183.29/28.74 | (323) ~ (all_130_2 = e4) | (op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ % 183.29/28.74 | (all_130_1 = e2) | ( ~ (all_130_0 = e0) & op(e1, e2) = all_130_0 % 183.29/28.74 | & $i(all_130_0)))) % 183.29/28.74 | % 183.29/28.74 | DELTA: instantiating (91) with fresh symbols all_132_0, all_132_1, all_132_2 % 183.29/28.74 | gives: % 183.29/28.74 | (324) op(e4, e0) = all_132_2 & $i(all_132_2) & ( ~ (all_132_2 = e1) | % 183.29/28.74 | (op(e1, e4) = all_132_1 & $i(all_132_1) & ( ~ (all_132_1 = e3) | ( % 183.29/28.74 | ~ (all_132_0 = e2) & op(e4, e3) = all_132_0 & % 183.29/28.74 | $i(all_132_0))))) % 183.29/28.74 | % 183.29/28.74 | ALPHA: (324) implies: % 183.30/28.74 | (325) op(e4, e0) = all_132_2 % 183.30/28.74 | (326) ~ (all_132_2 = e1) | (op(e1, e4) = all_132_1 & $i(all_132_1) & ( ~ % 183.30/28.74 | (all_132_1 = e3) | ( ~ (all_132_0 = e2) & op(e4, e3) = all_132_0 % 183.30/28.74 | & $i(all_132_0)))) % 183.30/28.74 | % 183.30/28.74 | DELTA: instantiating (34) with fresh symbols all_134_0, all_134_1, all_134_2 % 183.30/28.74 | gives: % 183.30/28.74 | (327) op(e2, e4) = all_134_2 & $i(all_134_2) & ( ~ (all_134_2 = e3) | % 183.30/28.74 | (op(e3, e2) = all_134_1 & $i(all_134_1) & ( ~ (all_134_1 = e0) | ( % 183.30/28.74 | ~ (all_134_0 = e1) & op(e2, e0) = all_134_0 & % 183.30/28.74 | $i(all_134_0))))) % 183.30/28.74 | % 183.30/28.74 | ALPHA: (327) implies: % 183.30/28.74 | (328) op(e2, e4) = all_134_2 % 183.30/28.75 | (329) ~ (all_134_2 = e3) | (op(e3, e2) = all_134_1 & $i(all_134_1) & ( ~ % 183.30/28.75 | (all_134_1 = e0) | ( ~ (all_134_0 = e1) & op(e2, e0) = all_134_0 % 183.30/28.75 | & $i(all_134_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (35) with fresh symbols all_136_0, all_136_1, all_136_2 % 183.30/28.75 | gives: % 183.30/28.75 | (330) op(e3, e4) = all_136_2 & $i(all_136_2) & ( ~ (all_136_2 = e2) | % 183.30/28.75 | (op(e2, e3) = all_136_1 & $i(all_136_1) & ( ~ (all_136_1 = e0) | ( % 183.30/28.75 | ~ (all_136_0 = e1) & op(e3, e0) = all_136_0 & % 183.30/28.75 | $i(all_136_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (330) implies: % 183.30/28.75 | (331) op(e3, e4) = all_136_2 % 183.30/28.75 | (332) ~ (all_136_2 = e2) | (op(e2, e3) = all_136_1 & $i(all_136_1) & ( ~ % 183.30/28.75 | (all_136_1 = e0) | ( ~ (all_136_0 = e1) & op(e3, e0) = all_136_0 % 183.30/28.75 | & $i(all_136_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (28) with fresh symbols all_138_0, all_138_1, all_138_2 % 183.30/28.75 | gives: % 183.30/28.75 | (333) op(e2, e3) = all_138_2 & $i(all_138_2) & ( ~ (all_138_2 = e4) | % 183.30/28.75 | (op(e4, e2) = all_138_1 & $i(all_138_1) & ( ~ (all_138_1 = e0) | ( % 183.30/28.75 | ~ (all_138_0 = e1) & op(e2, e0) = all_138_0 & % 183.30/28.75 | $i(all_138_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (333) implies: % 183.30/28.75 | (334) op(e2, e3) = all_138_2 % 183.30/28.75 | (335) ~ (all_138_2 = e4) | (op(e4, e2) = all_138_1 & $i(all_138_1) & ( ~ % 183.30/28.75 | (all_138_1 = e0) | ( ~ (all_138_0 = e1) & op(e2, e0) = all_138_0 % 183.30/28.75 | & $i(all_138_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (29) with fresh symbols all_140_0, all_140_1, all_140_2 % 183.30/28.75 | gives: % 183.30/28.75 | (336) op(e4, e3) = all_140_2 & $i(all_140_2) & ( ~ (all_140_2 = e2) | % 183.30/28.75 | (op(e2, e4) = all_140_1 & $i(all_140_1) & ( ~ (all_140_1 = e0) | ( % 183.30/28.75 | ~ (all_140_0 = e1) & op(e4, e0) = all_140_0 & % 183.30/28.75 | $i(all_140_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (336) implies: % 183.30/28.75 | (337) op(e4, e3) = all_140_2 % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (31) with fresh symbols all_142_0, all_142_1, all_142_2 % 183.30/28.75 | gives: % 183.30/28.75 | (338) op(e4, e3) = all_142_2 & $i(all_142_2) & ( ~ (all_142_2 = e1) | % 183.30/28.75 | (op(e1, e4) = all_142_1 & $i(all_142_1) & ( ~ (all_142_1 = e0) | ( % 183.30/28.75 | ~ (all_142_0 = e2) & op(e4, e0) = all_142_0 & % 183.30/28.75 | $i(all_142_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (338) implies: % 183.30/28.75 | (339) op(e4, e3) = all_142_2 % 183.30/28.75 | (340) ~ (all_142_2 = e1) | (op(e1, e4) = all_142_1 & $i(all_142_1) & ( ~ % 183.30/28.75 | (all_142_1 = e0) | ( ~ (all_142_0 = e2) & op(e4, e0) = all_142_0 % 183.30/28.75 | & $i(all_142_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (36) with fresh symbols all_144_0, all_144_1, all_144_2 % 183.30/28.75 | gives: % 183.30/28.75 | (341) op(e1, e4) = all_144_2 & $i(all_144_2) & ( ~ (all_144_2 = e3) | % 183.30/28.75 | (op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ (all_144_1 = e0) | ( % 183.30/28.75 | ~ (all_144_0 = e2) & op(e1, e0) = all_144_0 & % 183.30/28.75 | $i(all_144_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (341) implies: % 183.30/28.75 | (342) op(e1, e4) = all_144_2 % 183.30/28.75 | (343) ~ (all_144_2 = e3) | (op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ % 183.30/28.75 | (all_144_1 = e0) | ( ~ (all_144_0 = e2) & op(e1, e0) = all_144_0 % 183.30/28.75 | & $i(all_144_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (37) with fresh symbols all_146_0, all_146_1, all_146_2 % 183.30/28.75 | gives: % 183.30/28.75 | (344) op(e3, e4) = all_146_2 & $i(all_146_2) & ( ~ (all_146_2 = e1) | % 183.30/28.75 | (op(e1, e3) = all_146_1 & $i(all_146_1) & ( ~ (all_146_1 = e0) | ( % 183.30/28.75 | ~ (all_146_0 = e2) & op(e3, e0) = all_146_0 & % 183.30/28.75 | $i(all_146_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (344) implies: % 183.30/28.75 | (345) op(e3, e4) = all_146_2 % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (39) with fresh symbols all_148_0, all_148_1, all_148_2 % 183.30/28.75 | gives: % 183.30/28.75 | (346) op(e2, e4) = all_148_2 & $i(all_148_2) & ( ~ (all_148_2 = e1) | % 183.30/28.75 | (op(e1, e2) = all_148_1 & $i(all_148_1) & ( ~ (all_148_1 = e0) | ( % 183.30/28.75 | ~ (all_148_0 = e3) & op(e2, e0) = all_148_0 & % 183.30/28.75 | $i(all_148_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (346) implies: % 183.30/28.75 | (347) op(e2, e4) = all_148_2 % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (26) with fresh symbols all_150_0, all_150_1, all_150_2 % 183.30/28.75 | gives: % 183.30/28.75 | (348) op(e1, e2) = all_150_2 & $i(all_150_2) & ( ~ (all_150_2 = e3) | % 183.30/28.75 | (op(e3, e1) = all_150_1 & $i(all_150_1) & ( ~ (all_150_1 = e0) | ( % 183.30/28.75 | ~ (all_150_0 = e4) & op(e1, e0) = all_150_0 & % 183.30/28.75 | $i(all_150_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (348) implies: % 183.30/28.75 | (349) op(e1, e2) = all_150_2 % 183.30/28.75 | (350) ~ (all_150_2 = e3) | (op(e3, e1) = all_150_1 & $i(all_150_1) & ( ~ % 183.30/28.75 | (all_150_1 = e0) | ( ~ (all_150_0 = e4) & op(e1, e0) = all_150_0 % 183.30/28.75 | & $i(all_150_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (38) with fresh symbols all_152_0, all_152_1, all_152_2 % 183.30/28.75 | gives: % 183.30/28.75 | (351) op(e1, e4) = all_152_2 & $i(all_152_2) & ( ~ (all_152_2 = e2) | % 183.30/28.75 | (op(e2, e1) = all_152_1 & $i(all_152_1) & ( ~ (all_152_1 = e0) | ( % 183.30/28.75 | ~ (all_152_0 = e3) & op(e1, e0) = all_152_0 & % 183.30/28.75 | $i(all_152_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (351) implies: % 183.30/28.75 | (352) op(e1, e4) = all_152_2 % 183.30/28.75 | (353) ~ (all_152_2 = e2) | (op(e2, e1) = all_152_1 & $i(all_152_1) & ( ~ % 183.30/28.75 | (all_152_1 = e0) | ( ~ (all_152_0 = e3) & op(e1, e0) = all_152_0 % 183.30/28.75 | & $i(all_152_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (125) with fresh symbols all_154_0, all_154_1, all_154_2 % 183.30/28.75 | gives: % 183.30/28.75 | (354) op(e3, e2) = all_154_2 & $i(all_154_2) & ( ~ (all_154_2 = e1) | % 183.30/28.75 | (op(e1, e3) = all_154_1 & $i(all_154_1) & ( ~ (all_154_1 = e4) | ( % 183.30/28.75 | ~ (all_154_0 = e0) & op(e3, e4) = all_154_0 & % 183.30/28.75 | $i(all_154_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (354) implies: % 183.30/28.75 | (355) op(e3, e2) = all_154_2 % 183.30/28.75 | (356) ~ (all_154_2 = e1) | (op(e1, e3) = all_154_1 & $i(all_154_1) & ( ~ % 183.30/28.75 | (all_154_1 = e4) | ( ~ (all_154_0 = e0) & op(e3, e4) = all_154_0 % 183.30/28.75 | & $i(all_154_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (127) with fresh symbols all_156_0, all_156_1, all_156_2 % 183.30/28.75 | gives: % 183.30/28.75 | (357) op(e3, e2) = all_156_2 & $i(all_156_2) & ( ~ (all_156_2 = e0) | % 183.30/28.75 | (op(e0, e3) = all_156_1 & $i(all_156_1) & ( ~ (all_156_1 = e4) | ( % 183.30/28.75 | ~ (all_156_0 = e1) & op(e3, e4) = all_156_0 & % 183.30/28.75 | $i(all_156_0))))) % 183.30/28.75 | % 183.30/28.75 | ALPHA: (357) implies: % 183.30/28.75 | (358) op(e3, e2) = all_156_2 % 183.30/28.75 | (359) ~ (all_156_2 = e0) | (op(e0, e3) = all_156_1 & $i(all_156_1) & ( ~ % 183.30/28.75 | (all_156_1 = e4) | ( ~ (all_156_0 = e1) & op(e3, e4) = all_156_0 % 183.30/28.75 | & $i(all_156_0)))) % 183.30/28.75 | % 183.30/28.75 | DELTA: instantiating (126) with fresh symbols all_158_0, all_158_1, all_158_2 % 183.30/28.75 | gives: % 183.30/28.76 | (360) op(e0, e2) = all_158_2 & $i(all_158_2) & ( ~ (all_158_2 = e3) | % 183.30/28.76 | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ (all_158_1 = e4) | ( % 183.30/28.76 | ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 183.30/28.76 | $i(all_158_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (360) implies: % 183.30/28.76 | (361) op(e0, e2) = all_158_2 % 183.30/28.76 | (362) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 183.30/28.76 | (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 % 183.30/28.76 | & $i(all_158_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (124) with fresh symbols all_160_0, all_160_1, all_160_2 % 183.30/28.76 | gives: % 183.30/28.76 | (363) op(e1, e2) = all_160_2 & $i(all_160_2) & ( ~ (all_160_2 = e3) | % 183.30/28.76 | (op(e3, e1) = all_160_1 & $i(all_160_1) & ( ~ (all_160_1 = e4) | ( % 183.30/28.76 | ~ (all_160_0 = e0) & op(e1, e4) = all_160_0 & % 183.30/28.76 | $i(all_160_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (363) implies: % 183.30/28.76 | (364) op(e1, e2) = all_160_2 % 183.30/28.76 | (365) ~ (all_160_2 = e3) | (op(e3, e1) = all_160_1 & $i(all_160_1) & ( ~ % 183.30/28.76 | (all_160_1 = e4) | ( ~ (all_160_0 = e0) & op(e1, e4) = all_160_0 % 183.30/28.76 | & $i(all_160_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (128) with fresh symbols all_162_0, all_162_1, all_162_2 % 183.30/28.76 | gives: % 183.30/28.76 | (366) op(e0, e2) = all_162_2 & $i(all_162_2) & ( ~ (all_162_2 = e1) | % 183.30/28.76 | (op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ (all_162_1 = e4) | ( % 183.30/28.76 | ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 183.30/28.76 | $i(all_162_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (366) implies: % 183.30/28.76 | (367) op(e0, e2) = all_162_2 % 183.30/28.76 | (368) ~ (all_162_2 = e1) | (op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ % 183.30/28.76 | (all_162_1 = e4) | ( ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 % 183.30/28.76 | & $i(all_162_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (114) with fresh symbols all_164_0, all_164_1, all_164_2 % 183.30/28.76 | gives: % 183.30/28.76 | (369) op(e1, e0) = all_164_2 & $i(all_164_2) & ( ~ (all_164_2 = e3) | % 183.30/28.76 | (op(e3, e1) = all_164_1 & $i(all_164_1) & ( ~ (all_164_1 = e4) | ( % 183.30/28.76 | ~ (all_164_0 = e2) & op(e1, e4) = all_164_0 & % 183.30/28.76 | $i(all_164_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (369) implies: % 183.30/28.76 | (370) op(e1, e0) = all_164_2 % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (135) with fresh symbols all_166_0, all_166_1, all_166_2 % 183.30/28.76 | gives: % 183.30/28.76 | (371) op(e1, e3) = all_166_2 & $i(all_166_2) & ( ~ (all_166_2 = e0) | % 183.30/28.76 | (op(e0, e1) = all_166_1 & $i(all_166_1) & ( ~ (all_166_1 = e4) | ( % 183.30/28.76 | ~ (all_166_0 = e2) & op(e1, e4) = all_166_0 & % 183.30/28.76 | $i(all_166_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (371) implies: % 183.30/28.76 | (372) op(e1, e3) = all_166_2 % 183.30/28.76 | (373) ~ (all_166_2 = e0) | (op(e0, e1) = all_166_1 & $i(all_166_1) & ( ~ % 183.30/28.76 | (all_166_1 = e4) | ( ~ (all_166_0 = e2) & op(e1, e4) = all_166_0 % 183.30/28.76 | & $i(all_166_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (85) with fresh symbols all_168_0, all_168_1, all_168_2 % 183.30/28.76 | gives: % 183.30/28.76 | (374) op(e3, e4) = all_168_2 & $i(all_168_2) & ( ~ (all_168_2 = e0) | % 183.30/28.76 | (op(e0, e3) = all_168_1 & $i(all_168_1) & ( ~ (all_168_1 = e2) | ( % 183.30/28.76 | ~ (all_168_0 = e1) & op(e3, e2) = all_168_0 & % 183.30/28.76 | $i(all_168_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (374) implies: % 183.30/28.76 | (375) op(e3, e4) = all_168_2 % 183.30/28.76 | (376) ~ (all_168_2 = e0) | (op(e0, e3) = all_168_1 & $i(all_168_1) & ( ~ % 183.30/28.76 | (all_168_1 = e2) | ( ~ (all_168_0 = e1) & op(e3, e2) = all_168_0 % 183.30/28.76 | & $i(all_168_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (87) with fresh symbols all_170_0, all_170_1, all_170_2 % 183.30/28.76 | gives: % 183.30/28.76 | (377) op(e1, e4) = all_170_2 & $i(all_170_2) & ( ~ (all_170_2 = e0) | % 183.30/28.76 | (op(e0, e1) = all_170_1 & $i(all_170_1) & ( ~ (all_170_1 = e2) | ( % 183.30/28.76 | ~ (all_170_0 = e3) & op(e1, e2) = all_170_0 & % 183.30/28.76 | $i(all_170_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (377) implies: % 183.30/28.76 | (378) op(e1, e4) = all_170_2 % 183.30/28.76 | (379) ~ (all_170_2 = e0) | (op(e0, e1) = all_170_1 & $i(all_170_1) & ( ~ % 183.30/28.76 | (all_170_1 = e2) | ( ~ (all_170_0 = e3) & op(e1, e2) = all_170_0 % 183.30/28.76 | & $i(all_170_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (57) with fresh symbols all_172_0, all_172_1, all_172_2 % 183.30/28.76 | gives: % 183.30/28.76 | (380) op(e2, e3) = all_172_2 & $i(all_172_2) & ( ~ (all_172_2 = e0) | % 183.30/28.76 | (op(e0, e2) = all_172_1 & $i(all_172_1) & ( ~ (all_172_1 = e1) | ( % 183.30/28.76 | ~ (all_172_0 = e4) & op(e2, e1) = all_172_0 & % 183.30/28.76 | $i(all_172_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (380) implies: % 183.30/28.76 | (381) op(e2, e3) = all_172_2 % 183.30/28.76 | (382) ~ (all_172_2 = e0) | (op(e0, e2) = all_172_1 & $i(all_172_1) & ( ~ % 183.30/28.76 | (all_172_1 = e1) | ( ~ (all_172_0 = e4) & op(e2, e1) = all_172_0 % 183.30/28.76 | & $i(all_172_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (44) with fresh symbols all_174_0, all_174_1, all_174_2 % 183.30/28.76 | gives: % 183.30/28.76 | (383) op(e2, e0) = all_174_2 & $i(all_174_2) & ( ~ (all_174_2 = e3) | % 183.30/28.76 | (op(e3, e2) = all_174_1 & $i(all_174_1) & ( ~ (all_174_1 = e1) | ( % 183.30/28.76 | ~ (all_174_0 = e4) & op(e2, e1) = all_174_0 & % 183.30/28.76 | $i(all_174_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (383) implies: % 183.30/28.76 | (384) op(e2, e0) = all_174_2 % 183.30/28.76 | (385) ~ (all_174_2 = e3) | (op(e3, e2) = all_174_1 & $i(all_174_1) & ( ~ % 183.30/28.76 | (all_174_1 = e1) | ( ~ (all_174_0 = e4) & op(e2, e1) = all_174_0 % 183.30/28.76 | & $i(all_174_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (59) with fresh symbols all_176_0, all_176_1, all_176_2 % 183.30/28.76 | gives: % 183.30/28.76 | (386) op(e3, e4) = all_176_2 & $i(all_176_2) & ( ~ (all_176_2 = e2) | % 183.30/28.76 | (op(e2, e3) = all_176_1 & $i(all_176_1) & ( ~ (all_176_1 = e1) | ( % 183.30/28.76 | ~ (all_176_0 = e0) & op(e3, e1) = all_176_0 & % 183.30/28.76 | $i(all_176_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (386) implies: % 183.30/28.76 | (387) op(e3, e4) = all_176_2 % 183.30/28.76 | (388) ~ (all_176_2 = e2) | (op(e2, e3) = all_176_1 & $i(all_176_1) & ( ~ % 183.30/28.76 | (all_176_1 = e1) | ( ~ (all_176_0 = e0) & op(e3, e1) = all_176_0 % 183.30/28.76 | & $i(all_176_0)))) % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (88) with fresh symbols all_178_0, all_178_1, all_178_2 % 183.30/28.76 | gives: % 183.30/28.76 | (389) op(e2, e0) = all_178_2 & $i(all_178_2) & ( ~ (all_178_2 = e4) | % 183.30/28.76 | (op(e4, e2) = all_178_1 & $i(all_178_1) & ( ~ (all_178_1 = e3) | ( % 183.30/28.76 | ~ (all_178_0 = e1) & op(e2, e3) = all_178_0 & % 183.30/28.76 | $i(all_178_0))))) % 183.30/28.76 | % 183.30/28.76 | ALPHA: (389) implies: % 183.30/28.76 | (390) op(e2, e0) = all_178_2 % 183.30/28.76 | % 183.30/28.76 | DELTA: instantiating (24) with fresh symbols all_180_0, all_180_1, all_180_2 % 183.30/28.76 | gives: % 183.30/28.77 | (391) op(e1, e2) = all_180_2 & $i(all_180_2) & ( ~ (all_180_2 = e4) | % 183.30/28.77 | (op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ (all_180_1 = e0) | ( % 183.30/28.77 | ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 183.30/28.77 | $i(all_180_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (391) implies: % 183.30/28.77 | (392) op(e1, e2) = all_180_2 % 183.30/28.77 | (393) ~ (all_180_2 = e4) | (op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 183.30/28.77 | (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 % 183.30/28.77 | & $i(all_180_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (77) with fresh symbols all_182_0, all_182_1, all_182_2 % 183.30/28.77 | gives: % 183.30/28.77 | (394) op(e4, e3) = all_182_2 & $i(all_182_2) & ( ~ (all_182_2 = e1) | % 183.30/28.77 | (op(e1, e4) = all_182_1 & $i(all_182_1) & ( ~ (all_182_1 = e2) | ( % 183.30/28.77 | ~ (all_182_0 = e0) & op(e4, e2) = all_182_0 & % 183.30/28.77 | $i(all_182_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (394) implies: % 183.30/28.77 | (395) op(e4, e3) = all_182_2 % 183.30/28.77 | (396) ~ (all_182_2 = e1) | (op(e1, e4) = all_182_1 & $i(all_182_1) & ( ~ % 183.30/28.77 | (all_182_1 = e2) | ( ~ (all_182_0 = e0) & op(e4, e2) = all_182_0 % 183.30/28.77 | & $i(all_182_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (79) with fresh symbols all_184_0, all_184_1, all_184_2 % 183.30/28.77 | gives: % 183.30/28.77 | (397) op(e4, e3) = all_184_2 & $i(all_184_2) & ( ~ (all_184_2 = e0) | % 183.30/28.77 | (op(e0, e4) = all_184_1 & $i(all_184_1) & ( ~ (all_184_1 = e2) | ( % 183.30/28.77 | ~ (all_184_0 = e1) & op(e4, e2) = all_184_0 & % 183.30/28.77 | $i(all_184_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (397) implies: % 183.30/28.77 | (398) op(e4, e3) = all_184_2 % 183.30/28.77 | (399) ~ (all_184_2 = e0) | (op(e0, e4) = all_184_1 & $i(all_184_1) & ( ~ % 183.30/28.77 | (all_184_1 = e2) | ( ~ (all_184_0 = e1) & op(e4, e2) = all_184_0 % 183.30/28.77 | & $i(all_184_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (107) with fresh symbols all_186_0, all_186_1, all_186_2 % 183.30/28.77 | gives: % 183.30/28.77 | (400) op(e2, e4) = all_186_2 & $i(all_186_2) & ( ~ (all_186_2 = e1) | % 183.30/28.77 | (op(e1, e2) = all_186_1 & $i(all_186_1) & ( ~ (all_186_1 = e3) | ( % 183.30/28.77 | ~ (all_186_0 = e0) & op(e2, e3) = all_186_0 & % 183.30/28.77 | $i(all_186_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (400) implies: % 183.30/28.77 | (401) op(e2, e4) = all_186_2 % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (99) with fresh symbols all_188_0, all_188_1, all_188_2 % 183.30/28.77 | gives: % 183.30/28.77 | (402) op(e2, e1) = all_188_2 & $i(all_188_2) & ( ~ (all_188_2 = e0) | % 183.30/28.77 | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ (all_188_1 = e3) | ( % 183.30/28.77 | ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 183.30/28.77 | $i(all_188_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (402) implies: % 183.30/28.77 | (403) op(e2, e1) = all_188_2 % 183.30/28.77 | (404) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 183.30/28.77 | (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 % 183.30/28.77 | & $i(all_188_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (20) with fresh symbols all_190_0, all_190_1, all_190_2 % 183.30/28.77 | gives: % 183.30/28.77 | (405) op(e2, e1) = all_190_2 & $i(all_190_2) & ( ~ (all_190_2 = e3) | % 183.30/28.77 | (op(e3, e2) = all_190_1 & $i(all_190_1) & ( ~ (all_190_1 = e0) | ( % 183.30/28.77 | ~ (all_190_0 = e4) & op(e2, e0) = all_190_0 & % 183.30/28.77 | $i(all_190_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (405) implies: % 183.30/28.77 | (406) op(e2, e1) = all_190_2 % 183.30/28.77 | (407) ~ (all_190_2 = e3) | (op(e3, e2) = all_190_1 & $i(all_190_1) & ( ~ % 183.30/28.77 | (all_190_1 = e0) | ( ~ (all_190_0 = e4) & op(e2, e0) = all_190_0 % 183.30/28.77 | & $i(all_190_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (100) with fresh symbols all_192_0, all_192_1, all_192_2 % 183.30/28.77 | gives: % 183.30/28.77 | (408) op(e1, e2) = all_192_2 & $i(all_192_2) & ( ~ (all_192_2 = e4) | % 183.30/28.77 | (op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ (all_192_1 = e3) | ( % 183.30/28.77 | ~ (all_192_0 = e0) & op(e1, e3) = all_192_0 & % 183.30/28.77 | $i(all_192_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (408) implies: % 183.30/28.77 | (409) op(e1, e2) = all_192_2 % 183.30/28.77 | (410) ~ (all_192_2 = e4) | (op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 183.30/28.77 | (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, e3) = all_192_0 % 183.30/28.77 | & $i(all_192_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (101) with fresh symbols all_194_0, all_194_1, all_194_2 % 183.30/28.77 | gives: % 183.30/28.77 | (411) op(e4, e2) = all_194_2 & $i(all_194_2) & ( ~ (all_194_2 = e1) | % 183.30/28.77 | (op(e1, e4) = all_194_1 & $i(all_194_1) & ( ~ (all_194_1 = e3) | ( % 183.30/28.77 | ~ (all_194_0 = e0) & op(e4, e3) = all_194_0 & % 183.30/28.77 | $i(all_194_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (411) implies: % 183.30/28.77 | (412) op(e4, e2) = all_194_2 % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (103) with fresh symbols all_196_0, all_196_1, all_196_2 % 183.30/28.77 | gives: % 183.30/28.77 | (413) op(e4, e2) = all_196_2 & $i(all_196_2) & ( ~ (all_196_2 = e0) | % 183.30/28.77 | (op(e0, e4) = all_196_1 & $i(all_196_1) & ( ~ (all_196_1 = e3) | ( % 183.30/28.77 | ~ (all_196_0 = e1) & op(e4, e3) = all_196_0 & % 183.30/28.77 | $i(all_196_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (413) implies: % 183.30/28.77 | (414) op(e4, e2) = all_196_2 % 183.30/28.77 | (415) ~ (all_196_2 = e0) | (op(e0, e4) = all_196_1 & $i(all_196_1) & ( ~ % 183.30/28.77 | (all_196_1 = e3) | ( ~ (all_196_0 = e1) & op(e4, e3) = all_196_0 % 183.30/28.77 | & $i(all_196_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (68) with fresh symbols all_198_0, all_198_1, all_198_2 % 183.30/28.77 | gives: % 183.30/28.77 | (416) op(e1, e0) = all_198_2 & $i(all_198_2) & ( ~ (all_198_2 = e3) | % 183.30/28.77 | (op(e3, e1) = all_198_1 & $i(all_198_1) & ( ~ (all_198_1 = e2) | ( % 183.30/28.77 | ~ (all_198_0 = e4) & op(e1, e2) = all_198_0 & % 183.30/28.77 | $i(all_198_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (416) implies: % 183.30/28.77 | (417) op(e1, e0) = all_198_2 % 183.30/28.77 | (418) ~ (all_198_2 = e3) | (op(e3, e1) = all_198_1 & $i(all_198_1) & ( ~ % 183.30/28.77 | (all_198_1 = e2) | ( ~ (all_198_0 = e4) & op(e1, e2) = all_198_0 % 183.30/28.77 | & $i(all_198_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (69) with fresh symbols all_200_0, all_200_1, all_200_2 % 183.30/28.77 | gives: % 183.30/28.77 | (419) op(e3, e0) = all_200_2 & $i(all_200_2) & ( ~ (all_200_2 = e1) | % 183.30/28.77 | (op(e1, e3) = all_200_1 & $i(all_200_1) & ( ~ (all_200_1 = e2) | ( % 183.30/28.77 | ~ (all_200_0 = e4) & op(e3, e2) = all_200_0 & % 183.30/28.77 | $i(all_200_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (419) implies: % 183.30/28.77 | (420) op(e3, e0) = all_200_2 % 183.30/28.77 | (421) ~ (all_200_2 = e1) | (op(e1, e3) = all_200_1 & $i(all_200_1) & ( ~ % 183.30/28.77 | (all_200_1 = e2) | ( ~ (all_200_0 = e4) & op(e3, e2) = all_200_0 % 183.30/28.77 | & $i(all_200_0)))) % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (71) with fresh symbols all_202_0, all_202_1, all_202_2 % 183.30/28.77 | gives: % 183.30/28.77 | (422) op(e4, e1) = all_202_2 & $i(all_202_2) & ( ~ (all_202_2 = e3) | % 183.30/28.77 | (op(e3, e4) = all_202_1 & $i(all_202_1) & ( ~ (all_202_1 = e2) | ( % 183.30/28.77 | ~ (all_202_0 = e0) & op(e4, e2) = all_202_0 & % 183.30/28.77 | $i(all_202_0))))) % 183.30/28.77 | % 183.30/28.77 | ALPHA: (422) implies: % 183.30/28.77 | (423) op(e4, e1) = all_202_2 % 183.30/28.77 | % 183.30/28.77 | DELTA: instantiating (70) with fresh symbols all_204_0, all_204_1, all_204_2 % 183.30/28.77 | gives: % 183.30/28.78 | (424) op(e3, e1) = all_204_2 & $i(all_204_2) & ( ~ (all_204_2 = e4) | % 183.30/28.78 | (op(e4, e3) = all_204_1 & $i(all_204_1) & ( ~ (all_204_1 = e2) | ( % 183.30/28.78 | ~ (all_204_0 = e0) & op(e3, e2) = all_204_0 & % 183.30/28.78 | $i(all_204_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (424) implies: % 183.30/28.78 | (425) op(e3, e1) = all_204_2 % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (102) with fresh symbols all_206_0, all_206_1, all_206_2 % 183.30/28.78 | gives: % 183.30/28.78 | (426) op(e0, e2) = all_206_2 & $i(all_206_2) & ( ~ (all_206_2 = e4) | % 183.30/28.78 | (op(e4, e0) = all_206_1 & $i(all_206_1) & ( ~ (all_206_1 = e3) | ( % 183.30/28.78 | ~ (all_206_0 = e1) & op(e0, e3) = all_206_0 & % 183.30/28.78 | $i(all_206_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (426) implies: % 183.30/28.78 | (427) op(e0, e2) = all_206_2 % 183.30/28.78 | (428) ~ (all_206_2 = e4) | (op(e4, e0) = all_206_1 & $i(all_206_1) & ( ~ % 183.30/28.78 | (all_206_1 = e3) | ( ~ (all_206_0 = e1) & op(e0, e3) = all_206_0 % 183.30/28.78 | & $i(all_206_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (61) with fresh symbols all_208_0, all_208_1, all_208_2 % 183.30/28.78 | gives: % 183.30/28.78 | (429) op(e3, e4) = all_208_2 & $i(all_208_2) & ( ~ (all_208_2 = e0) | % 183.30/28.78 | (op(e0, e3) = all_208_1 & $i(all_208_1) & ( ~ (all_208_1 = e1) | ( % 183.30/28.78 | ~ (all_208_0 = e2) & op(e3, e1) = all_208_0 & % 183.30/28.78 | $i(all_208_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (429) implies: % 183.30/28.78 | (430) op(e3, e4) = all_208_2 % 183.30/28.78 | (431) ~ (all_208_2 = e0) | (op(e0, e3) = all_208_1 & $i(all_208_1) & ( ~ % 183.30/28.78 | (all_208_1 = e1) | ( ~ (all_208_0 = e2) & op(e3, e1) = all_208_0 % 183.30/28.78 | & $i(all_208_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (62) with fresh symbols all_210_0, all_210_1, all_210_2 % 183.30/28.78 | gives: % 183.30/28.78 | (432) op(e0, e4) = all_210_2 & $i(all_210_2) & ( ~ (all_210_2 = e2) | % 183.30/28.78 | (op(e2, e0) = all_210_1 & $i(all_210_1) & ( ~ (all_210_1 = e1) | ( % 183.30/28.78 | ~ (all_210_0 = e3) & op(e0, e1) = all_210_0 & % 183.30/28.78 | $i(all_210_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (432) implies: % 183.30/28.78 | (433) op(e0, e4) = all_210_2 % 183.30/28.78 | (434) ~ (all_210_2 = e2) | (op(e2, e0) = all_210_1 & $i(all_210_1) & ( ~ % 183.30/28.78 | (all_210_1 = e1) | ( ~ (all_210_0 = e3) & op(e0, e1) = all_210_0 % 183.30/28.78 | & $i(all_210_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (60) with fresh symbols all_212_0, all_212_1, all_212_2 % 183.30/28.78 | gives: % 183.30/28.78 | (435) op(e0, e4) = all_212_2 & $i(all_212_2) & ( ~ (all_212_2 = e3) | % 183.30/28.78 | (op(e3, e0) = all_212_1 & $i(all_212_1) & ( ~ (all_212_1 = e1) | ( % 183.30/28.78 | ~ (all_212_0 = e2) & op(e0, e1) = all_212_0 & % 183.30/28.78 | $i(all_212_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (435) implies: % 183.30/28.78 | (436) op(e0, e4) = all_212_2 % 183.30/28.78 | (437) ~ (all_212_2 = e3) | (op(e3, e0) = all_212_1 & $i(all_212_1) & ( ~ % 183.30/28.78 | (all_212_1 = e1) | ( ~ (all_212_0 = e2) & op(e0, e1) = all_212_0 % 183.30/28.78 | & $i(all_212_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (47) with fresh symbols all_214_0, all_214_1, all_214_2 % 183.30/28.78 | gives: % 183.30/28.78 | (438) op(e4, e2) = all_214_2 & $i(all_214_2) & ( ~ (all_214_2 = e3) | % 183.30/28.78 | (op(e3, e4) = all_214_1 & $i(all_214_1) & ( ~ (all_214_1 = e1) | ( % 183.30/28.78 | ~ (all_214_0 = e0) & op(e4, e1) = all_214_0 & % 183.30/28.78 | $i(all_214_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (438) implies: % 183.30/28.78 | (439) op(e4, e2) = all_214_2 % 183.30/28.78 | (440) ~ (all_214_2 = e3) | (op(e3, e4) = all_214_1 & $i(all_214_1) & ( ~ % 183.30/28.78 | (all_214_1 = e1) | ( ~ (all_214_0 = e0) & op(e4, e1) = all_214_0 % 183.30/28.78 | & $i(all_214_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (17) with fresh symbols all_216_0, all_216_1, all_216_2 % 183.30/28.78 | gives: % 183.30/28.78 | (441) op(e4, e1) = all_216_2 & $i(all_216_2) & ( ~ (all_216_2 = e3) | % 183.30/28.78 | (op(e3, e4) = all_216_1 & $i(all_216_1) & ( ~ (all_216_1 = e0) | ( % 183.30/28.78 | ~ (all_216_0 = e2) & op(e4, e0) = all_216_0 & % 183.30/28.78 | $i(all_216_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (441) implies: % 183.30/28.78 | (442) op(e4, e1) = all_216_2 % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (25) with fresh symbols all_218_0, all_218_1, all_218_2 % 183.30/28.78 | gives: % 183.30/28.78 | (443) op(e4, e2) = all_218_2 & $i(all_218_2) & ( ~ (all_218_2 = e1) | % 183.30/28.78 | (op(e1, e4) = all_218_1 & $i(all_218_1) & ( ~ (all_218_1 = e0) | ( % 183.30/28.78 | ~ (all_218_0 = e3) & op(e4, e0) = all_218_0 & % 183.30/28.78 | $i(all_218_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (443) implies: % 183.30/28.78 | (444) op(e4, e2) = all_218_2 % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (27) with fresh symbols all_220_0, all_220_1, all_220_2 % 183.30/28.78 | gives: % 183.30/28.78 | (445) op(e3, e2) = all_220_2 & $i(all_220_2) & ( ~ (all_220_2 = e1) | % 183.30/28.78 | (op(e1, e3) = all_220_1 & $i(all_220_1) & ( ~ (all_220_1 = e0) | ( % 183.30/28.78 | ~ (all_220_0 = e4) & op(e3, e0) = all_220_0 & % 183.30/28.78 | $i(all_220_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (445) implies: % 183.30/28.78 | (446) op(e3, e2) = all_220_2 % 183.30/28.78 | (447) ~ (all_220_2 = e1) | (op(e1, e3) = all_220_1 & $i(all_220_1) & ( ~ % 183.30/28.78 | (all_220_1 = e0) | ( ~ (all_220_0 = e4) & op(e3, e0) = all_220_0 % 183.30/28.78 | & $i(all_220_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (19) with fresh symbols all_222_0, all_222_1, all_222_2 % 183.30/28.78 | gives: % 183.30/28.78 | (448) op(e4, e1) = all_222_2 & $i(all_222_2) & ( ~ (all_222_2 = e2) | % 183.30/28.78 | (op(e2, e4) = all_222_1 & $i(all_222_1) & ( ~ (all_222_1 = e0) | ( % 183.30/28.78 | ~ (all_222_0 = e3) & op(e4, e0) = all_222_0 & % 183.30/28.78 | $i(all_222_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (448) implies: % 183.30/28.78 | (449) op(e4, e1) = all_222_2 % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (63) with fresh symbols all_224_0, all_224_1, all_224_2 % 183.30/28.78 | gives: % 183.30/28.78 | (450) op(e2, e4) = all_224_2 & $i(all_224_2) & ( ~ (all_224_2 = e0) | % 183.30/28.78 | (op(e0, e2) = all_224_1 & $i(all_224_1) & ( ~ (all_224_1 = e1) | ( % 183.30/28.78 | ~ (all_224_0 = e3) & op(e2, e1) = all_224_0 & % 183.30/28.78 | $i(all_224_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (450) implies: % 183.30/28.78 | (451) op(e2, e4) = all_224_2 % 183.30/28.78 | (452) ~ (all_224_2 = e0) | (op(e0, e2) = all_224_1 & $i(all_224_1) & ( ~ % 183.30/28.78 | (all_224_1 = e1) | ( ~ (all_224_0 = e3) & op(e2, e1) = all_224_0 % 183.30/28.78 | & $i(all_224_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (64) with fresh symbols all_226_0, all_226_1, all_226_2 % 183.30/28.78 | gives: % 183.30/28.78 | (453) op(e3, e0) = all_226_2 & $i(all_226_2) & ( ~ (all_226_2 = e4) | % 183.30/28.78 | (op(e4, e3) = all_226_1 & $i(all_226_1) & ( ~ (all_226_1 = e2) | ( % 183.30/28.78 | ~ (all_226_0 = e1) & op(e3, e2) = all_226_0 & % 183.30/28.78 | $i(all_226_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (453) implies: % 183.30/28.78 | (454) op(e3, e0) = all_226_2 % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (113) with fresh symbols all_228_0, all_228_1, all_228_2 % 183.30/28.78 | gives: % 183.30/28.78 | (455) op(e3, e0) = all_228_2 & $i(all_228_2) & ( ~ (all_228_2 = e2) | % 183.30/28.78 | (op(e2, e3) = all_228_1 & $i(all_228_1) & ( ~ (all_228_1 = e4) | ( % 183.30/28.78 | ~ (all_228_0 = e1) & op(e3, e4) = all_228_0 & % 183.30/28.78 | $i(all_228_0))))) % 183.30/28.78 | % 183.30/28.78 | ALPHA: (455) implies: % 183.30/28.78 | (456) op(e3, e0) = all_228_2 % 183.30/28.78 | (457) ~ (all_228_2 = e2) | (op(e2, e3) = all_228_1 & $i(all_228_1) & ( ~ % 183.30/28.78 | (all_228_1 = e4) | ( ~ (all_228_0 = e1) & op(e3, e4) = all_228_0 % 183.30/28.78 | & $i(all_228_0)))) % 183.30/28.78 | % 183.30/28.78 | DELTA: instantiating (74) with fresh symbols all_230_0, all_230_1, all_230_2 % 183.30/28.78 | gives: % 183.30/28.79 | (458) op(e0, e1) = all_230_2 & $i(all_230_2) & ( ~ (all_230_2 = e3) | % 183.30/28.79 | (op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ (all_230_1 = e2) | ( % 183.30/28.79 | ~ (all_230_0 = e4) & op(e0, e2) = all_230_0 & % 183.30/28.79 | $i(all_230_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (458) implies: % 183.30/28.79 | (459) op(e0, e1) = all_230_2 % 183.30/28.79 | (460) ~ (all_230_2 = e3) | (op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ % 183.30/28.79 | (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, e2) = all_230_0 % 183.30/28.79 | & $i(all_230_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (90) with fresh symbols all_232_0, all_232_1, all_232_2 % 183.30/28.79 | gives: % 183.30/28.79 | (461) op(e1, e0) = all_232_2 & $i(all_232_2) & ( ~ (all_232_2 = e4) | % 183.30/28.79 | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ (all_232_1 = e3) | ( % 183.30/28.79 | ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 & % 183.30/28.79 | $i(all_232_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (461) implies: % 183.30/28.79 | (462) op(e1, e0) = all_232_2 % 183.30/28.79 | (463) ~ (all_232_2 = e4) | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 183.30/28.79 | (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 % 183.30/28.79 | & $i(all_232_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (46) with fresh symbols all_234_0, all_234_1, all_234_2 % 183.30/28.79 | gives: % 183.30/28.79 | (464) op(e3, e2) = all_234_2 & $i(all_234_2) & ( ~ (all_234_2 = e4) | % 183.30/28.79 | (op(e4, e3) = all_234_1 & $i(all_234_1) & ( ~ (all_234_1 = e1) | ( % 183.30/28.79 | ~ (all_234_0 = e0) & op(e3, e1) = all_234_0 & % 183.30/28.79 | $i(all_234_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (464) implies: % 183.30/28.79 | (465) op(e3, e2) = all_234_2 % 183.30/28.79 | (466) ~ (all_234_2 = e4) | (op(e4, e3) = all_234_1 & $i(all_234_1) & ( ~ % 183.30/28.79 | (all_234_1 = e1) | ( ~ (all_234_0 = e0) & op(e3, e1) = all_234_0 % 183.30/28.79 | & $i(all_234_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (41) with fresh symbols all_236_0, all_236_1, all_236_2 % 183.30/28.79 | gives: % 183.30/28.79 | (467) op(e4, e0) = all_236_2 & $i(all_236_2) & ( ~ (all_236_2 = e3) | % 183.30/28.79 | (op(e3, e4) = all_236_1 & $i(all_236_1) & ( ~ (all_236_1 = e1) | ( % 183.30/28.79 | ~ (all_236_0 = e2) & op(e4, e1) = all_236_0 & % 183.30/28.79 | $i(all_236_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (467) implies: % 183.30/28.79 | (468) op(e4, e0) = all_236_2 % 183.30/28.79 | (469) ~ (all_236_2 = e3) | (op(e3, e4) = all_236_1 & $i(all_236_1) & ( ~ % 183.30/28.79 | (all_236_1 = e1) | ( ~ (all_236_0 = e2) & op(e4, e1) = all_236_0 % 183.30/28.79 | & $i(all_236_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (43) with fresh symbols all_238_0, all_238_1, all_238_2 % 183.30/28.79 | gives: % 183.30/28.79 | (470) op(e4, e0) = all_238_2 & $i(all_238_2) & ( ~ (all_238_2 = e2) | % 183.30/28.79 | (op(e2, e4) = all_238_1 & $i(all_238_1) & ( ~ (all_238_1 = e1) | ( % 183.30/28.79 | ~ (all_238_0 = e3) & op(e4, e1) = all_238_0 & % 183.30/28.79 | $i(all_238_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (470) implies: % 183.30/28.79 | (471) op(e4, e0) = all_238_2 % 183.30/28.79 | (472) ~ (all_238_2 = e2) | (op(e2, e4) = all_238_1 & $i(all_238_1) & ( ~ % 183.30/28.79 | (all_238_1 = e1) | ( ~ (all_238_0 = e3) & op(e4, e1) = all_238_0 % 183.30/28.79 | & $i(all_238_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (115) with fresh symbols all_240_0, all_240_1, all_240_2 % 183.30/28.79 | gives: % 183.30/28.79 | (473) op(e3, e0) = all_240_2 & $i(all_240_2) & ( ~ (all_240_2 = e1) | % 183.30/28.79 | (op(e1, e3) = all_240_1 & $i(all_240_1) & ( ~ (all_240_1 = e4) | ( % 183.30/28.79 | ~ (all_240_0 = e2) & op(e3, e4) = all_240_0 & % 183.30/28.79 | $i(all_240_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (473) implies: % 183.30/28.79 | (474) op(e3, e0) = all_240_2 % 183.30/28.79 | (475) ~ (all_240_2 = e1) | (op(e1, e3) = all_240_1 & $i(all_240_1) & ( ~ % 183.30/28.79 | (all_240_1 = e4) | ( ~ (all_240_0 = e2) & op(e3, e4) = all_240_0 % 183.30/28.79 | & $i(all_240_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (118) with fresh symbols all_242_0, all_242_1, all_242_2 % 183.30/28.79 | gives: % 183.30/28.79 | (476) op(e2, e1) = all_242_2 & $i(all_242_2) & ( ~ (all_242_2 = e3) | % 183.30/28.79 | (op(e3, e2) = all_242_1 & $i(all_242_1) & ( ~ (all_242_1 = e4) | ( % 183.30/28.79 | ~ (all_242_0 = e0) & op(e2, e4) = all_242_0 & % 183.30/28.79 | $i(all_242_0))))) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (476) implies: % 183.30/28.79 | (477) op(e2, e1) = all_242_2 % 183.30/28.79 | (478) ~ (all_242_2 = e3) | (op(e3, e2) = all_242_1 & $i(all_242_1) & ( ~ % 183.30/28.79 | (all_242_1 = e4) | ( ~ (all_242_0 = e0) & op(e2, e4) = all_242_0 % 183.30/28.79 | & $i(all_242_0)))) % 183.30/28.79 | % 183.30/28.79 | DELTA: instantiating (3) with fresh symbols all_244_0, all_244_1, all_244_2, % 183.30/28.79 | all_244_3, all_244_4, all_244_5, all_244_6, all_244_7, all_244_8, % 183.30/28.79 | all_244_9, all_244_10, all_244_11, all_244_12, all_244_13, all_244_14, % 183.30/28.79 | all_244_15, all_244_16, all_244_17, all_244_18, all_244_19, all_244_20, % 183.30/28.79 | all_244_21, all_244_22, all_244_23, all_244_24 gives: % 183.30/28.79 | (479) op(all_244_0, all_244_0) = e4 & op(all_244_1, all_244_2) = e4 & % 183.30/28.79 | op(all_244_2, all_244_1) = e3 & op(all_244_3, all_244_3) = e3 & % 183.30/28.79 | op(all_244_4, all_244_5) = e4 & op(all_244_5, all_244_4) = e2 & % 183.30/28.79 | op(all_244_6, all_244_7) = e3 & op(all_244_7, all_244_6) = e2 & % 183.30/28.79 | op(all_244_8, all_244_8) = e2 & op(all_244_9, all_244_10) = e4 & % 183.30/28.79 | op(all_244_10, all_244_9) = e1 & op(all_244_11, all_244_12) = e3 & % 183.30/28.79 | op(all_244_12, all_244_11) = e1 & op(all_244_13, all_244_14) = e2 & % 183.30/28.79 | op(all_244_14, all_244_13) = e1 & op(all_244_15, all_244_15) = e1 & % 183.30/28.79 | op(all_244_16, all_244_17) = e4 & op(all_244_17, all_244_16) = e0 & % 183.30/28.79 | op(all_244_18, all_244_19) = e3 & op(all_244_19, all_244_18) = e0 & % 183.30/28.79 | op(all_244_20, all_244_21) = e2 & op(all_244_21, all_244_20) = e0 & % 183.30/28.79 | op(all_244_22, all_244_23) = e1 & op(all_244_23, all_244_22) = e0 & % 183.30/28.79 | op(all_244_24, all_244_24) = e0 & op(e4, e4) = all_244_0 & op(e4, e3) % 183.30/28.79 | = all_244_2 & op(e4, e2) = all_244_5 & op(e4, e1) = all_244_10 & % 183.30/28.79 | op(e4, e0) = all_244_17 & op(e3, e4) = all_244_1 & op(e3, e3) = % 183.30/28.79 | all_244_3 & op(e3, e2) = all_244_7 & op(e3, e1) = all_244_12 & op(e3, % 183.30/28.79 | e0) = all_244_19 & op(e2, e4) = all_244_4 & op(e2, e3) = all_244_6 % 183.30/28.79 | & op(e2, e2) = all_244_8 & op(e2, e1) = all_244_14 & op(e2, e0) = % 183.30/28.79 | all_244_21 & op(e1, e4) = all_244_9 & op(e1, e3) = all_244_11 & % 183.30/28.79 | op(e1, e2) = all_244_13 & op(e1, e1) = all_244_15 & op(e1, e0) = % 183.30/28.79 | all_244_23 & op(e0, e4) = all_244_16 & op(e0, e3) = all_244_18 & % 183.30/28.79 | op(e0, e2) = all_244_20 & op(e0, e1) = all_244_22 & op(e0, e0) = % 183.30/28.79 | all_244_24 & $i(all_244_0) & $i(all_244_1) & $i(all_244_2) & % 183.30/28.79 | $i(all_244_3) & $i(all_244_4) & $i(all_244_5) & $i(all_244_6) & % 183.30/28.79 | $i(all_244_7) & $i(all_244_8) & $i(all_244_9) & $i(all_244_10) & % 183.30/28.79 | $i(all_244_11) & $i(all_244_12) & $i(all_244_13) & $i(all_244_14) & % 183.30/28.79 | $i(all_244_15) & $i(all_244_16) & $i(all_244_17) & $i(all_244_18) & % 183.30/28.79 | $i(all_244_19) & $i(all_244_20) & $i(all_244_21) & $i(all_244_22) & % 183.30/28.79 | $i(all_244_23) & $i(all_244_24) % 183.30/28.79 | % 183.30/28.79 | ALPHA: (479) implies: % 183.30/28.79 | (480) op(e0, e0) = all_244_24 % 183.30/28.79 | (481) op(e0, e1) = all_244_22 % 183.30/28.79 | (482) op(e0, e2) = all_244_20 % 183.30/28.79 | (483) op(e0, e3) = all_244_18 % 183.30/28.79 | (484) op(e0, e4) = all_244_16 % 183.30/28.79 | (485) op(e1, e0) = all_244_23 % 183.30/28.79 | (486) op(e1, e1) = all_244_15 % 183.30/28.79 | (487) op(e1, e2) = all_244_13 % 183.30/28.79 | (488) op(e1, e3) = all_244_11 % 183.30/28.79 | (489) op(e1, e4) = all_244_9 % 183.30/28.80 | (490) op(e2, e0) = all_244_21 % 183.30/28.80 | (491) op(e2, e1) = all_244_14 % 183.30/28.80 | (492) op(e2, e2) = all_244_8 % 183.30/28.80 | (493) op(e2, e3) = all_244_6 % 183.30/28.80 | (494) op(e2, e4) = all_244_4 % 183.30/28.80 | (495) op(e3, e0) = all_244_19 % 183.30/28.80 | (496) op(e3, e1) = all_244_12 % 183.30/28.80 | (497) op(e3, e2) = all_244_7 % 183.30/28.80 | (498) op(e3, e3) = all_244_3 % 183.30/28.80 | (499) op(e3, e4) = all_244_1 % 183.30/28.80 | (500) op(e4, e0) = all_244_17 % 183.30/28.80 | (501) op(e4, e1) = all_244_10 % 183.30/28.80 | (502) op(e4, e2) = all_244_5 % 183.30/28.80 | (503) op(e4, e3) = all_244_2 % 183.30/28.80 | (504) op(e4, e4) = all_244_0 % 183.30/28.80 | (505) op(all_244_24, all_244_24) = e0 % 183.30/28.80 | (506) op(all_244_23, all_244_22) = e0 % 183.30/28.80 | (507) op(all_244_22, all_244_23) = e1 % 183.30/28.80 | (508) op(all_244_21, all_244_20) = e0 % 183.30/28.80 | (509) op(all_244_20, all_244_21) = e2 % 183.30/28.80 | (510) op(all_244_19, all_244_18) = e0 % 183.30/28.80 | (511) op(all_244_18, all_244_19) = e3 % 183.30/28.80 | (512) op(all_244_17, all_244_16) = e0 % 183.30/28.80 | (513) op(all_244_16, all_244_17) = e4 % 183.30/28.80 | (514) op(all_244_15, all_244_15) = e1 % 183.30/28.80 | (515) op(all_244_14, all_244_13) = e1 % 183.30/28.80 | (516) op(all_244_13, all_244_14) = e2 % 183.30/28.80 | (517) op(all_244_12, all_244_11) = e1 % 183.30/28.80 | (518) op(all_244_11, all_244_12) = e3 % 183.30/28.80 | (519) op(all_244_10, all_244_9) = e1 % 183.30/28.80 | (520) op(all_244_9, all_244_10) = e4 % 183.30/28.80 | (521) op(all_244_8, all_244_8) = e2 % 183.30/28.80 | (522) op(all_244_7, all_244_6) = e2 % 183.30/28.80 | (523) op(all_244_6, all_244_7) = e3 % 183.30/28.80 | (524) op(all_244_5, all_244_4) = e2 % 183.30/28.80 | (525) op(all_244_4, all_244_5) = e4 % 183.30/28.80 | (526) op(all_244_3, all_244_3) = e3 % 183.30/28.80 | (527) op(all_244_2, all_244_1) = e3 % 183.30/28.80 | (528) op(all_244_1, all_244_2) = e4 % 183.30/28.80 | (529) op(all_244_0, all_244_0) = e4 % 183.30/28.80 | % 183.30/28.80 | DELTA: instantiating (15) with fresh symbols all_246_0, all_246_1, all_246_2, % 183.30/28.80 | all_246_3, all_246_4, all_246_5, all_246_6, all_246_7, all_246_8, % 183.30/28.80 | all_246_9, all_246_10, all_246_11, all_246_12, all_246_13, all_246_14, % 183.30/28.80 | all_246_15, all_246_16, all_246_17, all_246_18, all_246_19, all_246_20, % 183.30/28.80 | all_246_21, all_246_22, all_246_23, all_246_24 gives: % 183.30/28.80 | (530) op(e4, all_246_0) = e4 & op(e4, all_246_1) = e3 & op(e4, all_246_2) = % 183.30/28.80 | e2 & op(e4, all_246_3) = e1 & op(e4, all_246_4) = e0 & op(e4, e4) = % 183.30/28.80 | all_246_0 & op(e4, e3) = all_246_1 & op(e4, e2) = all_246_2 & op(e4, % 183.30/28.80 | e1) = all_246_3 & op(e4, e0) = all_246_4 & op(e3, all_246_5) = e4 & % 183.30/28.80 | op(e3, all_246_6) = e3 & op(e3, all_246_7) = e2 & op(e3, all_246_8) = % 183.30/28.80 | e1 & op(e3, all_246_9) = e0 & op(e3, e4) = all_246_5 & op(e3, e3) = % 183.30/28.80 | all_246_6 & op(e3, e2) = all_246_7 & op(e3, e1) = all_246_8 & op(e3, % 183.30/28.80 | e0) = all_246_9 & op(e2, all_246_10) = e4 & op(e2, all_246_11) = e3 % 183.30/28.80 | & op(e2, all_246_12) = e2 & op(e2, all_246_13) = e1 & op(e2, % 183.30/28.80 | all_246_14) = e0 & op(e2, e4) = all_246_10 & op(e2, e3) = % 183.30/28.80 | all_246_11 & op(e2, e2) = all_246_12 & op(e2, e1) = all_246_13 & % 183.30/28.80 | op(e2, e0) = all_246_14 & op(e1, all_246_15) = e4 & op(e1, % 183.30/28.80 | all_246_16) = e3 & op(e1, all_246_17) = e2 & op(e1, all_246_18) = % 183.30/28.80 | e1 & op(e1, all_246_19) = e0 & op(e1, e4) = all_246_15 & op(e1, e3) = % 183.30/28.80 | all_246_16 & op(e1, e2) = all_246_17 & op(e1, e1) = all_246_18 & % 183.30/28.80 | op(e1, e0) = all_246_19 & op(e0, all_246_20) = e4 & op(e0, % 183.30/28.80 | all_246_21) = e3 & op(e0, all_246_22) = e2 & op(e0, all_246_23) = % 183.30/28.80 | e1 & op(e0, all_246_24) = e0 & op(e0, e4) = all_246_20 & op(e0, e3) = % 183.30/28.80 | all_246_21 & op(e0, e2) = all_246_22 & op(e0, e1) = all_246_23 & % 183.30/28.80 | op(e0, e0) = all_246_24 & $i(all_246_0) & $i(all_246_1) & % 183.30/28.80 | $i(all_246_2) & $i(all_246_3) & $i(all_246_4) & $i(all_246_5) & % 183.30/28.80 | $i(all_246_6) & $i(all_246_7) & $i(all_246_8) & $i(all_246_9) & % 183.30/28.80 | $i(all_246_10) & $i(all_246_11) & $i(all_246_12) & $i(all_246_13) & % 183.30/28.80 | $i(all_246_14) & $i(all_246_15) & $i(all_246_16) & $i(all_246_17) & % 183.30/28.80 | $i(all_246_18) & $i(all_246_19) & $i(all_246_20) & $i(all_246_21) & % 183.30/28.80 | $i(all_246_22) & $i(all_246_23) & $i(all_246_24) % 183.30/28.80 | % 183.30/28.80 | ALPHA: (530) implies: % 183.54/28.80 | (531) op(e0, e0) = all_246_24 % 183.54/28.80 | (532) op(e0, e1) = all_246_23 % 183.54/28.80 | (533) op(e0, e2) = all_246_22 % 183.54/28.80 | (534) op(e0, e3) = all_246_21 % 183.54/28.80 | (535) op(e0, e4) = all_246_20 % 183.54/28.80 | (536) op(e0, all_246_23) = e1 % 183.54/28.80 | (537) op(e0, all_246_22) = e2 % 183.54/28.80 | (538) op(e0, all_246_21) = e3 % 183.54/28.80 | (539) op(e0, all_246_20) = e4 % 183.54/28.80 | (540) op(e1, e0) = all_246_19 % 183.54/28.80 | (541) op(e1, e1) = all_246_18 % 183.54/28.80 | (542) op(e1, e2) = all_246_17 % 183.54/28.80 | (543) op(e1, e3) = all_246_16 % 183.54/28.80 | (544) op(e1, e4) = all_246_15 % 183.54/28.80 | (545) op(e1, all_246_19) = e0 % 183.54/28.80 | (546) op(e1, all_246_17) = e2 % 183.54/28.80 | (547) op(e1, all_246_16) = e3 % 183.54/28.80 | (548) op(e1, all_246_15) = e4 % 183.54/28.80 | (549) op(e2, e0) = all_246_14 % 183.54/28.80 | (550) op(e2, e1) = all_246_13 % 183.54/28.80 | (551) op(e2, e2) = all_246_12 % 183.54/28.80 | (552) op(e2, e3) = all_246_11 % 183.54/28.80 | (553) op(e2, e4) = all_246_10 % 183.54/28.80 | (554) op(e2, all_246_14) = e0 % 183.54/28.80 | (555) op(e2, all_246_13) = e1 % 183.54/28.80 | (556) op(e2, all_246_11) = e3 % 183.54/28.80 | (557) op(e2, all_246_10) = e4 % 183.54/28.80 | (558) op(e3, e0) = all_246_9 % 183.54/28.80 | (559) op(e3, e1) = all_246_8 % 183.54/28.80 | (560) op(e3, e2) = all_246_7 % 183.54/28.80 | (561) op(e3, e3) = all_246_6 % 183.54/28.80 | (562) op(e3, e4) = all_246_5 % 183.54/28.80 | (563) op(e3, all_246_9) = e0 % 183.54/28.80 | (564) op(e3, all_246_8) = e1 % 183.54/28.80 | (565) op(e3, all_246_7) = e2 % 183.54/28.80 | (566) op(e3, all_246_6) = e3 % 183.54/28.80 | (567) op(e3, all_246_5) = e4 % 183.54/28.80 | (568) op(e4, e0) = all_246_4 % 183.54/28.80 | (569) op(e4, e1) = all_246_3 % 183.54/28.80 | (570) op(e4, e2) = all_246_2 % 183.54/28.80 | (571) op(e4, e3) = all_246_1 % 183.54/28.80 | (572) op(e4, e4) = all_246_0 % 183.54/28.80 | (573) op(e4, all_246_4) = e0 % 183.54/28.80 | (574) op(e4, all_246_3) = e1 % 183.54/28.80 | (575) op(e4, all_246_2) = e2 % 183.54/28.80 | (576) op(e4, all_246_1) = e3 % 183.54/28.80 | % 183.54/28.80 | DELTA: instantiating (4) with fresh symbols all_248_0, all_248_1, all_248_2, % 183.54/28.80 | all_248_3, all_248_4, all_248_5, all_248_6, all_248_7, all_248_8, % 183.54/28.80 | all_248_9, all_248_10, all_248_11, all_248_12, all_248_13, all_248_14, % 183.54/28.80 | all_248_15, all_248_16, all_248_17, all_248_18, all_248_19, all_248_20, % 183.54/28.80 | all_248_21, all_248_22, all_248_23, all_248_24 gives: % 183.54/28.81 | (577) ~ (all_248_0 = all_248_1) & ~ (all_248_0 = all_248_2) & ~ % 183.54/28.81 | (all_248_0 = all_248_3) & ~ (all_248_0 = all_248_4) & ~ (all_248_0 % 183.54/28.81 | = all_248_5) & ~ (all_248_0 = all_248_10) & ~ (all_248_0 = % 183.54/28.81 | all_248_15) & ~ (all_248_0 = all_248_20) & ~ (all_248_1 = % 183.54/28.81 | all_248_2) & ~ (all_248_1 = all_248_3) & ~ (all_248_1 = % 183.54/28.81 | all_248_4) & ~ (all_248_1 = all_248_6) & ~ (all_248_1 = % 183.54/28.81 | all_248_11) & ~ (all_248_1 = all_248_16) & ~ (all_248_1 = % 183.54/28.81 | all_248_21) & ~ (all_248_2 = all_248_3) & ~ (all_248_2 = % 183.54/28.81 | all_248_4) & ~ (all_248_2 = all_248_7) & ~ (all_248_2 = % 183.54/28.81 | all_248_12) & ~ (all_248_2 = all_248_17) & ~ (all_248_2 = % 183.54/28.81 | all_248_22) & ~ (all_248_3 = all_248_4) & ~ (all_248_3 = % 183.54/28.81 | all_248_8) & ~ (all_248_3 = all_248_13) & ~ (all_248_3 = % 183.54/28.81 | all_248_18) & ~ (all_248_3 = all_248_23) & ~ (all_248_4 = % 183.54/28.81 | all_248_9) & ~ (all_248_4 = all_248_14) & ~ (all_248_4 = % 183.54/28.81 | all_248_19) & ~ (all_248_4 = all_248_24) & ~ (all_248_5 = % 183.54/28.81 | all_248_6) & ~ (all_248_5 = all_248_7) & ~ (all_248_5 = % 183.54/28.81 | all_248_8) & ~ (all_248_5 = all_248_9) & ~ (all_248_5 = % 183.54/28.81 | all_248_10) & ~ (all_248_5 = all_248_15) & ~ (all_248_5 = % 183.54/28.81 | all_248_20) & ~ (all_248_6 = all_248_7) & ~ (all_248_6 = % 183.54/28.81 | all_248_8) & ~ (all_248_6 = all_248_9) & ~ (all_248_6 = % 183.54/28.81 | all_248_11) & ~ (all_248_6 = all_248_16) & ~ (all_248_6 = % 183.54/28.81 | all_248_21) & ~ (all_248_7 = all_248_8) & ~ (all_248_7 = % 183.54/28.81 | all_248_9) & ~ (all_248_7 = all_248_12) & ~ (all_248_7 = % 183.54/28.81 | all_248_17) & ~ (all_248_7 = all_248_22) & ~ (all_248_8 = % 183.54/28.81 | all_248_9) & ~ (all_248_8 = all_248_13) & ~ (all_248_8 = % 183.54/28.81 | all_248_18) & ~ (all_248_8 = all_248_23) & ~ (all_248_9 = % 183.54/28.81 | all_248_14) & ~ (all_248_9 = all_248_19) & ~ (all_248_9 = % 183.54/28.81 | all_248_24) & ~ (all_248_10 = all_248_11) & ~ (all_248_10 = % 183.54/28.81 | all_248_12) & ~ (all_248_10 = all_248_13) & ~ (all_248_10 = % 183.54/28.81 | all_248_14) & ~ (all_248_10 = all_248_15) & ~ (all_248_10 = % 183.54/28.81 | all_248_20) & ~ (all_248_11 = all_248_12) & ~ (all_248_11 = % 183.54/28.81 | all_248_13) & ~ (all_248_11 = all_248_14) & ~ (all_248_11 = % 183.54/28.81 | all_248_16) & ~ (all_248_11 = all_248_21) & ~ (all_248_12 = % 183.54/28.81 | all_248_13) & ~ (all_248_12 = all_248_14) & ~ (all_248_12 = % 183.54/28.81 | all_248_17) & ~ (all_248_12 = all_248_22) & ~ (all_248_13 = % 183.54/28.81 | all_248_14) & ~ (all_248_13 = all_248_18) & ~ (all_248_13 = % 183.54/28.81 | all_248_23) & ~ (all_248_14 = all_248_19) & ~ (all_248_14 = % 183.54/28.81 | all_248_24) & ~ (all_248_15 = all_248_16) & ~ (all_248_15 = % 183.54/28.81 | all_248_17) & ~ (all_248_15 = all_248_18) & ~ (all_248_15 = % 183.54/28.81 | all_248_19) & ~ (all_248_15 = all_248_20) & ~ (all_248_16 = % 183.54/28.81 | all_248_17) & ~ (all_248_16 = all_248_18) & ~ (all_248_16 = % 183.54/28.81 | all_248_19) & ~ (all_248_16 = all_248_21) & ~ (all_248_17 = % 183.54/28.81 | all_248_18) & ~ (all_248_17 = all_248_19) & ~ (all_248_17 = % 183.54/28.81 | all_248_22) & ~ (all_248_18 = all_248_19) & ~ (all_248_18 = % 183.54/28.81 | all_248_23) & ~ (all_248_19 = all_248_24) & ~ (all_248_20 = % 183.54/28.81 | all_248_21) & ~ (all_248_20 = all_248_22) & ~ (all_248_20 = % 183.54/28.81 | all_248_23) & ~ (all_248_20 = all_248_24) & ~ (all_248_21 = % 183.54/28.81 | all_248_22) & ~ (all_248_21 = all_248_23) & ~ (all_248_21 = % 183.54/28.81 | all_248_24) & ~ (all_248_22 = all_248_23) & ~ (all_248_22 = % 183.54/28.81 | all_248_24) & ~ (all_248_23 = all_248_24) & op(e4, e4) = all_248_0 % 183.54/28.81 | & op(e4, e3) = all_248_5 & op(e4, e2) = all_248_10 & op(e4, e1) = % 183.54/28.81 | all_248_15 & op(e4, e0) = all_248_20 & op(e3, e4) = all_248_1 & % 183.54/28.81 | op(e3, e3) = all_248_6 & op(e3, e2) = all_248_11 & op(e3, e1) = % 183.54/28.81 | all_248_16 & op(e3, e0) = all_248_21 & op(e2, e4) = all_248_2 & % 183.54/28.81 | op(e2, e3) = all_248_7 & op(e2, e2) = all_248_12 & op(e2, e1) = % 183.54/28.81 | all_248_17 & op(e2, e0) = all_248_22 & op(e1, e4) = all_248_3 & % 183.54/28.81 | op(e1, e3) = all_248_8 & op(e1, e2) = all_248_13 & op(e1, e1) = % 183.54/28.81 | all_248_18 & op(e1, e0) = all_248_23 & op(e0, e4) = all_248_4 & % 183.54/28.81 | op(e0, e3) = all_248_9 & op(e0, e2) = all_248_14 & op(e0, e1) = % 183.54/28.81 | all_248_19 & op(e0, e0) = all_248_24 & $i(all_248_0) & $i(all_248_1) % 183.54/28.81 | & $i(all_248_2) & $i(all_248_3) & $i(all_248_4) & $i(all_248_5) & % 183.54/28.81 | $i(all_248_6) & $i(all_248_7) & $i(all_248_8) & $i(all_248_9) & % 183.54/28.81 | $i(all_248_10) & $i(all_248_11) & $i(all_248_12) & $i(all_248_13) & % 183.54/28.81 | $i(all_248_14) & $i(all_248_15) & $i(all_248_16) & $i(all_248_17) & % 183.54/28.81 | $i(all_248_18) & $i(all_248_19) & $i(all_248_20) & $i(all_248_21) & % 183.54/28.81 | $i(all_248_22) & $i(all_248_23) & $i(all_248_24) % 183.54/28.81 | % 183.54/28.81 | ALPHA: (577) implies: % 183.54/28.81 | (578) ~ (all_248_23 = all_248_24) % 183.54/28.81 | (579) ~ (all_248_22 = all_248_24) % 183.54/28.81 | (580) ~ (all_248_22 = all_248_23) % 183.54/28.81 | (581) ~ (all_248_21 = all_248_24) % 183.54/28.81 | (582) ~ (all_248_21 = all_248_23) % 183.54/28.81 | (583) ~ (all_248_21 = all_248_22) % 183.54/28.81 | (584) ~ (all_248_20 = all_248_24) % 183.54/28.81 | (585) ~ (all_248_20 = all_248_23) % 183.54/28.81 | (586) ~ (all_248_20 = all_248_22) % 183.54/28.81 | (587) ~ (all_248_20 = all_248_21) % 183.54/28.81 | (588) ~ (all_248_19 = all_248_24) % 183.54/28.81 | (589) ~ (all_248_18 = all_248_23) % 183.54/28.81 | (590) ~ (all_248_18 = all_248_19) % 183.54/28.81 | (591) ~ (all_248_17 = all_248_22) % 183.54/28.81 | (592) ~ (all_248_17 = all_248_19) % 183.54/28.81 | (593) ~ (all_248_17 = all_248_18) % 183.54/28.81 | (594) ~ (all_248_16 = all_248_21) % 183.54/28.81 | (595) ~ (all_248_16 = all_248_19) % 183.54/28.81 | (596) ~ (all_248_16 = all_248_18) % 183.54/28.81 | (597) ~ (all_248_16 = all_248_17) % 183.54/28.81 | (598) ~ (all_248_15 = all_248_20) % 183.54/28.81 | (599) ~ (all_248_15 = all_248_19) % 183.54/28.81 | (600) ~ (all_248_15 = all_248_18) % 183.54/28.81 | (601) ~ (all_248_15 = all_248_17) % 183.54/28.81 | (602) ~ (all_248_15 = all_248_16) % 183.54/28.81 | (603) ~ (all_248_14 = all_248_24) % 183.54/28.81 | (604) ~ (all_248_14 = all_248_19) % 183.54/28.81 | (605) ~ (all_248_13 = all_248_23) % 183.54/28.81 | (606) ~ (all_248_13 = all_248_18) % 183.54/28.81 | (607) ~ (all_248_13 = all_248_14) % 183.54/28.81 | (608) ~ (all_248_12 = all_248_17) % 183.54/28.81 | (609) ~ (all_248_12 = all_248_14) % 183.54/28.81 | (610) ~ (all_248_12 = all_248_13) % 183.54/28.81 | (611) ~ (all_248_11 = all_248_21) % 183.54/28.81 | (612) ~ (all_248_11 = all_248_16) % 183.54/28.81 | (613) ~ (all_248_11 = all_248_14) % 183.54/28.81 | (614) ~ (all_248_11 = all_248_13) % 183.54/28.81 | (615) ~ (all_248_11 = all_248_12) % 183.54/28.81 | (616) ~ (all_248_10 = all_248_20) % 183.54/28.81 | (617) ~ (all_248_10 = all_248_15) % 183.54/28.81 | (618) ~ (all_248_10 = all_248_14) % 183.54/28.81 | (619) ~ (all_248_10 = all_248_13) % 183.54/28.81 | (620) ~ (all_248_10 = all_248_12) % 183.54/28.81 | (621) ~ (all_248_10 = all_248_11) % 183.54/28.81 | (622) ~ (all_248_9 = all_248_24) % 183.54/28.81 | (623) ~ (all_248_9 = all_248_19) % 183.54/28.81 | (624) ~ (all_248_9 = all_248_14) % 183.54/28.81 | (625) ~ (all_248_8 = all_248_23) % 183.54/28.81 | (626) ~ (all_248_8 = all_248_18) % 183.54/28.81 | (627) ~ (all_248_8 = all_248_13) % 183.54/28.81 | (628) ~ (all_248_8 = all_248_9) % 183.54/28.81 | (629) ~ (all_248_7 = all_248_22) % 183.54/28.81 | (630) ~ (all_248_7 = all_248_17) % 183.54/28.81 | (631) ~ (all_248_7 = all_248_12) % 183.54/28.81 | (632) ~ (all_248_7 = all_248_9) % 183.54/28.81 | (633) ~ (all_248_7 = all_248_8) % 183.54/28.81 | (634) ~ (all_248_6 = all_248_21) % 183.54/28.81 | (635) ~ (all_248_6 = all_248_16) % 183.54/28.81 | (636) ~ (all_248_6 = all_248_11) % 183.54/28.81 | (637) ~ (all_248_6 = all_248_9) % 183.54/28.81 | (638) ~ (all_248_6 = all_248_8) % 183.54/28.81 | (639) ~ (all_248_6 = all_248_7) % 183.54/28.81 | (640) ~ (all_248_5 = all_248_20) % 183.54/28.81 | (641) ~ (all_248_5 = all_248_15) % 183.54/28.81 | (642) ~ (all_248_5 = all_248_10) % 183.54/28.81 | (643) ~ (all_248_5 = all_248_9) % 183.54/28.81 | (644) ~ (all_248_5 = all_248_8) % 183.54/28.81 | (645) ~ (all_248_5 = all_248_7) % 183.54/28.81 | (646) ~ (all_248_5 = all_248_6) % 183.54/28.81 | (647) ~ (all_248_4 = all_248_24) % 183.54/28.81 | (648) ~ (all_248_4 = all_248_19) % 183.54/28.81 | (649) ~ (all_248_4 = all_248_14) % 183.54/28.81 | (650) ~ (all_248_4 = all_248_9) % 183.54/28.81 | (651) ~ (all_248_3 = all_248_23) % 183.54/28.81 | (652) ~ (all_248_3 = all_248_18) % 183.54/28.81 | (653) ~ (all_248_3 = all_248_13) % 183.54/28.81 | (654) ~ (all_248_3 = all_248_8) % 183.54/28.81 | (655) ~ (all_248_3 = all_248_4) % 183.54/28.81 | (656) ~ (all_248_2 = all_248_22) % 183.54/28.81 | (657) ~ (all_248_2 = all_248_17) % 183.54/28.81 | (658) ~ (all_248_2 = all_248_7) % 183.54/28.81 | (659) ~ (all_248_2 = all_248_4) % 183.54/28.82 | (660) ~ (all_248_2 = all_248_3) % 183.54/28.82 | (661) ~ (all_248_1 = all_248_21) % 183.54/28.82 | (662) ~ (all_248_1 = all_248_16) % 183.54/28.82 | (663) ~ (all_248_1 = all_248_11) % 183.54/28.82 | (664) ~ (all_248_1 = all_248_6) % 183.54/28.82 | (665) ~ (all_248_1 = all_248_4) % 183.54/28.82 | (666) ~ (all_248_1 = all_248_3) % 183.54/28.82 | (667) ~ (all_248_1 = all_248_2) % 183.54/28.82 | (668) ~ (all_248_0 = all_248_20) % 183.54/28.82 | (669) ~ (all_248_0 = all_248_10) % 183.54/28.82 | (670) ~ (all_248_0 = all_248_5) % 183.54/28.82 | (671) ~ (all_248_0 = all_248_4) % 183.54/28.82 | (672) ~ (all_248_0 = all_248_3) % 183.54/28.82 | (673) ~ (all_248_0 = all_248_2) % 183.54/28.82 | (674) ~ (all_248_0 = all_248_1) % 183.54/28.82 | (675) op(e0, e0) = all_248_24 % 183.54/28.82 | (676) op(e0, e1) = all_248_19 % 183.54/28.82 | (677) op(e0, e2) = all_248_14 % 183.54/28.82 | (678) op(e0, e3) = all_248_9 % 183.54/28.82 | (679) op(e0, e4) = all_248_4 % 183.54/28.82 | (680) op(e1, e0) = all_248_23 % 183.54/28.82 | (681) op(e1, e1) = all_248_18 % 183.54/28.82 | (682) op(e1, e2) = all_248_13 % 183.54/28.82 | (683) op(e1, e3) = all_248_8 % 183.54/28.82 | (684) op(e1, e4) = all_248_3 % 183.54/28.82 | (685) op(e2, e0) = all_248_22 % 183.54/28.82 | (686) op(e2, e1) = all_248_17 % 183.54/28.82 | (687) op(e2, e2) = all_248_12 % 183.54/28.82 | (688) op(e2, e3) = all_248_7 % 183.54/28.82 | (689) op(e2, e4) = all_248_2 % 183.54/28.82 | (690) op(e3, e0) = all_248_21 % 183.54/28.82 | (691) op(e3, e1) = all_248_16 % 183.54/28.82 | (692) op(e3, e2) = all_248_11 % 183.54/28.82 | (693) op(e3, e3) = all_248_6 % 183.54/28.82 | (694) op(e3, e4) = all_248_1 % 183.54/28.82 | (695) op(e4, e0) = all_248_20 % 183.54/28.82 | (696) op(e4, e1) = all_248_15 % 183.54/28.82 | (697) op(e4, e2) = all_248_10 % 183.54/28.82 | (698) op(e4, e3) = all_248_5 % 183.54/28.82 | (699) op(e4, e4) = all_248_0 % 183.54/28.82 | % 183.54/28.82 | DELTA: instantiating (1) with fresh symbols all_250_0, all_250_1, all_250_2, % 183.54/28.82 | all_250_3, all_250_4, all_250_5, all_250_6, all_250_7, all_250_8, % 183.54/28.82 | all_250_9, all_250_10, all_250_11, all_250_12, all_250_13, all_250_14, % 183.54/28.82 | all_250_15, all_250_16, all_250_17, all_250_18, all_250_19, all_250_20, % 183.54/28.82 | all_250_21, all_250_22, all_250_23, all_250_24 gives: % 183.54/28.82 | (700) op(e4, e4) = all_250_0 & op(e4, e3) = all_250_1 & op(e4, e2) = % 183.54/28.82 | all_250_2 & op(e4, e1) = all_250_3 & op(e4, e0) = all_250_4 & op(e3, % 183.54/28.82 | e4) = all_250_5 & op(e3, e3) = all_250_6 & op(e3, e2) = all_250_7 & % 183.54/28.82 | op(e3, e1) = all_250_8 & op(e3, e0) = all_250_9 & op(e2, e4) = % 183.54/28.82 | all_250_10 & op(e2, e3) = all_250_11 & op(e2, e2) = all_250_12 & % 183.54/28.82 | op(e2, e1) = all_250_13 & op(e2, e0) = all_250_14 & op(e1, e4) = % 183.54/28.82 | all_250_15 & op(e1, e3) = all_250_16 & op(e1, e2) = all_250_17 & % 183.54/28.82 | op(e1, e1) = all_250_18 & op(e1, e0) = all_250_19 & op(e0, e4) = % 183.54/28.82 | all_250_20 & op(e0, e3) = all_250_21 & op(e0, e2) = all_250_22 & % 183.54/28.82 | op(e0, e1) = all_250_23 & op(e0, e0) = all_250_24 & $i(all_250_0) & % 183.54/28.82 | $i(all_250_1) & $i(all_250_2) & $i(all_250_3) & $i(all_250_4) & % 183.54/28.82 | $i(all_250_5) & $i(all_250_6) & $i(all_250_7) & $i(all_250_8) & % 183.54/28.82 | $i(all_250_9) & $i(all_250_10) & $i(all_250_11) & $i(all_250_12) & % 183.54/28.82 | $i(all_250_13) & $i(all_250_14) & $i(all_250_15) & $i(all_250_16) & % 183.54/28.82 | $i(all_250_17) & $i(all_250_18) & $i(all_250_19) & $i(all_250_20) & % 183.54/28.82 | $i(all_250_21) & $i(all_250_22) & $i(all_250_23) & $i(all_250_24) & % 183.54/28.82 | (all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 | % 183.54/28.82 | all_250_0 = e0) & (all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 % 183.54/28.82 | | all_250_1 = e1 | all_250_1 = e0) & (all_250_2 = e4 | all_250_2 = % 183.54/28.82 | e3 | all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0) & (all_250_3 % 183.54/28.82 | = e4 | all_250_3 = e3 | all_250_3 = e2 | all_250_3 = e1 | all_250_3 % 183.54/28.82 | = e0) & (all_250_4 = e4 | all_250_4 = e3 | all_250_4 = e2 | % 183.54/28.82 | all_250_4 = e1 | all_250_4 = e0) & (all_250_5 = e4 | all_250_5 = e3 % 183.54/28.82 | | all_250_5 = e2 | all_250_5 = e1 | all_250_5 = e0) & (all_250_6 = % 183.54/28.82 | e4 | all_250_6 = e3 | all_250_6 = e2 | all_250_6 = e1 | all_250_6 = % 183.54/28.82 | e0) & (all_250_7 = e4 | all_250_7 = e3 | all_250_7 = e2 | all_250_7 % 183.54/28.82 | = e1 | all_250_7 = e0) & (all_250_8 = e4 | all_250_8 = e3 | % 183.54/28.82 | all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0) & (all_250_9 = e4 % 183.54/28.82 | | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | all_250_9 = % 183.54/28.82 | e0) & (all_250_10 = e4 | all_250_10 = e3 | all_250_10 = e2 | % 183.54/28.82 | all_250_10 = e1 | all_250_10 = e0) & (all_250_11 = e4 | all_250_11 % 183.54/28.82 | = e3 | all_250_11 = e2 | all_250_11 = e1 | all_250_11 = e0) & % 183.54/28.82 | (all_250_12 = e4 | all_250_12 = e3 | all_250_12 = e2 | all_250_12 = % 183.54/28.82 | e1 | all_250_12 = e0) & (all_250_13 = e4 | all_250_13 = e3 | % 183.54/28.82 | all_250_13 = e2 | all_250_13 = e1 | all_250_13 = e0) & (all_250_14 % 183.54/28.82 | = e4 | all_250_14 = e3 | all_250_14 = e2 | all_250_14 = e1 | % 183.54/28.82 | all_250_14 = e0) & (all_250_15 = e4 | all_250_15 = e3 | all_250_15 % 183.54/28.82 | = e2 | all_250_15 = e1 | all_250_15 = e0) & (all_250_16 = e4 | % 183.54/28.82 | all_250_16 = e3 | all_250_16 = e2 | all_250_16 = e1 | all_250_16 = % 183.54/28.82 | e0) & (all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | % 183.54/28.82 | all_250_17 = e1 | all_250_17 = e0) & (all_250_18 = e4 | all_250_18 % 183.54/28.82 | = e3 | all_250_18 = e2 | all_250_18 = e1 | all_250_18 = e0) & % 183.54/28.82 | (all_250_19 = e4 | all_250_19 = e3 | all_250_19 = e2 | all_250_19 = % 183.54/28.82 | e1 | all_250_19 = e0) & (all_250_20 = e4 | all_250_20 = e3 | % 183.54/28.82 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0) & (all_250_21 % 183.54/28.82 | = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | % 183.54/28.82 | all_250_21 = e0) & (all_250_22 = e4 | all_250_22 = e3 | all_250_22 % 183.54/28.82 | = e2 | all_250_22 = e1 | all_250_22 = e0) & (all_250_23 = e4 | % 183.54/28.82 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 183.54/28.82 | e0) & (all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | % 183.54/28.82 | all_250_24 = e1 | all_250_24 = e0) % 183.54/28.82 | % 183.54/28.82 | ALPHA: (700) implies: % 183.54/28.82 | (701) op(e0, e0) = all_250_24 % 183.54/28.82 | (702) op(e0, e1) = all_250_23 % 183.54/28.82 | (703) op(e0, e2) = all_250_22 % 183.54/28.82 | (704) op(e0, e3) = all_250_21 % 183.54/28.82 | (705) op(e0, e4) = all_250_20 % 183.54/28.82 | (706) op(e1, e0) = all_250_19 % 183.54/28.82 | (707) op(e1, e1) = all_250_18 % 183.54/28.82 | (708) op(e1, e2) = all_250_17 % 183.54/28.82 | (709) op(e1, e3) = all_250_16 % 183.54/28.82 | (710) op(e1, e4) = all_250_15 % 183.54/28.82 | (711) op(e2, e0) = all_250_14 % 183.54/28.82 | (712) op(e2, e1) = all_250_13 % 183.54/28.82 | (713) op(e2, e2) = all_250_12 % 183.54/28.82 | (714) op(e2, e3) = all_250_11 % 183.54/28.82 | (715) op(e2, e4) = all_250_10 % 183.54/28.82 | (716) op(e3, e0) = all_250_9 % 183.54/28.82 | (717) op(e3, e1) = all_250_8 % 183.54/28.82 | (718) op(e3, e2) = all_250_7 % 183.54/28.82 | (719) op(e3, e3) = all_250_6 % 183.54/28.82 | (720) op(e3, e4) = all_250_5 % 183.54/28.82 | (721) op(e4, e0) = all_250_4 % 183.54/28.82 | (722) op(e4, e1) = all_250_3 % 183.54/28.82 | (723) op(e4, e2) = all_250_2 % 183.54/28.82 | (724) op(e4, e3) = all_250_1 % 183.54/28.82 | (725) op(e4, e4) = all_250_0 % 183.54/28.82 | (726) all_250_24 = e4 | all_250_24 = e3 | all_250_24 = e2 | all_250_24 = e1 % 183.54/28.82 | | all_250_24 = e0 % 183.54/28.82 | (727) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 % 183.54/28.82 | | all_250_23 = e0 % 183.54/28.82 | (728) all_250_22 = e4 | all_250_22 = e3 | all_250_22 = e2 | all_250_22 = e1 % 183.54/28.82 | | all_250_22 = e0 % 183.54/28.83 | (729) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 % 183.54/28.83 | | all_250_21 = e0 % 183.54/28.83 | (730) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 % 183.54/28.83 | | all_250_20 = e0 % 183.54/28.83 | (731) all_250_19 = e4 | all_250_19 = e3 | all_250_19 = e2 | all_250_19 = e1 % 183.54/28.83 | | all_250_19 = e0 % 183.54/28.83 | (732) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 % 183.54/28.83 | | all_250_17 = e0 % 183.54/28.83 | (733) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 % 183.54/28.83 | | all_250_15 = e0 % 183.54/28.83 | (734) all_250_14 = e4 | all_250_14 = e3 | all_250_14 = e2 | all_250_14 = e1 % 183.54/28.83 | | all_250_14 = e0 % 183.54/28.83 | (735) all_250_13 = e4 | all_250_13 = e3 | all_250_13 = e2 | all_250_13 = e1 % 183.54/28.83 | | all_250_13 = e0 % 183.54/28.83 | (736) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 % 183.54/28.83 | | all_250_11 = e0 % 183.54/28.83 | (737) all_250_10 = e4 | all_250_10 = e3 | all_250_10 = e2 | all_250_10 = e1 % 183.54/28.83 | | all_250_10 = e0 % 183.54/28.83 | (738) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | % 183.54/28.83 | all_250_9 = e0 % 183.54/28.83 | (739) all_250_8 = e4 | all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | % 183.54/28.83 | all_250_8 = e0 % 183.54/28.83 | (740) all_250_7 = e4 | all_250_7 = e3 | all_250_7 = e2 | all_250_7 = e1 | % 183.54/28.83 | all_250_7 = e0 % 183.54/28.83 | (741) all_250_6 = e4 | all_250_6 = e3 | all_250_6 = e2 | all_250_6 = e1 | % 183.54/28.83 | all_250_6 = e0 % 183.54/28.83 | (742) all_250_5 = e4 | all_250_5 = e3 | all_250_5 = e2 | all_250_5 = e1 | % 183.54/28.83 | all_250_5 = e0 % 183.54/28.83 | (743) all_250_4 = e4 | all_250_4 = e3 | all_250_4 = e2 | all_250_4 = e1 | % 183.54/28.83 | all_250_4 = e0 % 183.54/28.83 | (744) all_250_3 = e4 | all_250_3 = e3 | all_250_3 = e2 | all_250_3 = e1 | % 183.54/28.83 | all_250_3 = e0 % 183.54/28.83 | (745) all_250_2 = e4 | all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 | % 183.54/28.83 | all_250_2 = e0 % 183.54/28.83 | (746) all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 | % 183.54/28.83 | all_250_1 = e0 % 183.54/28.83 | (747) all_250_0 = e4 | all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 | % 183.54/28.83 | all_250_0 = e0 % 183.54/28.83 | % 183.54/28.83 | DELTA: instantiating (2) with fresh symbols all_252_0, all_252_1, all_252_2, % 183.54/28.83 | all_252_3, all_252_4, all_252_5, all_252_6, all_252_7, all_252_8, % 183.54/28.83 | all_252_9, all_252_10, all_252_11, all_252_12, all_252_13, all_252_14, % 183.54/28.83 | all_252_15, all_252_16, all_252_17, all_252_18, all_252_19, all_252_20, % 183.54/28.83 | all_252_21, all_252_22, all_252_23, all_252_24 gives: % 183.54/28.84 | (748) ((all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = % 183.54/28.84 | e4) | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & % 183.54/28.84 | op(e4, e1) = e4) | (all_252_16 = e4 & op(e4, e0) = e4)) & % 183.54/28.84 | ((all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = % 183.54/28.84 | e4) | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & % 183.54/28.84 | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4)) & % 183.54/28.84 | ((all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = % 183.54/28.84 | e3) | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & % 183.54/28.84 | op(e4, e1) = e3) | (all_252_16 = e3 & op(e4, e0) = e3)) & % 183.54/28.84 | ((all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = % 183.54/28.84 | e3) | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & % 183.54/28.84 | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3)) & % 183.54/28.84 | ((all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = % 183.54/28.84 | e2) | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & % 183.54/28.84 | op(e4, e1) = e2) | (all_252_16 = e2 & op(e4, e0) = e2)) & % 183.54/28.84 | ((all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = % 183.54/28.84 | e2) | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & % 183.54/28.84 | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2)) & % 183.54/28.84 | ((all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = % 183.54/28.84 | e1) | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & % 183.54/28.84 | op(e4, e1) = e1) | (all_252_16 = e1 & op(e4, e0) = e1)) & % 183.54/28.84 | ((all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = % 183.54/28.84 | e1) | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & % 183.54/28.84 | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1)) & % 183.54/28.84 | ((all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = % 183.54/28.84 | e0) | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & % 183.54/28.84 | op(e4, e1) = e0) | (all_252_16 = e0 & op(e4, e0) = e0)) & % 183.54/28.84 | ((all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = % 183.54/28.84 | e0) | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & % 183.54/28.84 | op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0)) & % 183.54/28.84 | ((all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = % 183.54/28.84 | e4) | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & % 183.54/28.84 | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4)) & % 183.54/28.84 | ((all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = % 183.54/28.84 | e3) | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & % 183.54/28.84 | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3)) & % 183.54/28.84 | ((all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = % 183.54/28.84 | e2) | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 183.54/28.84 | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2)) & % 183.54/28.84 | ((all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = % 183.54/28.84 | e1) | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & % 183.54/28.84 | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1)) & % 183.54/28.84 | ((all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = % 183.54/28.84 | e0) | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & % 183.54/28.84 | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0)) & % 183.54/28.84 | ((all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = % 183.54/28.84 | e4) | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & % 183.54/28.84 | op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4)) & % 183.54/28.84 | ((all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = % 183.54/28.84 | e3) | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & % 183.54/28.84 | op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3)) & % 183.54/28.84 | ((all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = % 183.54/28.84 | e2) | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & % 183.54/28.84 | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2)) & % 183.54/28.84 | ((all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = % 183.54/28.84 | e1) | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & % 183.54/28.84 | op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1)) & % 183.54/28.84 | ((all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = % 183.54/28.84 | e0) | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & % 183.54/28.84 | op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0)) & % 183.54/28.84 | ((all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = % 183.54/28.84 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & % 183.54/28.84 | op(e1, e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4)) & % 183.54/28.84 | ((all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = % 183.54/28.84 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & % 183.54/28.84 | op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3)) & % 183.54/28.84 | ((all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = % 183.54/28.84 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & % 183.54/28.84 | op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2)) & % 183.54/28.84 | ((all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = % 183.54/28.84 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & % 183.54/28.84 | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1)) & % 183.54/28.84 | ((all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = % 183.54/28.84 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & % 183.54/28.84 | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0)) & % 183.54/28.84 | ((all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = % 183.54/28.84 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & % 183.54/28.84 | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4)) & % 183.54/28.84 | ((all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = % 183.54/28.84 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & % 183.54/28.84 | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3)) & % 183.54/28.84 | ((all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = % 183.54/28.84 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & % 183.54/28.84 | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2)) & % 183.54/28.84 | ((all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = % 183.54/28.84 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & % 183.54/28.84 | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1)) & % 183.54/28.84 | ((all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = % 183.54/28.84 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & % 183.54/28.84 | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0)) & % 183.54/28.84 | ((all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = % 183.54/28.84 | e4) | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & % 183.54/28.84 | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4)) & % 183.54/28.84 | ((all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = % 183.54/28.84 | e3) | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 183.54/28.84 | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3)) & % 183.54/28.84 | ((all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 183.54/28.84 | e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & % 183.54/28.84 | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2)) & % 183.54/28.84 | ((all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = % 183.54/28.84 | e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & % 183.54/28.84 | op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1)) & % 183.54/28.84 | ((all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = % 183.54/28.84 | e0) | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & % 183.54/28.84 | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)) & % 183.54/28.84 | ((all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) % 183.54/28.84 | = e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & % 183.54/28.84 | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4)) & % 183.54/28.84 | ((all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) % 183.54/28.84 | = e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & % 183.54/28.84 | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3)) & % 183.54/28.84 | ((all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 183.54/28.84 | = e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & % 183.54/28.84 | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2)) & % 183.54/28.84 | ((all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 183.54/28.84 | = e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & % 183.54/28.84 | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1)) & % 183.54/28.84 | ((all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) % 183.54/28.84 | = e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & % 183.54/28.84 | op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 183.54/28.84 | ((all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) % 183.54/28.84 | = e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & % 183.54/28.84 | op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)) & % 183.54/28.84 | ((all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) % 183.54/28.84 | = e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & % 183.54/28.84 | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)) & % 183.54/28.84 | ((all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) % 183.54/28.84 | = e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & % 183.54/28.84 | op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)) & % 183.54/28.84 | ((all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) % 183.54/28.84 | = e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & % 183.54/28.84 | op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)) & % 183.54/28.84 | ((all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) % 183.54/28.84 | = e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & % 183.54/28.84 | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4)) & % 183.54/28.84 | ((all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) % 183.54/28.84 | = e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & % 183.54/28.84 | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3)) & % 183.54/28.84 | ((all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) % 183.54/28.84 | = e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & % 183.54/28.84 | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2)) & % 183.54/28.84 | ((all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 183.54/28.84 | = e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & % 183.54/28.84 | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1)) & % 183.54/28.84 | ((all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, % 183.54/28.84 | e0) = e0) | (all_252_17 = e0 & op(e3, e0) = e0) | % 183.54/28.84 | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 183.54/28.84 | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) | % 183.54/28.84 | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, % 183.54/28.84 | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)))) % 183.54/28.84 | % 183.54/28.84 | ALPHA: (748) implies: % 183.54/28.84 | (749) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) % 183.54/28.84 | = e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 % 183.54/28.84 | & op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 183.54/28.84 | ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, % 183.54/28.84 | e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 183.54/28.84 | = e0 & op(e0, e1) = e0))) % 183.54/28.84 | (750) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 183.54/28.84 | e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & % 183.54/28.84 | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 183.54/28.84 | (751) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 183.54/28.84 | e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & % 183.54/28.84 | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 183.54/28.84 | (752) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 183.54/28.84 | e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & % 183.54/28.84 | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 183.54/28.85 | (753) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = % 183.54/28.85 | e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & % 183.54/28.85 | op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 183.54/28.85 | (754) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 183.54/28.85 | e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & % 183.54/28.85 | op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 183.54/28.85 | (755) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = e2 & op(e3, e0) = % 183.54/28.85 | e2) | (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & % 183.54/28.85 | op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 183.54/28.85 | (756) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 183.54/28.85 | e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & % 183.54/28.85 | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 183.54/28.85 | (757) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 = e4 & op(e3, e0) = % 183.54/28.85 | e4) | (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 = e4 & % 183.54/28.85 | op(e1, e0) = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 183.54/28.85 | (758) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 183.54/28.85 | e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & % 183.54/28.85 | op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 183.54/28.85 | (759) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 183.54/28.85 | e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & % 183.54/28.85 | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 183.54/28.85 | (760) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 183.54/28.85 | e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & % 183.54/28.85 | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 183.54/28.85 | (761) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 183.54/28.85 | e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & % 183.54/28.85 | op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 183.54/28.85 | (762) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 = e4 & op(e1, e3) = % 183.54/28.85 | e4) | (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 = e4 & % 183.54/28.85 | op(e1, e1) = e4) | (all_252_19 = e4 & op(e1, e0) = e4) % 183.54/28.85 | (763) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = % 183.54/28.85 | e0) | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & % 183.54/28.85 | op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 183.54/28.85 | (764) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = % 183.54/28.85 | e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & % 183.54/28.85 | op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 183.54/28.85 | (765) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 183.54/28.85 | e2) | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & % 183.54/28.85 | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 183.54/28.85 | (766) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = % 183.54/28.85 | e3) | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 183.54/28.85 | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 183.54/28.85 | (767) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = % 183.54/28.85 | e4) | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & % 183.54/28.85 | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 183.54/28.85 | (768) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = % 183.54/28.85 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & % 183.54/28.85 | op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) % 183.54/28.85 | (769) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = % 183.54/28.85 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & % 183.54/28.85 | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 183.54/28.85 | (770) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = % 183.54/28.85 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & % 183.54/28.85 | op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 183.54/28.85 | (771) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = % 183.54/28.85 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & % 183.54/28.85 | op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, e0) = e3) % 183.54/28.85 | (772) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = % 183.54/28.85 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & % 183.54/28.85 | op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 183.75/28.85 | (773) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = % 183.75/28.85 | e0) | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & % 183.75/28.85 | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 183.75/28.85 | (774) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = % 183.75/28.85 | e1) | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & % 183.75/28.85 | op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 183.75/28.85 | (775) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = % 183.75/28.85 | e2) | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & % 183.75/28.85 | op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 183.75/28.86 | (776) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = % 183.75/28.86 | e3) | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & % 183.75/28.86 | op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 183.75/28.86 | (777) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = % 183.75/28.86 | e4) | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & % 183.75/28.86 | op(e1, e2) = e4) | (all_252_22 = e4 & op(e0, e2) = e4) % 183.75/28.86 | (778) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = % 183.75/28.86 | e0) | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & % 183.75/28.86 | op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0) % 183.75/28.86 | (779) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = % 183.75/28.86 | e1) | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & % 183.75/28.86 | op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 183.75/28.86 | (780) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = % 183.75/28.86 | e2) | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & % 183.75/28.86 | op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2) % 183.75/28.86 | (781) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = % 183.75/28.86 | e3) | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & % 183.75/28.86 | op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 183.75/28.86 | (782) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = % 183.75/28.86 | e4) | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & % 183.75/28.86 | op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 183.75/28.86 | (783) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = % 183.75/28.86 | e0) | (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & % 183.75/28.86 | op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) % 183.75/28.86 | (784) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = % 183.75/28.86 | e1) | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & % 183.75/28.86 | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 183.75/28.86 | (785) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = % 183.75/28.86 | e2) | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 183.75/28.86 | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 183.75/28.86 | (786) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = % 183.75/28.86 | e3) | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & % 183.75/28.86 | op(e1, e3) = e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 183.75/28.86 | (787) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = % 183.75/28.86 | e4) | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & % 183.75/28.86 | op(e1, e3) = e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 183.75/28.86 | (788) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = % 183.75/28.86 | e0) | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & % 183.75/28.86 | op(e1, e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 183.75/28.86 | (789) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = % 183.75/28.86 | e0) | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, % 183.75/28.86 | e1) = e0) | (all_252_16 = e0 & op(e4, e0) = e0) % 183.75/28.86 | (790) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = % 183.75/28.86 | e1) | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & % 183.75/28.86 | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 183.75/28.86 | (791) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = % 183.75/28.86 | e1) | (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, % 183.75/28.86 | e1) = e1) | (all_252_16 = e1 & op(e4, e0) = e1) % 183.75/28.86 | (792) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = % 183.75/28.86 | e2) | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & % 183.75/28.86 | op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2) % 183.75/28.86 | (793) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = % 183.75/28.86 | e2) | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, % 183.75/28.86 | e1) = e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 183.75/28.86 | (794) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = % 183.75/28.86 | e3) | (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & % 183.75/28.86 | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 183.75/28.86 | (795) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = % 183.75/28.86 | e3) | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, % 183.75/28.86 | e1) = e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 183.75/28.86 | (796) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = % 183.75/28.86 | e4) | (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & % 183.75/28.86 | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4) % 183.75/28.86 | (797) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = % 183.75/28.86 | e4) | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, % 183.75/28.86 | e1) = e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 183.75/28.86 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_248_24, all_250_24, e0, % 183.75/28.87 | e0, simplifying with (675), (701) gives: % 183.75/28.87 | (798) all_250_24 = all_248_24 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_246_24, all_250_24, e0, % 183.75/28.87 | e0, simplifying with (531), (701) gives: % 183.75/28.87 | (799) all_250_24 = all_246_24 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_24, all_250_24, e0, % 183.75/28.87 | e0, simplifying with (480), (701) gives: % 183.75/28.87 | (800) all_250_24 = all_244_24 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_58_2, all_60_2, e1, e0, % 183.75/28.87 | simplifying with (218), (221) gives: % 183.75/28.87 | (801) all_60_2 = all_58_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_60_2, e1, e0, % 183.75/28.87 | simplifying with (161), (221) gives: % 183.75/28.87 | (802) all_60_2 = all_20_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_92_2, all_244_22, e1, % 183.75/28.87 | e0, simplifying with (268), (481) gives: % 183.75/28.87 | (803) all_244_22 = all_92_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_60_2, all_244_22, e1, % 183.75/28.87 | e0, simplifying with (221), (481) gives: % 183.75/28.87 | (804) all_244_22 = all_60_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_22, all_246_23, e1, % 183.75/28.87 | e0, simplifying with (481), (532) gives: % 183.75/28.87 | (805) all_246_23 = all_244_22 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_22, all_248_19, e1, % 183.75/28.87 | e0, simplifying with (481), (676) gives: % 183.75/28.87 | (806) all_248_19 = all_244_22 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_230_2, all_248_19, e1, % 183.75/28.87 | e0, simplifying with (459), (676) gives: % 183.75/28.87 | (807) all_248_19 = all_230_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_246_23, all_250_23, e1, % 183.75/28.87 | e0, simplifying with (532), (702) gives: % 183.75/28.87 | (808) all_250_23 = all_246_23 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_250_23, e1, % 183.75/28.87 | e0, simplifying with (179), (702) gives: % 183.75/28.87 | (809) all_250_23 = all_32_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_162_2, all_206_2, e2, % 183.75/28.87 | e0, simplifying with (367), (427) gives: % 183.75/28.87 | (810) all_206_2 = all_162_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_158_2, all_206_2, e2, % 183.75/28.87 | e0, simplifying with (361), (427) gives: % 183.75/28.87 | (811) all_206_2 = all_158_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_108_2, all_206_2, e2, % 183.75/28.87 | e0, simplifying with (291), (427) gives: % 183.75/28.87 | (812) all_206_2 = all_108_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_162_2, all_244_20, e2, % 183.75/28.87 | e0, simplifying with (367), (482) gives: % 183.75/28.87 | (813) all_244_20 = all_162_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_246_22, all_248_14, e2, % 183.75/28.87 | e0, simplifying with (533), (677) gives: % 183.75/28.87 | (814) all_248_14 = all_246_22 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_20, all_248_14, e2, % 183.75/28.87 | e0, simplifying with (482), (677) gives: % 183.75/28.87 | (815) all_248_14 = all_244_20 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_248_14, e2, % 183.75/28.87 | e0, simplifying with (173), (677) gives: % 183.75/28.87 | (816) all_248_14 = all_28_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_158_2, all_250_22, e2, % 183.75/28.87 | e0, simplifying with (361), (703) gives: % 183.75/28.87 | (817) all_250_22 = all_158_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_82_2, all_250_22, e2, % 183.75/28.87 | e0, simplifying with (254), (703) gives: % 183.75/28.87 | (818) all_250_22 = all_82_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_68_2, all_72_2, e3, e0, % 183.75/28.87 | simplifying with (233), (239) gives: % 183.75/28.87 | (819) all_72_2 = all_68_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_18, all_246_21, e3, % 183.75/28.87 | e0, simplifying with (483), (534) gives: % 183.75/28.87 | (820) all_246_21 = all_244_18 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_104_2, all_246_21, e3, % 183.75/28.87 | e0, simplifying with (286), (534) gives: % 183.75/28.87 | (821) all_246_21 = all_104_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_246_21, all_248_9, e3, % 183.75/28.87 | e0, simplifying with (534), (678) gives: % 183.75/28.87 | (822) all_248_9 = all_246_21 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_248_9, e3, e0, % 183.75/28.87 | simplifying with (164), (678) gives: % 183.75/28.87 | (823) all_248_9 = all_22_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_118_2, all_250_21, e3, % 183.75/28.87 | e0, simplifying with (305), (704) gives: % 183.75/28.87 | (824) all_250_21 = all_118_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_104_2, all_250_21, e3, % 183.75/28.87 | e0, simplifying with (286), (704) gives: % 183.75/28.87 | (825) all_250_21 = all_104_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_90_2, all_250_21, e3, % 183.75/28.87 | e0, simplifying with (265), (704) gives: % 183.75/28.87 | (826) all_250_21 = all_90_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_72_2, all_250_21, e3, % 183.75/28.87 | e0, simplifying with (239), (704) gives: % 183.75/28.87 | (827) all_250_21 = all_72_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_210_2, e4, e0, % 183.75/28.87 | simplifying with (149), (433) gives: % 183.75/28.87 | (828) all_210_2 = all_12_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_212_2, e4, e0, % 183.75/28.87 | simplifying with (194), (436) gives: % 183.75/28.87 | (829) all_212_2 = all_42_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_212_2, all_244_16, e4, % 183.75/28.87 | e0, simplifying with (436), (484) gives: % 183.75/28.87 | (830) all_244_16 = all_212_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_16, all_246_20, e4, % 183.75/28.87 | e0, simplifying with (484), (535) gives: % 183.75/28.87 | (831) all_246_20 = all_244_16 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_246_20, all_248_4, e4, % 183.75/28.87 | e0, simplifying with (535), (679) gives: % 183.75/28.87 | (832) all_248_4 = all_246_20 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_248_4, e4, e0, % 183.75/28.87 | simplifying with (152), (679) gives: % 183.75/28.87 | (833) all_248_4 = all_14_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_210_2, all_250_20, e4, % 183.75/28.87 | e0, simplifying with (433), (705) gives: % 183.75/28.87 | (834) all_250_20 = all_210_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_250_20, e4, % 183.75/28.87 | e0, simplifying with (194), (705) gives: % 183.75/28.87 | (835) all_250_20 = all_42_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_250_20, e4, % 183.75/28.87 | e0, simplifying with (158), (705) gives: % 183.75/28.87 | (836) all_250_20 = all_18_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_164_2, all_198_2, e0, % 183.75/28.87 | e1, simplifying with (370), (417) gives: % 183.75/28.87 | (837) all_198_2 = all_164_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_96_2, all_198_2, e0, e1, % 183.75/28.87 | simplifying with (274), (417) gives: % 183.75/28.87 | (838) all_198_2 = all_96_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_198_2, all_232_2, e0, % 183.75/28.87 | e1, simplifying with (417), (462) gives: % 183.75/28.87 | (839) all_232_2 = all_198_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_110_2, all_232_2, e0, % 183.75/28.87 | e1, simplifying with (294), (462) gives: % 183.75/28.87 | (840) all_232_2 = all_110_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_164_2, all_244_23, e0, % 183.75/28.87 | e1, simplifying with (370), (485) gives: % 183.75/28.87 | (841) all_244_23 = all_164_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_23, all_246_19, e0, % 183.75/28.87 | e1, simplifying with (485), (540) gives: % 183.75/28.87 | (842) all_246_19 = all_244_23 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_246_19, all_248_23, e0, % 183.75/28.87 | e1, simplifying with (540), (680) gives: % 183.75/28.87 | (843) all_248_23 = all_246_19 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_248_23, all_250_19, e0, % 183.75/28.87 | e1, simplifying with (680), (706) gives: % 183.75/28.87 | (844) all_250_19 = all_248_23 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_250_19, e0, % 183.75/28.87 | e1, simplifying with (182), (706) gives: % 183.75/28.87 | (845) all_250_19 = all_34_2 % 183.75/28.87 | % 183.75/28.87 | GROUND_INST: instantiating (function-axioms) with all_244_15, all_248_18, e1, % 183.75/28.87 | e1, simplifying with (486), (681) gives: % 183.75/28.88 | (846) all_248_18 = all_244_15 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_248_18, all_250_18, e1, % 183.75/28.88 | e1, simplifying with (681), (707) gives: % 183.75/28.88 | (847) all_250_18 = all_248_18 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_246_18, all_250_18, e1, % 183.75/28.88 | e1, simplifying with (541), (707) gives: % 183.75/28.88 | (848) all_250_18 = all_246_18 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_150_2, all_180_2, e2, % 183.75/28.88 | e1, simplifying with (349), (392) gives: % 183.75/28.88 | (849) all_180_2 = all_150_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_180_2, all_192_2, e2, % 183.75/28.88 | e1, simplifying with (392), (409) gives: % 183.75/28.88 | (850) all_192_2 = all_180_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_160_2, all_246_17, e2, % 183.75/28.88 | e1, simplifying with (364), (542) gives: % 183.75/28.88 | (851) all_246_17 = all_160_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_246_17, all_248_13, e2, % 183.75/28.88 | e1, simplifying with (542), (682) gives: % 183.75/28.88 | (852) all_248_13 = all_246_17 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_13, all_248_13, e2, % 183.75/28.88 | e1, simplifying with (487), (682) gives: % 183.75/28.88 | (853) all_248_13 = all_244_13 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_150_2, all_248_13, e2, % 183.75/28.88 | e1, simplifying with (349), (682) gives: % 183.75/28.88 | (854) all_248_13 = all_150_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_248_13, e2, % 183.75/28.88 | e1, simplifying with (206), (682) gives: % 183.75/28.88 | (855) all_248_13 = all_50_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_192_2, all_250_17, e2, % 183.75/28.88 | e1, simplifying with (409), (708) gives: % 183.75/28.88 | (856) all_250_17 = all_192_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_250_17, e2, e1, % 183.75/28.88 | simplifying with (137), (708) gives: % 183.75/28.88 | (857) all_250_17 = all_4_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_112_2, all_130_2, e3, % 183.75/28.88 | e1, simplifying with (297), (322) gives: % 183.75/28.88 | (858) all_130_2 = all_112_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_70_2, all_130_2, e3, e1, % 183.75/28.88 | simplifying with (236), (322) gives: % 183.75/28.88 | (859) all_130_2 = all_70_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_62_2, all_130_2, e3, e1, % 183.75/28.88 | simplifying with (224), (322) gives: % 183.75/28.88 | (860) all_130_2 = all_62_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_130_2, all_166_2, e3, % 183.75/28.88 | e1, simplifying with (322), (372) gives: % 183.75/28.88 | (861) all_166_2 = all_130_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_166_2, all_246_16, e3, % 183.75/28.88 | e1, simplifying with (372), (543) gives: % 183.75/28.88 | (862) all_246_16 = all_166_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_114_2, all_246_16, e3, % 183.75/28.88 | e1, simplifying with (300), (543) gives: % 183.75/28.88 | (863) all_246_16 = all_114_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_248_8, all_250_16, e3, % 183.75/28.88 | e1, simplifying with (683), (709) gives: % 183.75/28.88 | (864) all_250_16 = all_248_8 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_246_16, all_250_16, e3, % 183.75/28.88 | e1, simplifying with (543), (709) gives: % 183.75/28.88 | (865) all_250_16 = all_246_16 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_11, all_250_16, e3, % 183.75/28.88 | e1, simplifying with (488), (709) gives: % 183.75/28.88 | (866) all_250_16 = all_244_11 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_152_2, e4, e1, % 183.75/28.88 | simplifying with (155), (352) gives: % 183.75/28.88 | (867) all_152_2 = all_16_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_170_2, all_246_15, e4, % 183.75/28.88 | e1, simplifying with (378), (544) gives: % 183.75/28.88 | (868) all_246_15 = all_170_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_246_15, all_248_3, e4, % 183.75/28.88 | e1, simplifying with (544), (684) gives: % 183.75/28.88 | (869) all_248_3 = all_246_15 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_66_2, all_248_3, e4, e1, % 183.75/28.88 | simplifying with (230), (684) gives: % 183.75/28.88 | (870) all_248_3 = all_66_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_9, all_250_15, e4, % 183.75/28.88 | e1, simplifying with (489), (710) gives: % 183.75/28.88 | (871) all_250_15 = all_244_9 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_170_2, all_250_15, e4, % 183.75/28.88 | e1, simplifying with (378), (710) gives: % 183.75/28.88 | (872) all_250_15 = all_170_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_152_2, all_250_15, e4, % 183.75/28.88 | e1, simplifying with (352), (710) gives: % 183.75/28.88 | (873) all_250_15 = all_152_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_144_2, all_250_15, e4, % 183.75/28.88 | e1, simplifying with (342), (710) gives: % 183.75/28.88 | (874) all_250_15 = all_144_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_250_15, e4, % 183.75/28.88 | e1, simplifying with (167), (710) gives: % 183.75/28.88 | (875) all_250_15 = all_24_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_76_2, all_116_2, e0, e2, % 183.75/28.88 | simplifying with (245), (303) gives: % 183.75/28.88 | (876) all_116_2 = all_76_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_116_2, all_174_2, e0, % 183.75/28.88 | e2, simplifying with (303), (384) gives: % 183.75/28.88 | (877) all_174_2 = all_116_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_174_2, all_178_2, e0, % 183.75/28.88 | e2, simplifying with (384), (390) gives: % 183.75/28.88 | (878) all_178_2 = all_174_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_116_2, all_244_21, e0, % 183.75/28.88 | e2, simplifying with (303), (490) gives: % 183.75/28.88 | (879) all_244_21 = all_116_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_21, all_246_14, e0, % 183.75/28.88 | e2, simplifying with (490), (549) gives: % 183.75/28.88 | (880) all_246_14 = all_244_21 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_246_14, e0, % 183.75/28.88 | e2, simplifying with (191), (549) gives: % 183.75/28.88 | (881) all_246_14 = all_40_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_178_2, all_248_22, e0, % 183.75/28.88 | e2, simplifying with (390), (685) gives: % 183.75/28.88 | (882) all_248_22 = all_178_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_248_22, all_250_14, e0, % 183.75/28.88 | e2, simplifying with (685), (711) gives: % 183.75/28.88 | (883) all_250_14 = all_248_22 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_86_2, all_250_14, e0, % 183.75/28.88 | e2, simplifying with (260), (711) gives: % 183.75/28.88 | (884) all_250_14 = all_86_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_190_2, all_242_2, e1, % 183.75/28.88 | e2, simplifying with (406), (477) gives: % 183.75/28.88 | (885) all_242_2 = all_190_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_188_2, all_242_2, e1, % 183.75/28.88 | e2, simplifying with (403), (477) gives: % 183.75/28.88 | (886) all_242_2 = all_188_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_242_2, e1, e2, % 183.75/28.88 | simplifying with (188), (477) gives: % 183.75/28.88 | (887) all_242_2 = all_38_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_188_2, all_244_14, e1, % 183.75/28.88 | e2, simplifying with (403), (491) gives: % 183.75/28.88 | (888) all_244_14 = all_188_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_14, all_246_13, e1, % 183.75/28.88 | e2, simplifying with (491), (550) gives: % 183.75/28.88 | (889) all_246_13 = all_244_14 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_246_13, all_248_17, e1, % 183.75/28.88 | e2, simplifying with (550), (686) gives: % 183.75/28.88 | (890) all_248_17 = all_246_13 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_94_2, all_248_17, e1, % 183.75/28.88 | e2, simplifying with (271), (686) gives: % 183.75/28.88 | (891) all_248_17 = all_94_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_14, all_250_13, e1, % 183.75/28.88 | e2, simplifying with (491), (712) gives: % 183.75/28.88 | (892) all_250_13 = all_244_14 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_106_2, all_250_13, e1, % 183.75/28.88 | e2, simplifying with (289), (712) gives: % 183.75/28.88 | (893) all_250_13 = all_106_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_246_12, all_248_12, e2, % 183.75/28.88 | e2, simplifying with (551), (687) gives: % 183.75/28.88 | (894) all_248_12 = all_246_12 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_248_12, all_250_12, e2, % 183.75/28.88 | e2, simplifying with (687), (713) gives: % 183.75/28.88 | (895) all_250_12 = all_248_12 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_244_8, all_250_12, e2, % 183.75/28.88 | e2, simplifying with (492), (713) gives: % 183.75/28.88 | (896) all_250_12 = all_244_8 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_124_2, e3, e2, % 183.75/28.88 | simplifying with (146), (314) gives: % 183.75/28.88 | (897) all_124_2 = all_10_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_124_2, all_172_2, e3, % 183.75/28.88 | e2, simplifying with (314), (381) gives: % 183.75/28.88 | (898) all_172_2 = all_124_2 % 183.75/28.88 | % 183.75/28.88 | GROUND_INST: instantiating (function-axioms) with all_102_2, all_172_2, e3, % 183.75/28.88 | e2, simplifying with (283), (381) gives: % 183.75/28.88 | (899) all_172_2 = all_102_2 % 183.75/28.88 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_124_2, all_244_6, e3, % 183.75/28.89 | e2, simplifying with (314), (493) gives: % 183.75/28.89 | (900) all_244_6 = all_124_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_78_2, all_244_6, e3, e2, % 183.75/28.89 | simplifying with (248), (493) gives: % 183.75/28.89 | (901) all_244_6 = all_78_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_172_2, all_248_7, e3, % 183.75/28.89 | e2, simplifying with (381), (688) gives: % 183.75/28.89 | (902) all_248_7 = all_172_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_138_2, all_248_7, e3, % 183.75/28.89 | e2, simplifying with (334), (688) gives: % 183.75/28.89 | (903) all_248_7 = all_138_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_248_7, all_250_11, e3, % 183.75/28.89 | e2, simplifying with (688), (714) gives: % 183.75/28.89 | (904) all_250_11 = all_248_7 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_11, all_250_11, e3, % 183.75/28.89 | e2, simplifying with (552), (714) gives: % 183.75/28.89 | (905) all_250_11 = all_246_11 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_120_2, all_148_2, e4, % 183.75/28.89 | e2, simplifying with (308), (347) gives: % 183.75/28.89 | (906) all_148_2 = all_120_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_64_2, all_148_2, e4, e2, % 183.75/28.89 | simplifying with (227), (347) gives: % 183.75/28.89 | (907) all_148_2 = all_64_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_134_2, all_244_4, e4, % 183.75/28.89 | e2, simplifying with (328), (494) gives: % 183.75/28.89 | (908) all_244_4 = all_134_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_10, all_248_2, e4, % 183.75/28.89 | e2, simplifying with (553), (689) gives: % 183.75/28.89 | (909) all_248_2 = all_246_10 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_244_4, all_248_2, e4, % 183.75/28.89 | e2, simplifying with (494), (689) gives: % 183.75/28.89 | (910) all_248_2 = all_244_4 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_224_2, all_248_2, e4, % 183.75/28.89 | e2, simplifying with (451), (689) gives: % 183.75/28.89 | (911) all_248_2 = all_224_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_148_2, all_248_2, e4, % 183.75/28.89 | e2, simplifying with (347), (689) gives: % 183.75/28.89 | (912) all_248_2 = all_148_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_10, all_250_10, e4, % 183.75/28.89 | e2, simplifying with (553), (715) gives: % 183.75/28.89 | (913) all_250_10 = all_246_10 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_186_2, all_250_10, e4, % 183.75/28.89 | e2, simplifying with (401), (715) gives: % 183.75/28.89 | (914) all_250_10 = all_186_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_226_2, all_228_2, e0, % 183.75/28.89 | e3, simplifying with (454), (456) gives: % 183.75/28.89 | (915) all_228_2 = all_226_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_226_2, all_244_19, e0, % 183.75/28.89 | e3, simplifying with (454), (495) gives: % 183.75/28.89 | (916) all_244_19 = all_226_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_200_2, all_244_19, e0, % 183.75/28.89 | e3, simplifying with (420), (495) gives: % 183.75/28.89 | (917) all_244_19 = all_200_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_126_2, all_244_19, e0, % 183.75/28.89 | e3, simplifying with (317), (495) gives: % 183.75/28.89 | (918) all_244_19 = all_126_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_228_2, all_248_21, e0, % 183.75/28.89 | e3, simplifying with (456), (690) gives: % 183.75/28.89 | (919) all_248_21 = all_228_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_248_21, e0, % 183.75/28.89 | e3, simplifying with (203), (690) gives: % 183.75/28.89 | (920) all_248_21 = all_48_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_9, all_250_9, e0, % 183.75/28.89 | e3, simplifying with (558), (716) gives: % 183.75/28.89 | (921) all_250_9 = all_246_9 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_244_19, all_250_9, e0, % 183.75/28.89 | e3, simplifying with (495), (716) gives: % 183.75/28.89 | (922) all_250_9 = all_244_19 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_240_2, all_250_9, e0, % 183.75/28.89 | e3, simplifying with (474), (716) gives: % 183.75/28.89 | (923) all_250_9 = all_240_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_74_2, e1, e3, % 183.75/28.89 | simplifying with (209), (242) gives: % 183.75/28.89 | (924) all_74_2 = all_52_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_122_2, e1, e3, % 183.75/28.89 | simplifying with (209), (311) gives: % 183.75/28.89 | (925) all_122_2 = all_52_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_122_2, all_204_2, e1, % 183.75/28.89 | e3, simplifying with (311), (425) gives: % 183.75/28.89 | (926) all_204_2 = all_122_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_74_2, all_244_12, e1, % 183.75/28.89 | e3, simplifying with (242), (496) gives: % 183.75/28.89 | (927) all_244_12 = all_74_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_204_2, all_246_8, e1, % 183.75/28.89 | e3, simplifying with (425), (559) gives: % 183.75/28.89 | (928) all_246_8 = all_204_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_8, all_248_16, e1, % 183.75/28.89 | e3, simplifying with (559), (691) gives: % 183.75/28.89 | (929) all_248_16 = all_246_8 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_248_16, e1, % 183.75/28.89 | e3, simplifying with (200), (691) gives: % 183.75/28.89 | (930) all_248_16 = all_46_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_244_12, all_250_8, e1, % 183.75/28.89 | e3, simplifying with (496), (717) gives: % 183.75/28.89 | (931) all_250_8 = all_244_12 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_250_8, e1, e3, % 183.75/28.89 | simplifying with (185), (717) gives: % 183.75/28.89 | (932) all_250_8 = all_36_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_154_2, all_156_2, e2, % 183.75/28.89 | e3, simplifying with (355), (358) gives: % 183.75/28.89 | (933) all_156_2 = all_154_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_234_2, all_244_7, e2, % 183.75/28.89 | e3, simplifying with (465), (497) gives: % 183.75/28.89 | (934) all_244_7 = all_234_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_154_2, all_244_7, e2, % 183.75/28.89 | e3, simplifying with (355), (497) gives: % 183.75/28.89 | (935) all_244_7 = all_154_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_56_2, all_244_7, e2, e3, % 183.75/28.89 | simplifying with (215), (497) gives: % 183.75/28.89 | (936) all_244_7 = all_56_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_248_11, e2, e3, % 183.75/28.89 | simplifying with (143), (692) gives: % 183.75/28.89 | (937) all_248_11 = all_8_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_248_11, all_250_7, e2, % 183.75/28.89 | e3, simplifying with (692), (718) gives: % 183.75/28.89 | (938) all_250_7 = all_248_11 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_7, all_250_7, e2, % 183.75/28.89 | e3, simplifying with (560), (718) gives: % 183.75/28.89 | (939) all_250_7 = all_246_7 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_220_2, all_250_7, e2, % 183.75/28.89 | e3, simplifying with (446), (718) gives: % 183.75/28.89 | (940) all_250_7 = all_220_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_156_2, all_250_7, e2, % 183.75/28.89 | e3, simplifying with (358), (718) gives: % 183.75/28.89 | (941) all_250_7 = all_156_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_6, all_248_6, e3, % 183.75/28.89 | e3, simplifying with (561), (693) gives: % 183.75/28.89 | (942) all_248_6 = all_246_6 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_248_6, all_250_6, e3, % 183.75/28.89 | e3, simplifying with (693), (719) gives: % 183.75/28.89 | (943) all_250_6 = all_248_6 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_244_3, all_250_6, e3, % 183.75/28.89 | e3, simplifying with (498), (719) gives: % 183.75/28.89 | (944) all_250_6 = all_244_3 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_146_2, all_208_2, e4, % 183.75/28.89 | e3, simplifying with (345), (430) gives: % 183.75/28.89 | (945) all_208_2 = all_146_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_136_2, all_208_2, e4, % 183.75/28.89 | e3, simplifying with (331), (430) gives: % 183.75/28.89 | (946) all_208_2 = all_136_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_208_2, all_244_1, e4, % 183.75/28.89 | e3, simplifying with (430), (499) gives: % 183.75/28.89 | (947) all_244_1 = all_208_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_168_2, all_244_1, e4, % 183.75/28.89 | e3, simplifying with (375), (499) gives: % 183.75/28.89 | (948) all_244_1 = all_168_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_246_5, all_248_1, e4, % 183.75/28.89 | e3, simplifying with (562), (694) gives: % 183.75/28.89 | (949) all_248_1 = all_246_5 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_208_2, all_248_1, e4, % 183.75/28.89 | e3, simplifying with (430), (694) gives: % 183.75/28.89 | (950) all_248_1 = all_208_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_176_2, all_248_1, e4, % 183.75/28.89 | e3, simplifying with (387), (694) gives: % 183.75/28.89 | (951) all_248_1 = all_176_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_244_1, all_250_5, e4, % 183.75/28.89 | e3, simplifying with (499), (720) gives: % 183.75/28.89 | (952) all_250_5 = all_244_1 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_100_2, all_250_5, e4, % 183.75/28.89 | e3, simplifying with (280), (720) gives: % 183.75/28.89 | (953) all_250_5 = all_100_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_128_2, all_132_2, e0, % 183.75/28.89 | e4, simplifying with (319), (325) gives: % 183.75/28.89 | (954) all_132_2 = all_128_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_132_2, all_236_2, e0, % 183.75/28.89 | e4, simplifying with (325), (468) gives: % 183.75/28.89 | (955) all_236_2 = all_132_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_236_2, all_238_2, e0, % 183.75/28.89 | e4, simplifying with (468), (471) gives: % 183.75/28.89 | (956) all_238_2 = all_236_2 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_244_17, all_246_4, e0, % 183.75/28.89 | e4, simplifying with (500), (568) gives: % 183.75/28.89 | (957) all_246_4 = all_244_17 % 183.75/28.89 | % 183.75/28.89 | GROUND_INST: instantiating (function-axioms) with all_128_2, all_246_4, e0, % 183.75/28.89 | e4, simplifying with (319), (568) gives: % 183.75/28.89 | (958) all_246_4 = all_128_2 % 183.75/28.89 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_54_2, all_246_4, e0, e4, % 183.75/28.90 | simplifying with (212), (568) gives: % 183.75/28.90 | (959) all_246_4 = all_54_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_238_2, all_248_20, e0, % 183.75/28.90 | e4, simplifying with (471), (695) gives: % 183.75/28.90 | (960) all_248_20 = all_238_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_248_20, all_250_4, e0, % 183.75/28.90 | e4, simplifying with (695), (721) gives: % 183.75/28.90 | (961) all_250_4 = all_248_20 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_250_4, e0, e4, % 183.75/28.90 | simplifying with (176), (721) gives: % 183.75/28.90 | (962) all_250_4 = all_30_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_202_2, e1, e4, % 183.75/28.90 | simplifying with (170), (423) gives: % 183.75/28.90 | (963) all_202_2 = all_26_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_202_2, all_222_2, e1, % 183.75/28.90 | e4, simplifying with (423), (449) gives: % 183.75/28.90 | (964) all_222_2 = all_202_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_88_2, all_222_2, e1, e4, % 183.75/28.90 | simplifying with (262), (449) gives: % 183.75/28.90 | (965) all_222_2 = all_88_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_222_2, e1, e4, % 183.75/28.90 | simplifying with (197), (449) gives: % 183.75/28.90 | (966) all_222_2 = all_44_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_244_10, all_246_3, e1, % 183.75/28.90 | e4, simplifying with (501), (569) gives: % 183.75/28.90 | (967) all_246_3 = all_244_10 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_222_2, all_246_3, e1, % 183.75/28.90 | e4, simplifying with (449), (569) gives: % 183.75/28.90 | (968) all_246_3 = all_222_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_246_3, all_248_15, e1, % 183.75/28.90 | e4, simplifying with (569), (696) gives: % 183.75/28.90 | (969) all_248_15 = all_246_3 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_248_15, all_250_3, e1, % 183.75/28.90 | e4, simplifying with (696), (722) gives: % 183.75/28.90 | (970) all_250_3 = all_248_15 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_216_2, all_250_3, e1, % 183.75/28.90 | e4, simplifying with (442), (722) gives: % 183.75/28.90 | (971) all_250_3 = all_216_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_214_2, e2, e4, % 183.75/28.90 | simplifying with (140), (439) gives: % 183.75/28.90 | (972) all_214_2 = all_6_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_246_2, all_248_10, e2, % 183.75/28.90 | e4, simplifying with (570), (697) gives: % 183.75/28.90 | (973) all_248_10 = all_246_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_244_5, all_248_10, e2, % 183.75/28.90 | e4, simplifying with (502), (697) gives: % 183.75/28.90 | (974) all_248_10 = all_244_5 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_214_2, all_248_10, e2, % 183.75/28.90 | e4, simplifying with (439), (697) gives: % 183.75/28.90 | (975) all_248_10 = all_214_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_196_2, all_248_10, e2, % 183.75/28.90 | e4, simplifying with (414), (697) gives: % 183.75/28.90 | (976) all_248_10 = all_196_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_80_2, all_248_10, e2, % 183.75/28.90 | e4, simplifying with (251), (697) gives: % 183.75/28.90 | (977) all_248_10 = all_80_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_218_2, all_250_2, e2, % 183.75/28.90 | e4, simplifying with (444), (723) gives: % 183.75/28.90 | (978) all_250_2 = all_218_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_214_2, all_250_2, e2, % 183.75/28.90 | e4, simplifying with (439), (723) gives: % 183.75/28.90 | (979) all_250_2 = all_214_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_194_2, all_250_2, e2, % 183.75/28.90 | e4, simplifying with (412), (723) gives: % 183.75/28.90 | (980) all_250_2 = all_194_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_98_2, all_140_2, e3, e4, % 183.75/28.90 | simplifying with (277), (337) gives: % 183.75/28.90 | (981) all_140_2 = all_98_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_140_2, all_182_2, e3, % 183.75/28.90 | e4, simplifying with (337), (395) gives: % 183.75/28.90 | (982) all_182_2 = all_140_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_184_2, all_244_2, e3, % 183.75/28.90 | e4, simplifying with (398), (503) gives: % 183.75/28.90 | (983) all_244_2 = all_184_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_182_2, all_244_2, e3, % 183.75/28.90 | e4, simplifying with (395), (503) gives: % 183.75/28.90 | (984) all_244_2 = all_182_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_182_2, all_246_1, e3, % 183.75/28.90 | e4, simplifying with (395), (571) gives: % 183.75/28.90 | (985) all_246_1 = all_182_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_246_1, all_248_5, e3, % 183.75/28.90 | e4, simplifying with (571), (698) gives: % 183.75/28.90 | (986) all_248_5 = all_246_1 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_142_2, all_248_5, e3, % 183.75/28.90 | e4, simplifying with (339), (698) gives: % 183.75/28.90 | (987) all_248_5 = all_142_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_244_2, all_250_1, e3, % 183.75/28.90 | e4, simplifying with (503), (724) gives: % 183.75/28.90 | (988) all_250_1 = all_244_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_84_2, all_250_1, e3, e4, % 183.75/28.90 | simplifying with (257), (724) gives: % 183.75/28.90 | (989) all_250_1 = all_84_2 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_246_0, all_248_0, e4, % 183.75/28.90 | e4, simplifying with (572), (699) gives: % 183.75/28.90 | (990) all_248_0 = all_246_0 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_248_0, all_250_0, e4, % 183.75/28.90 | e4, simplifying with (699), (725) gives: % 183.75/28.90 | (991) all_250_0 = all_248_0 % 183.75/28.90 | % 183.75/28.90 | GROUND_INST: instantiating (function-axioms) with all_244_0, all_250_0, e4, % 183.75/28.90 | e4, simplifying with (504), (725) gives: % 183.75/28.90 | (992) all_250_0 = all_244_0 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (991), (992) imply: % 183.75/28.90 | (993) all_248_0 = all_244_0 % 183.75/28.90 | % 183.75/28.90 | SIMP: (993) implies: % 183.75/28.90 | (994) all_248_0 = all_244_0 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (988), (989) imply: % 183.75/28.90 | (995) all_244_2 = all_84_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (995) implies: % 183.75/28.90 | (996) all_244_2 = all_84_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (978), (979) imply: % 183.75/28.90 | (997) all_218_2 = all_214_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (978), (980) imply: % 183.75/28.90 | (998) all_218_2 = all_194_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (970), (971) imply: % 183.75/28.90 | (999) all_248_15 = all_216_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (999) implies: % 183.75/28.90 | (1000) all_248_15 = all_216_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (961), (962) imply: % 183.75/28.90 | (1001) all_248_20 = all_30_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1001) implies: % 183.75/28.90 | (1002) all_248_20 = all_30_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (952), (953) imply: % 183.75/28.90 | (1003) all_244_1 = all_100_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1003) implies: % 183.75/28.90 | (1004) all_244_1 = all_100_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (943), (944) imply: % 183.75/28.90 | (1005) all_248_6 = all_244_3 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1005) implies: % 183.75/28.90 | (1006) all_248_6 = all_244_3 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (938), (939) imply: % 183.75/28.90 | (1007) all_248_11 = all_246_7 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1007) implies: % 183.75/28.90 | (1008) all_248_11 = all_246_7 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (939), (941) imply: % 183.75/28.90 | (1009) all_246_7 = all_156_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (939), (940) imply: % 183.75/28.90 | (1010) all_246_7 = all_220_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (931), (932) imply: % 183.75/28.90 | (1011) all_244_12 = all_36_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1011) implies: % 183.75/28.90 | (1012) all_244_12 = all_36_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (921), (923) imply: % 183.75/28.90 | (1013) all_246_9 = all_240_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (921), (922) imply: % 183.75/28.90 | (1014) all_246_9 = all_244_19 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (913), (914) imply: % 183.75/28.90 | (1015) all_246_10 = all_186_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1015) implies: % 183.75/28.90 | (1016) all_246_10 = all_186_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (904), (905) imply: % 183.75/28.90 | (1017) all_248_7 = all_246_11 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1017) implies: % 183.75/28.90 | (1018) all_248_7 = all_246_11 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (895), (896) imply: % 183.75/28.90 | (1019) all_248_12 = all_244_8 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1019) implies: % 183.75/28.90 | (1020) all_248_12 = all_244_8 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (892), (893) imply: % 183.75/28.90 | (1021) all_244_14 = all_106_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1021) implies: % 183.75/28.90 | (1022) all_244_14 = all_106_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (883), (884) imply: % 183.75/28.90 | (1023) all_248_22 = all_86_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1023) implies: % 183.75/28.90 | (1024) all_248_22 = all_86_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (871), (873) imply: % 183.75/28.90 | (1025) all_244_9 = all_152_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (871), (872) imply: % 183.75/28.90 | (1026) all_244_9 = all_170_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (871), (874) imply: % 183.75/28.90 | (1027) all_244_9 = all_144_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (871), (875) imply: % 183.75/28.90 | (1028) all_244_9 = all_24_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (864), (866) imply: % 183.75/28.90 | (1029) all_248_8 = all_244_11 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (864), (865) imply: % 183.75/28.90 | (1030) all_248_8 = all_246_16 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (856), (857) imply: % 183.75/28.90 | (1031) all_192_2 = all_4_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1031) implies: % 183.75/28.90 | (1032) all_192_2 = all_4_2 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (847), (848) imply: % 183.75/28.90 | (1033) all_248_18 = all_246_18 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1033) implies: % 183.75/28.90 | (1034) all_248_18 = all_246_18 % 183.75/28.90 | % 183.75/28.90 | COMBINE_EQS: (844), (845) imply: % 183.75/28.90 | (1035) all_248_23 = all_34_2 % 183.75/28.90 | % 183.75/28.90 | SIMP: (1035) implies: % 183.75/28.91 | (1036) all_248_23 = all_34_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (835), (836) imply: % 183.75/28.91 | (1037) all_42_2 = all_18_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1037) implies: % 183.75/28.91 | (1038) all_42_2 = all_18_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (834), (836) imply: % 183.75/28.91 | (1039) all_210_2 = all_18_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1039) implies: % 183.75/28.91 | (1040) all_210_2 = all_18_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (824), (827) imply: % 183.75/28.91 | (1041) all_118_2 = all_72_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (824), (826) imply: % 183.75/28.91 | (1042) all_118_2 = all_90_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (824), (825) imply: % 183.75/28.91 | (1043) all_118_2 = all_104_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (817), (818) imply: % 183.75/28.91 | (1044) all_158_2 = all_82_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1044) implies: % 183.75/28.91 | (1045) all_158_2 = all_82_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (808), (809) imply: % 183.75/28.91 | (1046) all_246_23 = all_32_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1046) implies: % 183.75/28.91 | (1047) all_246_23 = all_32_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (798), (800) imply: % 183.75/28.91 | (1048) all_248_24 = all_244_24 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (798), (799) imply: % 183.75/28.91 | (1049) all_248_24 = all_246_24 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (990), (994) imply: % 183.75/28.91 | (1050) all_246_0 = all_244_0 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1050) implies: % 183.75/28.91 | (1051) all_246_0 = all_244_0 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (949), (950) imply: % 183.75/28.91 | (1052) all_246_5 = all_208_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (949), (951) imply: % 183.75/28.91 | (1053) all_246_5 = all_176_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (910), (911) imply: % 183.75/28.91 | (1054) all_244_4 = all_224_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1054) implies: % 183.75/28.91 | (1055) all_244_4 = all_224_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (909), (911) imply: % 183.75/28.91 | (1056) all_246_10 = all_224_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1056) implies: % 183.75/28.91 | (1057) all_246_10 = all_224_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (911), (912) imply: % 183.75/28.91 | (1058) all_224_2 = all_148_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (869), (870) imply: % 183.75/28.91 | (1059) all_246_15 = all_66_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1059) implies: % 183.75/28.91 | (1060) all_246_15 = all_66_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (832), (833) imply: % 183.75/28.91 | (1061) all_246_20 = all_14_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1061) implies: % 183.75/28.91 | (1062) all_246_20 = all_14_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (986), (987) imply: % 183.75/28.91 | (1063) all_246_1 = all_142_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1063) implies: % 183.75/28.91 | (1064) all_246_1 = all_142_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (942), (1006) imply: % 183.75/28.91 | (1065) all_246_6 = all_244_3 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1065) implies: % 183.75/28.91 | (1066) all_246_6 = all_244_3 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (903), (1018) imply: % 183.75/28.91 | (1067) all_246_11 = all_138_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (902), (1018) imply: % 183.75/28.91 | (1068) all_246_11 = all_172_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1029), (1030) imply: % 183.75/28.91 | (1069) all_246_16 = all_244_11 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1069) implies: % 183.75/28.91 | (1070) all_246_16 = all_244_11 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (822), (823) imply: % 183.75/28.91 | (1071) all_246_21 = all_22_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1071) implies: % 183.75/28.91 | (1072) all_246_21 = all_22_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (973), (975) imply: % 183.75/28.91 | (1073) all_246_2 = all_214_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (973), (976) imply: % 183.75/28.91 | (1074) all_246_2 = all_196_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (973), (977) imply: % 183.75/28.91 | (1075) all_246_2 = all_80_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (973), (974) imply: % 183.75/28.91 | (1076) all_246_2 = all_244_5 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (937), (1008) imply: % 183.75/28.91 | (1077) all_246_7 = all_8_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1077) implies: % 183.75/28.91 | (1078) all_246_7 = all_8_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (894), (1020) imply: % 183.75/28.91 | (1079) all_246_12 = all_244_8 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1079) implies: % 183.75/28.91 | (1080) all_246_12 = all_244_8 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (852), (853) imply: % 183.75/28.91 | (1081) all_246_17 = all_244_13 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1081) implies: % 183.75/28.91 | (1082) all_246_17 = all_244_13 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (853), (854) imply: % 183.75/28.91 | (1083) all_244_13 = all_150_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (853), (855) imply: % 183.75/28.91 | (1084) all_244_13 = all_50_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (814), (815) imply: % 183.75/28.91 | (1085) all_246_22 = all_244_20 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (814), (816) imply: % 183.75/28.91 | (1086) all_246_22 = all_28_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (969), (1000) imply: % 183.75/28.91 | (1087) all_246_3 = all_216_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1087) implies: % 183.75/28.91 | (1088) all_246_3 = all_216_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (929), (930) imply: % 183.75/28.91 | (1089) all_246_8 = all_46_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1089) implies: % 183.75/28.91 | (1090) all_246_8 = all_46_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (890), (891) imply: % 183.75/28.91 | (1091) all_246_13 = all_94_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1091) implies: % 183.75/28.91 | (1092) all_246_13 = all_94_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (846), (1034) imply: % 183.75/28.91 | (1093) all_246_18 = all_244_15 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (806), (807) imply: % 183.75/28.91 | (1094) all_244_22 = all_230_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1094) implies: % 183.75/28.91 | (1095) all_244_22 = all_230_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (960), (1002) imply: % 183.75/28.91 | (1096) all_238_2 = all_30_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1096) implies: % 183.75/28.91 | (1097) all_238_2 = all_30_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (919), (920) imply: % 183.75/28.91 | (1098) all_228_2 = all_48_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1098) implies: % 183.75/28.91 | (1099) all_228_2 = all_48_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (882), (1024) imply: % 183.75/28.91 | (1100) all_178_2 = all_86_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1100) implies: % 183.75/28.91 | (1101) all_178_2 = all_86_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (843), (1036) imply: % 183.75/28.91 | (1102) all_246_19 = all_34_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1102) implies: % 183.75/28.91 | (1103) all_246_19 = all_34_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1048), (1049) imply: % 183.75/28.91 | (1104) all_246_24 = all_244_24 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (985), (1064) imply: % 183.75/28.91 | (1105) all_182_2 = all_142_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1105) implies: % 183.75/28.91 | (1106) all_182_2 = all_142_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1073), (1076) imply: % 183.75/28.91 | (1107) all_244_5 = all_214_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1074), (1076) imply: % 183.75/28.91 | (1108) all_244_5 = all_196_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1075), (1076) imply: % 183.75/28.91 | (1109) all_244_5 = all_80_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (967), (968) imply: % 183.75/28.91 | (1110) all_244_10 = all_222_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (967), (1088) imply: % 183.75/28.91 | (1111) all_244_10 = all_216_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (957), (958) imply: % 183.75/28.91 | (1112) all_244_17 = all_128_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (957), (959) imply: % 183.75/28.91 | (1113) all_244_17 = all_54_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1052), (1053) imply: % 183.75/28.91 | (1114) all_208_2 = all_176_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1114) implies: % 183.75/28.91 | (1115) all_208_2 = all_176_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1010), (1078) imply: % 183.75/28.91 | (1116) all_220_2 = all_8_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1009), (1010) imply: % 183.75/28.91 | (1117) all_220_2 = all_156_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (928), (1090) imply: % 183.75/28.91 | (1118) all_204_2 = all_46_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1118) implies: % 183.75/28.91 | (1119) all_204_2 = all_46_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1013), (1014) imply: % 183.75/28.91 | (1120) all_244_19 = all_240_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1120) implies: % 183.75/28.91 | (1121) all_244_19 = all_240_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1016), (1057) imply: % 183.75/28.91 | (1122) all_224_2 = all_186_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1122) implies: % 183.75/28.91 | (1123) all_224_2 = all_186_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1067), (1068) imply: % 183.75/28.91 | (1124) all_172_2 = all_138_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1124) implies: % 183.75/28.91 | (1125) all_172_2 = all_138_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (889), (1092) imply: % 183.75/28.91 | (1126) all_244_14 = all_94_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1126) implies: % 183.75/28.91 | (1127) all_244_14 = all_94_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (880), (881) imply: % 183.75/28.91 | (1128) all_244_21 = all_40_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1128) implies: % 183.75/28.91 | (1129) all_244_21 = all_40_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (868), (1060) imply: % 183.75/28.91 | (1130) all_170_2 = all_66_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1130) implies: % 183.75/28.91 | (1131) all_170_2 = all_66_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (862), (1070) imply: % 183.75/28.91 | (1132) all_244_11 = all_166_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (863), (1070) imply: % 183.75/28.91 | (1133) all_244_11 = all_114_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (851), (1082) imply: % 183.75/28.91 | (1134) all_244_13 = all_160_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1134) implies: % 183.75/28.91 | (1135) all_244_13 = all_160_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (842), (1103) imply: % 183.75/28.91 | (1136) all_244_23 = all_34_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1136) implies: % 183.75/28.91 | (1137) all_244_23 = all_34_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (831), (1062) imply: % 183.75/28.91 | (1138) all_244_16 = all_14_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1138) implies: % 183.75/28.91 | (1139) all_244_16 = all_14_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (820), (1072) imply: % 183.75/28.91 | (1140) all_244_18 = all_22_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (820), (821) imply: % 183.75/28.91 | (1141) all_244_18 = all_104_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1085), (1086) imply: % 183.75/28.91 | (1142) all_244_20 = all_28_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1142) implies: % 183.75/28.91 | (1143) all_244_20 = all_28_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (805), (1047) imply: % 183.75/28.91 | (1144) all_244_22 = all_32_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1144) implies: % 183.75/28.91 | (1145) all_244_22 = all_32_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (947), (948) imply: % 183.75/28.91 | (1146) all_208_2 = all_168_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1146) implies: % 183.75/28.91 | (1147) all_208_2 = all_168_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (948), (1004) imply: % 183.75/28.91 | (1148) all_168_2 = all_100_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (983), (996) imply: % 183.75/28.91 | (1149) all_184_2 = all_84_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (983), (984) imply: % 183.75/28.91 | (1150) all_184_2 = all_182_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (908), (1055) imply: % 183.75/28.91 | (1151) all_224_2 = all_134_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1151) implies: % 183.75/28.91 | (1152) all_224_2 = all_134_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1108), (1109) imply: % 183.75/28.91 | (1153) all_196_2 = all_80_2 % 183.75/28.91 | % 183.75/28.91 | COMBINE_EQS: (1107), (1108) imply: % 183.75/28.91 | (1154) all_214_2 = all_196_2 % 183.75/28.91 | % 183.75/28.91 | SIMP: (1154) implies: % 183.75/28.92 | (1155) all_214_2 = all_196_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (900), (901) imply: % 183.75/28.92 | (1156) all_124_2 = all_78_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1156) implies: % 183.75/28.92 | (1157) all_124_2 = all_78_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (934), (936) imply: % 183.75/28.92 | (1158) all_234_2 = all_56_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (934), (935) imply: % 183.75/28.92 | (1159) all_234_2 = all_154_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1027), (1028) imply: % 183.75/28.92 | (1160) all_144_2 = all_24_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1026), (1027) imply: % 183.75/28.92 | (1161) all_170_2 = all_144_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1161) implies: % 183.75/28.92 | (1162) all_170_2 = all_144_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1025), (1027) imply: % 183.75/28.92 | (1163) all_152_2 = all_144_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1163) implies: % 183.75/28.92 | (1164) all_152_2 = all_144_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1110), (1111) imply: % 183.75/28.92 | (1165) all_222_2 = all_216_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1165) implies: % 183.75/28.92 | (1166) all_222_2 = all_216_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1132), (1133) imply: % 183.75/28.92 | (1167) all_166_2 = all_114_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1167) implies: % 183.75/28.92 | (1168) all_166_2 = all_114_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (927), (1012) imply: % 183.75/28.92 | (1169) all_74_2 = all_36_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1169) implies: % 183.75/28.92 | (1170) all_74_2 = all_36_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1084), (1135) imply: % 183.75/28.92 | (1171) all_160_2 = all_50_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1083), (1135) imply: % 183.75/28.92 | (1172) all_160_2 = all_150_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (888), (1022) imply: % 183.75/28.92 | (1173) all_188_2 = all_106_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1173) implies: % 183.75/28.92 | (1174) all_188_2 = all_106_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1022), (1127) imply: % 183.75/28.92 | (1175) all_106_2 = all_94_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (830), (1139) imply: % 183.75/28.92 | (1176) all_212_2 = all_14_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1176) implies: % 183.75/28.92 | (1177) all_212_2 = all_14_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1112), (1113) imply: % 183.75/28.92 | (1178) all_128_2 = all_54_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1178) implies: % 183.75/28.92 | (1179) all_128_2 = all_54_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1140), (1141) imply: % 183.75/28.92 | (1180) all_104_2 = all_22_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1180) implies: % 183.75/28.92 | (1181) all_104_2 = all_22_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (916), (1121) imply: % 183.75/28.92 | (1182) all_240_2 = all_226_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (918), (1121) imply: % 183.75/28.92 | (1183) all_240_2 = all_126_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (917), (1121) imply: % 183.75/28.92 | (1184) all_240_2 = all_200_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (813), (1143) imply: % 183.75/28.92 | (1185) all_162_2 = all_28_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1185) implies: % 183.75/28.92 | (1186) all_162_2 = all_28_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (879), (1129) imply: % 183.75/28.92 | (1187) all_116_2 = all_40_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1187) implies: % 183.75/28.92 | (1188) all_116_2 = all_40_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1095), (1145) imply: % 183.75/28.92 | (1189) all_230_2 = all_32_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (804), (1095) imply: % 183.75/28.92 | (1190) all_230_2 = all_60_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (803), (1095) imply: % 183.75/28.92 | (1191) all_230_2 = all_92_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (841), (1137) imply: % 183.75/28.92 | (1192) all_164_2 = all_34_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1192) implies: % 183.75/28.92 | (1193) all_164_2 = all_34_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (885), (886) imply: % 183.75/28.92 | (1194) all_190_2 = all_188_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (885), (887) imply: % 183.75/28.92 | (1195) all_190_2 = all_38_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1183), (1184) imply: % 183.75/28.92 | (1196) all_200_2 = all_126_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1182), (1184) imply: % 183.75/28.92 | (1197) all_226_2 = all_200_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1197) implies: % 183.75/28.92 | (1198) all_226_2 = all_200_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (956), (1097) imply: % 183.75/28.92 | (1199) all_236_2 = all_30_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1199) implies: % 183.75/28.92 | (1200) all_236_2 = all_30_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (955), (1200) imply: % 183.75/28.92 | (1201) all_132_2 = all_30_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1201) implies: % 183.75/28.92 | (1202) all_132_2 = all_30_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1158), (1159) imply: % 183.75/28.92 | (1203) all_154_2 = all_56_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1203) implies: % 183.75/28.92 | (1204) all_154_2 = all_56_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (839), (840) imply: % 183.75/28.92 | (1205) all_198_2 = all_110_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1205) implies: % 183.75/28.92 | (1206) all_198_2 = all_110_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1190), (1191) imply: % 183.75/28.92 | (1207) all_92_2 = all_60_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1189), (1191) imply: % 183.75/28.92 | (1208) all_92_2 = all_32_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (915), (1099) imply: % 183.75/28.92 | (1209) all_226_2 = all_48_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1209) implies: % 183.75/28.92 | (1210) all_226_2 = all_48_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1198), (1210) imply: % 183.75/28.92 | (1211) all_200_2 = all_48_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1211) implies: % 183.75/28.92 | (1212) all_200_2 = all_48_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1058), (1123) imply: % 183.75/28.92 | (1213) all_186_2 = all_148_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1123), (1152) imply: % 183.75/28.92 | (1214) all_186_2 = all_134_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (966), (1166) imply: % 183.75/28.92 | (1215) all_216_2 = all_44_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (965), (1166) imply: % 183.75/28.92 | (1216) all_216_2 = all_88_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (964), (1166) imply: % 183.75/28.92 | (1217) all_216_2 = all_202_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1116), (1117) imply: % 183.75/28.92 | (1218) all_156_2 = all_8_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1218) implies: % 183.75/28.92 | (1219) all_156_2 = all_8_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (997), (998) imply: % 183.75/28.92 | (1220) all_214_2 = all_194_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1220) implies: % 183.75/28.92 | (1221) all_214_2 = all_194_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1215), (1216) imply: % 183.75/28.92 | (1222) all_88_2 = all_44_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1216), (1217) imply: % 183.75/28.92 | (1223) all_202_2 = all_88_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1223) implies: % 183.75/28.92 | (1224) all_202_2 = all_88_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (972), (1221) imply: % 183.75/28.92 | (1225) all_194_2 = all_6_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1155), (1221) imply: % 183.75/28.92 | (1226) all_196_2 = all_194_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1226) implies: % 183.75/28.92 | (1227) all_196_2 = all_194_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (829), (1177) imply: % 183.75/28.92 | (1228) all_42_2 = all_14_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1228) implies: % 183.75/28.92 | (1229) all_42_2 = all_14_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (828), (1040) imply: % 183.75/28.92 | (1230) all_18_2 = all_12_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1230) implies: % 183.75/28.92 | (1231) all_18_2 = all_12_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (946), (1115) imply: % 183.75/28.92 | (1232) all_176_2 = all_136_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (945), (1115) imply: % 183.75/28.92 | (1233) all_176_2 = all_146_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1115), (1147) imply: % 183.75/28.92 | (1234) all_176_2 = all_168_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (810), (812) imply: % 183.75/28.92 | (1235) all_162_2 = all_108_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1235) implies: % 183.75/28.92 | (1236) all_162_2 = all_108_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (811), (812) imply: % 183.75/28.92 | (1237) all_158_2 = all_108_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1237) implies: % 183.75/28.92 | (1238) all_158_2 = all_108_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (926), (1119) imply: % 183.75/28.92 | (1239) all_122_2 = all_46_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1239) implies: % 183.75/28.92 | (1240) all_122_2 = all_46_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (963), (1224) imply: % 183.75/28.92 | (1241) all_88_2 = all_26_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1241) implies: % 183.75/28.92 | (1242) all_88_2 = all_26_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1196), (1212) imply: % 183.75/28.92 | (1243) all_126_2 = all_48_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1243) implies: % 183.75/28.92 | (1244) all_126_2 = all_48_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (838), (1206) imply: % 183.75/28.92 | (1245) all_110_2 = all_96_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (837), (1206) imply: % 183.75/28.92 | (1246) all_164_2 = all_110_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1246) implies: % 183.75/28.92 | (1247) all_164_2 = all_110_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1153), (1227) imply: % 183.75/28.92 | (1248) all_194_2 = all_80_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1248) implies: % 183.75/28.92 | (1249) all_194_2 = all_80_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1225), (1249) imply: % 183.75/28.92 | (1250) all_80_2 = all_6_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1250) implies: % 183.75/28.92 | (1251) all_80_2 = all_6_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (850), (1032) imply: % 183.75/28.92 | (1252) all_180_2 = all_4_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1252) implies: % 183.75/28.92 | (1253) all_180_2 = all_4_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1194), (1195) imply: % 183.75/28.92 | (1254) all_188_2 = all_38_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1254) implies: % 183.75/28.92 | (1255) all_188_2 = all_38_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1174), (1255) imply: % 183.75/28.92 | (1256) all_106_2 = all_38_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1256) implies: % 183.75/28.92 | (1257) all_106_2 = all_38_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1213), (1214) imply: % 183.75/28.92 | (1258) all_148_2 = all_134_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1258) implies: % 183.75/28.92 | (1259) all_148_2 = all_134_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1149), (1150) imply: % 183.75/28.92 | (1260) all_182_2 = all_84_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1260) implies: % 183.75/28.92 | (1261) all_182_2 = all_84_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (982), (1106) imply: % 183.75/28.92 | (1262) all_142_2 = all_140_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1106), (1261) imply: % 183.75/28.92 | (1263) all_142_2 = all_84_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (849), (1253) imply: % 183.75/28.92 | (1264) all_150_2 = all_4_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1264) implies: % 183.75/28.92 | (1265) all_150_2 = all_4_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (878), (1101) imply: % 183.75/28.92 | (1266) all_174_2 = all_86_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1266) implies: % 183.75/28.92 | (1267) all_174_2 = all_86_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1232), (1233) imply: % 183.75/28.92 | (1268) all_146_2 = all_136_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1233), (1234) imply: % 183.75/28.92 | (1269) all_168_2 = all_146_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1269) implies: % 183.75/28.92 | (1270) all_168_2 = all_146_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (877), (1267) imply: % 183.75/28.92 | (1271) all_116_2 = all_86_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1271) implies: % 183.75/28.92 | (1272) all_116_2 = all_86_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (898), (1125) imply: % 183.75/28.92 | (1273) all_138_2 = all_124_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (899), (1125) imply: % 183.75/28.92 | (1274) all_138_2 = all_102_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1131), (1162) imply: % 183.75/28.92 | (1275) all_144_2 = all_66_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1275) implies: % 183.75/28.92 | (1276) all_144_2 = all_66_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1148), (1270) imply: % 183.75/28.92 | (1277) all_146_2 = all_100_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1277) implies: % 183.75/28.92 | (1278) all_146_2 = all_100_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (861), (1168) imply: % 183.75/28.92 | (1279) all_130_2 = all_114_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1279) implies: % 183.75/28.92 | (1280) all_130_2 = all_114_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1193), (1247) imply: % 183.75/28.92 | (1281) all_110_2 = all_34_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1281) implies: % 183.75/28.92 | (1282) all_110_2 = all_34_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1186), (1236) imply: % 183.75/28.92 | (1283) all_108_2 = all_28_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1283) implies: % 183.75/28.92 | (1284) all_108_2 = all_28_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1171), (1172) imply: % 183.75/28.92 | (1285) all_150_2 = all_50_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1285) implies: % 183.75/28.92 | (1286) all_150_2 = all_50_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (1045), (1238) imply: % 183.75/28.92 | (1287) all_108_2 = all_82_2 % 183.75/28.92 | % 183.75/28.92 | SIMP: (1287) implies: % 183.75/28.92 | (1288) all_108_2 = all_82_2 % 183.75/28.92 | % 183.75/28.92 | COMBINE_EQS: (933), (1219) imply: % 183.75/28.92 | (1289) all_154_2 = all_8_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1289) implies: % 183.75/28.93 | (1290) all_154_2 = all_8_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1204), (1290) imply: % 183.75/28.93 | (1291) all_56_2 = all_8_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1291) implies: % 183.75/28.93 | (1292) all_56_2 = all_8_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (867), (1164) imply: % 183.75/28.93 | (1293) all_144_2 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1293) implies: % 183.75/28.93 | (1294) all_144_2 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1265), (1286) imply: % 183.75/28.93 | (1295) all_50_2 = all_4_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1295) implies: % 183.75/28.93 | (1296) all_50_2 = all_4_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (907), (1259) imply: % 183.75/28.93 | (1297) all_134_2 = all_64_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (906), (1259) imply: % 183.75/28.93 | (1298) all_134_2 = all_120_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1268), (1278) imply: % 183.75/28.93 | (1299) all_136_2 = all_100_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1299) implies: % 183.75/28.93 | (1300) all_136_2 = all_100_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1160), (1276) imply: % 183.75/28.93 | (1301) all_66_2 = all_24_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1276), (1294) imply: % 183.75/28.93 | (1302) all_66_2 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1262), (1263) imply: % 183.75/28.93 | (1303) all_140_2 = all_84_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1303) implies: % 183.75/28.93 | (1304) all_140_2 = all_84_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (981), (1304) imply: % 183.75/28.93 | (1305) all_98_2 = all_84_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1305) implies: % 183.75/28.93 | (1306) all_98_2 = all_84_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1273), (1274) imply: % 183.75/28.93 | (1307) all_124_2 = all_102_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1307) implies: % 183.75/28.93 | (1308) all_124_2 = all_102_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1297), (1298) imply: % 183.75/28.93 | (1309) all_120_2 = all_64_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (954), (1202) imply: % 183.75/28.93 | (1310) all_128_2 = all_30_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1310) implies: % 183.75/28.93 | (1311) all_128_2 = all_30_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (859), (1280) imply: % 183.75/28.93 | (1312) all_114_2 = all_70_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (858), (1280) imply: % 183.75/28.93 | (1313) all_114_2 = all_112_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (860), (1280) imply: % 183.75/28.93 | (1314) all_114_2 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1179), (1311) imply: % 183.75/28.93 | (1315) all_54_2 = all_30_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1315) implies: % 183.75/28.93 | (1316) all_54_2 = all_30_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (897), (1308) imply: % 183.75/28.93 | (1317) all_102_2 = all_10_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1157), (1308) imply: % 183.75/28.93 | (1318) all_102_2 = all_78_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (925), (1240) imply: % 183.75/28.93 | (1319) all_52_2 = all_46_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1319) implies: % 183.75/28.93 | (1320) all_52_2 = all_46_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1041), (1042) imply: % 183.75/28.93 | (1321) all_90_2 = all_72_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1042), (1043) imply: % 183.75/28.93 | (1322) all_104_2 = all_90_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1322) implies: % 183.75/28.93 | (1323) all_104_2 = all_90_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (876), (1272) imply: % 183.75/28.93 | (1324) all_86_2 = all_76_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1188), (1272) imply: % 183.75/28.93 | (1325) all_86_2 = all_40_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1313), (1314) imply: % 183.75/28.93 | (1326) all_112_2 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1312), (1313) imply: % 183.75/28.93 | (1327) all_112_2 = all_70_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1326), (1327) imply: % 183.75/28.93 | (1328) all_70_2 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1245), (1282) imply: % 183.75/28.93 | (1329) all_96_2 = all_34_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1329) implies: % 183.75/28.93 | (1330) all_96_2 = all_34_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1284), (1288) imply: % 183.75/28.93 | (1331) all_82_2 = all_28_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1331) implies: % 183.75/28.93 | (1332) all_82_2 = all_28_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1175), (1257) imply: % 183.75/28.93 | (1333) all_94_2 = all_38_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1181), (1323) imply: % 183.75/28.93 | (1334) all_90_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1334) implies: % 183.75/28.93 | (1335) all_90_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1317), (1318) imply: % 183.75/28.93 | (1336) all_78_2 = all_10_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1207), (1208) imply: % 183.75/28.93 | (1337) all_60_2 = all_32_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1337) implies: % 183.75/28.93 | (1338) all_60_2 = all_32_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1321), (1335) imply: % 183.75/28.93 | (1339) all_72_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1339) implies: % 183.75/28.93 | (1340) all_72_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1222), (1242) imply: % 183.75/28.93 | (1341) all_44_2 = all_26_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1324), (1325) imply: % 183.75/28.93 | (1342) all_76_2 = all_40_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1342) implies: % 183.75/28.93 | (1343) all_76_2 = all_40_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (924), (1170) imply: % 183.75/28.93 | (1344) all_52_2 = all_36_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1344) implies: % 183.75/28.93 | (1345) all_52_2 = all_36_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (819), (1340) imply: % 183.75/28.93 | (1346) all_68_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1346) implies: % 183.75/28.93 | (1347) all_68_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1301), (1302) imply: % 183.75/28.93 | (1348) all_24_2 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1348) implies: % 183.75/28.93 | (1349) all_24_2 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (801), (802) imply: % 183.75/28.93 | (1350) all_58_2 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (801), (1338) imply: % 183.75/28.93 | (1351) all_58_2 = all_32_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1350), (1351) imply: % 183.75/28.93 | (1352) all_32_2 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1320), (1345) imply: % 183.75/28.93 | (1353) all_46_2 = all_36_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1038), (1229) imply: % 183.75/28.93 | (1354) all_18_2 = all_14_2 % 183.75/28.93 | % 183.75/28.93 | SIMP: (1354) implies: % 183.75/28.93 | (1355) all_18_2 = all_14_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1231), (1355) imply: % 183.75/28.93 | (1356) all_14_2 = all_12_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1229), (1356) imply: % 183.75/28.93 | (1357) all_42_2 = all_12_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1208), (1352) imply: % 183.75/28.93 | (1358) all_92_2 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1042), (1335) imply: % 183.75/28.93 | (1359) all_118_2 = all_22_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1240), (1353) imply: % 183.75/28.93 | (1360) all_122_2 = all_36_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1274), (1317) imply: % 183.75/28.93 | (1361) all_138_2 = all_10_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1045), (1332) imply: % 183.75/28.93 | (1362) all_158_2 = all_28_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1171), (1296) imply: % 183.75/28.93 | (1363) all_160_2 = all_4_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1168), (1314) imply: % 183.75/28.93 | (1364) all_166_2 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1131), (1302) imply: % 183.75/28.93 | (1365) all_170_2 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1125), (1361) imply: % 183.75/28.93 | (1366) all_172_2 = all_10_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1267), (1325) imply: % 183.75/28.93 | (1367) all_174_2 = all_40_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1233), (1278) imply: % 183.75/28.93 | (1368) all_176_2 = all_100_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1214), (1297) imply: % 183.75/28.93 | (1369) all_186_2 = all_64_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1153), (1251) imply: % 183.75/28.93 | (1370) all_196_2 = all_6_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1206), (1282) imply: % 183.75/28.93 | (1371) all_198_2 = all_34_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (812), (1284) imply: % 183.75/28.93 | (1372) all_206_2 = all_28_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1115), (1368) imply: % 183.75/28.93 | (1373) all_208_2 = all_100_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1177), (1356) imply: % 183.75/28.93 | (1374) all_212_2 = all_12_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1216), (1242) imply: % 183.75/28.93 | (1375) all_216_2 = all_26_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (998), (1225) imply: % 183.75/28.93 | (1376) all_218_2 = all_6_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1123), (1369) imply: % 183.75/28.93 | (1377) all_224_2 = all_64_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1191), (1358) imply: % 183.75/28.93 | (1378) all_230_2 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (840), (1282) imply: % 183.75/28.93 | (1379) all_232_2 = all_34_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1158), (1292) imply: % 183.75/28.93 | (1380) all_234_2 = all_8_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1184), (1212) imply: % 183.75/28.93 | (1381) all_240_2 = all_48_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1095), (1378) imply: % 183.75/28.93 | (1382) all_244_22 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1121), (1381) imply: % 183.75/28.93 | (1383) all_244_19 = all_48_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1113), (1316) imply: % 183.75/28.93 | (1384) all_244_17 = all_30_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1139), (1356) imply: % 183.75/28.93 | (1385) all_244_16 = all_12_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1022), (1257) imply: % 183.75/28.93 | (1386) all_244_14 = all_38_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1135), (1363) imply: % 183.75/28.93 | (1387) all_244_13 = all_4_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1133), (1314) imply: % 183.75/28.93 | (1388) all_244_11 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1111), (1375) imply: % 183.75/28.93 | (1389) all_244_10 = all_26_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1027), (1294) imply: % 183.75/28.93 | (1390) all_244_9 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (934), (1380) imply: % 183.75/28.93 | (1391) all_244_7 = all_8_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (901), (1336) imply: % 183.75/28.93 | (1392) all_244_6 = all_10_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1108), (1370) imply: % 183.75/28.93 | (1393) all_244_5 = all_6_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (908), (1297) imply: % 183.75/28.93 | (1394) all_244_4 = all_64_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1047), (1352) imply: % 183.75/28.93 | (1395) all_246_23 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1062), (1356) imply: % 183.75/28.93 | (1396) all_246_20 = all_12_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (851), (1363) imply: % 183.75/28.93 | (1397) all_246_17 = all_4_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1070), (1388) imply: % 183.75/28.93 | (1398) all_246_16 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1060), (1302) imply: % 183.75/28.93 | (1399) all_246_15 = all_16_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1092), (1333) imply: % 183.75/28.93 | (1400) all_246_13 = all_38_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1067), (1361) imply: % 183.75/28.93 | (1401) all_246_11 = all_10_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1016), (1369) imply: % 183.75/28.93 | (1402) all_246_10 = all_64_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1013), (1381) imply: % 183.75/28.93 | (1403) all_246_9 = all_48_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1090), (1353) imply: % 183.75/28.93 | (1404) all_246_8 = all_36_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1053), (1368) imply: % 183.75/28.93 | (1405) all_246_5 = all_100_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (957), (1384) imply: % 183.75/28.93 | (1406) all_246_4 = all_30_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (967), (1389) imply: % 183.75/28.93 | (1407) all_246_3 = all_26_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1076), (1393) imply: % 183.75/28.93 | (1408) all_246_2 = all_6_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1064), (1263) imply: % 183.75/28.93 | (1409) all_246_1 = all_84_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1024), (1325) imply: % 183.75/28.93 | (1410) all_248_22 = all_40_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (807), (1378) imply: % 183.75/28.93 | (1411) all_248_19 = all_20_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (891), (1333) imply: % 183.75/28.93 | (1412) all_248_17 = all_38_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (930), (1353) imply: % 183.75/28.93 | (1413) all_248_16 = all_36_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1000), (1375) imply: % 183.75/28.93 | (1414) all_248_15 = all_26_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (853), (1387) imply: % 183.75/28.93 | (1415) all_248_13 = all_4_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (973), (1408) imply: % 183.75/28.93 | (1416) all_248_10 = all_6_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1029), (1388) imply: % 183.75/28.93 | (1417) all_248_8 = all_62_2 % 183.75/28.93 | % 183.75/28.93 | COMBINE_EQS: (1018), (1401) imply: % 183.75/28.94 | (1418) all_248_7 = all_10_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (987), (1263) imply: % 183.75/28.94 | (1419) all_248_5 = all_84_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (833), (1356) imply: % 183.75/28.94 | (1420) all_248_4 = all_12_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (870), (1302) imply: % 183.75/28.94 | (1421) all_248_3 = all_16_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (911), (1377) imply: % 183.75/28.94 | (1422) all_248_2 = all_64_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (949), (1405) imply: % 183.75/28.94 | (1423) all_248_1 = all_100_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (809), (1352) imply: % 183.75/28.94 | (1424) all_250_23 = all_20_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (818), (1332) imply: % 183.75/28.94 | (1425) all_250_22 = all_28_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (824), (1359) imply: % 183.75/28.94 | (1426) all_250_21 = all_22_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (836), (1231) imply: % 183.75/28.94 | (1427) all_250_20 = all_12_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (871), (1390) imply: % 183.75/28.94 | (1428) all_250_15 = all_16_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (884), (1325) imply: % 183.75/28.94 | (1429) all_250_14 = all_40_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (893), (1257) imply: % 183.75/28.94 | (1430) all_250_13 = all_38_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (905), (1401) imply: % 183.75/28.94 | (1431) all_250_11 = all_10_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (914), (1369) imply: % 183.75/28.94 | (1432) all_250_10 = all_64_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (921), (1403) imply: % 183.75/28.94 | (1433) all_250_9 = all_48_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (939), (1078) imply: % 183.75/28.94 | (1434) all_250_7 = all_8_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (971), (1375) imply: % 183.75/28.94 | (1435) all_250_3 = all_26_2 % 183.75/28.94 | % 183.75/28.94 | COMBINE_EQS: (978), (1376) imply: % 183.75/28.94 | (1436) all_250_2 = all_6_2 % 183.75/28.94 | % 183.75/28.94 | REDUCE: (674), (994), (1423) imply: % 183.75/28.94 | (1437) ~ (all_244_0 = all_100_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (673), (994), (1422) imply: % 183.75/28.94 | (1438) ~ (all_244_0 = all_64_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (672), (994), (1421) imply: % 183.75/28.94 | (1439) ~ (all_244_0 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (671), (994), (1420) imply: % 183.75/28.94 | (1440) ~ (all_244_0 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (670), (994), (1419) imply: % 183.75/28.94 | (1441) ~ (all_244_0 = all_84_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (669), (994), (1416) imply: % 183.75/28.94 | (1442) ~ (all_244_0 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (668), (994), (1002) imply: % 183.75/28.94 | (1443) ~ (all_244_0 = all_30_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (667), (1422), (1423) imply: % 183.75/28.94 | (1444) ~ (all_100_2 = all_64_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (666), (1421), (1423) imply: % 183.75/28.94 | (1445) ~ (all_100_2 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (665), (1420), (1423) imply: % 183.75/28.94 | (1446) ~ (all_100_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (664), (1006), (1423) imply: % 183.75/28.94 | (1447) ~ (all_244_3 = all_100_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1447) implies: % 183.75/28.94 | (1448) ~ (all_244_3 = all_100_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (663), (937), (1423) imply: % 183.75/28.94 | (1449) ~ (all_100_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (662), (1413), (1423) imply: % 183.75/28.94 | (1450) ~ (all_100_2 = all_36_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (661), (920), (1423) imply: % 183.75/28.94 | (1451) ~ (all_100_2 = all_48_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (660), (1421), (1422) imply: % 183.75/28.94 | (1452) ~ (all_64_2 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (659), (1420), (1422) imply: % 183.75/28.94 | (1453) ~ (all_64_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (658), (1418), (1422) imply: % 183.75/28.94 | (1454) ~ (all_64_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (657), (1412), (1422) imply: % 183.75/28.94 | (1455) ~ (all_64_2 = all_38_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (656), (1410), (1422) imply: % 183.75/28.94 | (1456) ~ (all_64_2 = all_40_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (655), (1420), (1421) imply: % 183.75/28.94 | (1457) ~ (all_16_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (654), (1417), (1421) imply: % 183.75/28.94 | (1458) ~ (all_62_2 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1458) implies: % 183.75/28.94 | (1459) ~ (all_62_2 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (653), (1415), (1421) imply: % 183.75/28.94 | (1460) ~ (all_16_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (652), (846), (1421) imply: % 183.75/28.94 | (1461) ~ (all_244_15 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1461) implies: % 183.75/28.94 | (1462) ~ (all_244_15 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (651), (1036), (1421) imply: % 183.75/28.94 | (1463) ~ (all_34_2 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1463) implies: % 183.75/28.94 | (1464) ~ (all_34_2 = all_16_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (650), (823), (1420) imply: % 183.75/28.94 | (1465) ~ (all_22_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1465) implies: % 183.75/28.94 | (1466) ~ (all_22_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (649), (816), (1420) imply: % 183.75/28.94 | (1467) ~ (all_28_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1467) implies: % 183.75/28.94 | (1468) ~ (all_28_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (648), (1411), (1420) imply: % 183.75/28.94 | (1469) ~ (all_20_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1469) implies: % 183.75/28.94 | (1470) ~ (all_20_2 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (647), (1048), (1420) imply: % 183.75/28.94 | (1471) ~ (all_244_24 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1471) implies: % 183.75/28.94 | (1472) ~ (all_244_24 = all_12_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (646), (1006), (1419) imply: % 183.75/28.94 | (1473) ~ (all_244_3 = all_84_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1473) implies: % 183.75/28.94 | (1474) ~ (all_244_3 = all_84_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (645), (1418), (1419) imply: % 183.75/28.94 | (1475) ~ (all_84_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (644), (1417), (1419) imply: % 183.75/28.94 | (1476) ~ (all_84_2 = all_62_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (643), (823), (1419) imply: % 183.75/28.94 | (1477) ~ (all_84_2 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (642), (1416), (1419) imply: % 183.75/28.94 | (1478) ~ (all_84_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (641), (1414), (1419) imply: % 183.75/28.94 | (1479) ~ (all_84_2 = all_26_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (640), (1002), (1419) imply: % 183.75/28.94 | (1480) ~ (all_84_2 = all_30_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (639), (1006), (1418) imply: % 183.75/28.94 | (1481) ~ (all_244_3 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (638), (1006), (1417) imply: % 183.75/28.94 | (1482) ~ (all_244_3 = all_62_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (637), (823), (1006) imply: % 183.75/28.94 | (1483) ~ (all_244_3 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (636), (937), (1006) imply: % 183.75/28.94 | (1484) ~ (all_244_3 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (635), (1006), (1413) imply: % 183.75/28.94 | (1485) ~ (all_244_3 = all_36_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (634), (920), (1006) imply: % 183.75/28.94 | (1486) ~ (all_244_3 = all_48_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (633), (1417), (1418) imply: % 183.75/28.94 | (1487) ~ (all_62_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1487) implies: % 183.75/28.94 | (1488) ~ (all_62_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (632), (823), (1418) imply: % 183.75/28.94 | (1489) ~ (all_22_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1489) implies: % 183.75/28.94 | (1490) ~ (all_22_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (631), (1020), (1418) imply: % 183.75/28.94 | (1491) ~ (all_244_8 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1491) implies: % 183.75/28.94 | (1492) ~ (all_244_8 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (630), (1412), (1418) imply: % 183.75/28.94 | (1493) ~ (all_38_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1493) implies: % 183.75/28.94 | (1494) ~ (all_38_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (629), (1410), (1418) imply: % 183.75/28.94 | (1495) ~ (all_40_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1495) implies: % 183.75/28.94 | (1496) ~ (all_40_2 = all_10_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (628), (823), (1417) imply: % 183.75/28.94 | (1497) ~ (all_62_2 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (627), (1415), (1417) imply: % 183.75/28.94 | (1498) ~ (all_62_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (626), (846), (1417) imply: % 183.75/28.94 | (1499) ~ (all_244_15 = all_62_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1499) implies: % 183.75/28.94 | (1500) ~ (all_244_15 = all_62_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (625), (1036), (1417) imply: % 183.75/28.94 | (1501) ~ (all_62_2 = all_34_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (624), (816), (823) imply: % 183.75/28.94 | (1502) ~ (all_28_2 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1502) implies: % 183.75/28.94 | (1503) ~ (all_28_2 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (623), (823), (1411) imply: % 183.75/28.94 | (1504) ~ (all_22_2 = all_20_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (622), (823), (1048) imply: % 183.75/28.94 | (1505) ~ (all_244_24 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1505) implies: % 183.75/28.94 | (1506) ~ (all_244_24 = all_22_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (621), (937), (1416) imply: % 183.75/28.94 | (1507) ~ (all_8_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1507) implies: % 183.75/28.94 | (1508) ~ (all_8_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (620), (1020), (1416) imply: % 183.75/28.94 | (1509) ~ (all_244_8 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1509) implies: % 183.75/28.94 | (1510) ~ (all_244_8 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (619), (1415), (1416) imply: % 183.75/28.94 | (1511) ~ (all_6_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (618), (816), (1416) imply: % 183.75/28.94 | (1512) ~ (all_28_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1512) implies: % 183.75/28.94 | (1513) ~ (all_28_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (617), (1414), (1416) imply: % 183.75/28.94 | (1514) ~ (all_26_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1514) implies: % 183.75/28.94 | (1515) ~ (all_26_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (616), (1002), (1416) imply: % 183.75/28.94 | (1516) ~ (all_30_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1516) implies: % 183.75/28.94 | (1517) ~ (all_30_2 = all_6_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (615), (937), (1020) imply: % 183.75/28.94 | (1518) ~ (all_244_8 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1518) implies: % 183.75/28.94 | (1519) ~ (all_244_8 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (614), (937), (1415) imply: % 183.75/28.94 | (1520) ~ (all_8_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (613), (816), (937) imply: % 183.75/28.94 | (1521) ~ (all_28_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1521) implies: % 183.75/28.94 | (1522) ~ (all_28_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (612), (937), (1413) imply: % 183.75/28.94 | (1523) ~ (all_36_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1523) implies: % 183.75/28.94 | (1524) ~ (all_36_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (611), (920), (937) imply: % 183.75/28.94 | (1525) ~ (all_48_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1525) implies: % 183.75/28.94 | (1526) ~ (all_48_2 = all_8_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (610), (1020), (1415) imply: % 183.75/28.94 | (1527) ~ (all_244_8 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (609), (816), (1020) imply: % 183.75/28.94 | (1528) ~ (all_244_8 = all_28_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (608), (1020), (1412) imply: % 183.75/28.94 | (1529) ~ (all_244_8 = all_38_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (607), (816), (1415) imply: % 183.75/28.94 | (1530) ~ (all_28_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1530) implies: % 183.75/28.94 | (1531) ~ (all_28_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (606), (846), (1415) imply: % 183.75/28.94 | (1532) ~ (all_244_15 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1532) implies: % 183.75/28.94 | (1533) ~ (all_244_15 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | REDUCE: (605), (1036), (1415) imply: % 183.75/28.94 | (1534) ~ (all_34_2 = all_4_2) % 183.75/28.94 | % 183.75/28.94 | SIMP: (1534) implies: % 183.75/28.95 | (1535) ~ (all_34_2 = all_4_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (604), (816), (1411) imply: % 183.75/28.95 | (1536) ~ (all_28_2 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (603), (816), (1048) imply: % 183.75/28.95 | (1537) ~ (all_244_24 = all_28_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1537) implies: % 183.75/28.95 | (1538) ~ (all_244_24 = all_28_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (602), (1413), (1414) imply: % 183.75/28.95 | (1539) ~ (all_36_2 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1539) implies: % 183.75/28.95 | (1540) ~ (all_36_2 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (601), (1412), (1414) imply: % 183.75/28.95 | (1541) ~ (all_38_2 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1541) implies: % 183.75/28.95 | (1542) ~ (all_38_2 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (600), (846), (1414) imply: % 183.75/28.95 | (1543) ~ (all_244_15 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1543) implies: % 183.75/28.95 | (1544) ~ (all_244_15 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (599), (1411), (1414) imply: % 183.75/28.95 | (1545) ~ (all_26_2 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (598), (1002), (1414) imply: % 183.75/28.95 | (1546) ~ (all_30_2 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1546) implies: % 183.75/28.95 | (1547) ~ (all_30_2 = all_26_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (597), (1412), (1413) imply: % 183.75/28.95 | (1548) ~ (all_38_2 = all_36_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1548) implies: % 183.75/28.95 | (1549) ~ (all_38_2 = all_36_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (596), (846), (1413) imply: % 183.75/28.95 | (1550) ~ (all_244_15 = all_36_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1550) implies: % 183.75/28.95 | (1551) ~ (all_244_15 = all_36_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (595), (1411), (1413) imply: % 183.75/28.95 | (1552) ~ (all_36_2 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (594), (920), (1413) imply: % 183.75/28.95 | (1553) ~ (all_48_2 = all_36_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1553) implies: % 183.75/28.95 | (1554) ~ (all_48_2 = all_36_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (593), (846), (1412) imply: % 183.75/28.95 | (1555) ~ (all_244_15 = all_38_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1555) implies: % 183.75/28.95 | (1556) ~ (all_244_15 = all_38_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (592), (1411), (1412) imply: % 183.75/28.95 | (1557) ~ (all_38_2 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (591), (1410), (1412) imply: % 183.75/28.95 | (1558) ~ (all_40_2 = all_38_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1558) implies: % 183.75/28.95 | (1559) ~ (all_40_2 = all_38_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (590), (846), (1411) imply: % 183.75/28.95 | (1560) ~ (all_244_15 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (589), (846), (1036) imply: % 183.75/28.95 | (1561) ~ (all_244_15 = all_34_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (588), (1048), (1411) imply: % 183.75/28.95 | (1562) ~ (all_244_24 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1562) implies: % 183.75/28.95 | (1563) ~ (all_244_24 = all_20_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (587), (920), (1002) imply: % 183.75/28.95 | (1564) ~ (all_48_2 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1564) implies: % 183.75/28.95 | (1565) ~ (all_48_2 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (586), (1002), (1410) imply: % 183.75/28.95 | (1566) ~ (all_40_2 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1566) implies: % 183.75/28.95 | (1567) ~ (all_40_2 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (585), (1002), (1036) imply: % 183.75/28.95 | (1568) ~ (all_34_2 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1568) implies: % 183.75/28.95 | (1569) ~ (all_34_2 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (584), (1002), (1048) imply: % 183.75/28.95 | (1570) ~ (all_244_24 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1570) implies: % 183.75/28.95 | (1571) ~ (all_244_24 = all_30_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (583), (920), (1410) imply: % 183.75/28.95 | (1572) ~ (all_48_2 = all_40_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (582), (920), (1036) imply: % 183.75/28.95 | (1573) ~ (all_48_2 = all_34_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (581), (920), (1048) imply: % 183.75/28.95 | (1574) ~ (all_244_24 = all_48_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1574) implies: % 183.75/28.95 | (1575) ~ (all_244_24 = all_48_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (580), (1036), (1410) imply: % 183.75/28.95 | (1576) ~ (all_40_2 = all_34_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (579), (1048), (1410) imply: % 183.75/28.95 | (1577) ~ (all_244_24 = all_40_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1577) implies: % 183.75/28.95 | (1578) ~ (all_244_24 = all_40_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (578), (1036), (1048) imply: % 183.75/28.95 | (1579) ~ (all_244_24 = all_34_2) % 183.75/28.95 | % 183.75/28.95 | SIMP: (1579) implies: % 183.75/28.95 | (1580) ~ (all_244_24 = all_34_2) % 183.75/28.95 | % 183.75/28.95 | REDUCE: (528), (996), (1004) imply: % 183.75/28.95 | (1581) op(all_100_2, all_84_2) = e4 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (527), (996), (1004) imply: % 183.75/28.95 | (1582) op(all_84_2, all_100_2) = e3 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (525), (1393), (1394) imply: % 183.75/28.95 | (1583) op(all_64_2, all_6_2) = e4 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (524), (1393), (1394) imply: % 183.75/28.95 | (1584) op(all_6_2, all_64_2) = e2 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (523), (1391), (1392) imply: % 183.75/28.95 | (1585) op(all_10_2, all_8_2) = e3 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (522), (1391), (1392) imply: % 183.75/28.95 | (1586) op(all_8_2, all_10_2) = e2 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (520), (1389), (1390) imply: % 183.75/28.95 | (1587) op(all_16_2, all_26_2) = e4 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (519), (1389), (1390) imply: % 183.75/28.95 | (1588) op(all_26_2, all_16_2) = e1 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (518), (1012), (1388) imply: % 183.75/28.95 | (1589) op(all_62_2, all_36_2) = e3 % 183.75/28.95 | % 183.75/28.95 | REDUCE: (517), (1012), (1388) imply: % 184.19/28.95 | (1590) op(all_36_2, all_62_2) = e1 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (516), (1386), (1387) imply: % 184.19/28.95 | (1591) op(all_4_2, all_38_2) = e2 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (515), (1386), (1387) imply: % 184.19/28.95 | (1592) op(all_38_2, all_4_2) = e1 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (513), (1384), (1385) imply: % 184.19/28.95 | (1593) op(all_12_2, all_30_2) = e4 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (512), (1384), (1385) imply: % 184.19/28.95 | (1594) op(all_30_2, all_12_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (511), (1140), (1383) imply: % 184.19/28.95 | (1595) op(all_22_2, all_48_2) = e3 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (510), (1140), (1383) imply: % 184.19/28.95 | (1596) op(all_48_2, all_22_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (509), (1129), (1143) imply: % 184.19/28.95 | (1597) op(all_28_2, all_40_2) = e2 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (508), (1129), (1143) imply: % 184.19/28.95 | (1598) op(all_40_2, all_28_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (507), (1137), (1382) imply: % 184.19/28.95 | (1599) op(all_20_2, all_34_2) = e1 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (506), (1137), (1382) imply: % 184.19/28.95 | (1600) op(all_34_2, all_20_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (576), (1409) imply: % 184.19/28.95 | (1601) op(e4, all_84_2) = e3 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (575), (1408) imply: % 184.19/28.95 | (1602) op(e4, all_6_2) = e2 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (574), (1407) imply: % 184.19/28.95 | (1603) op(e4, all_26_2) = e1 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (573), (1406) imply: % 184.19/28.95 | (1604) op(e4, all_30_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (567), (1405) imply: % 184.19/28.95 | (1605) op(e3, all_100_2) = e4 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (566), (1066) imply: % 184.19/28.95 | (1606) op(e3, all_244_3) = e3 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (565), (1078) imply: % 184.19/28.95 | (1607) op(e3, all_8_2) = e2 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (564), (1404) imply: % 184.19/28.95 | (1608) op(e3, all_36_2) = e1 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (563), (1403) imply: % 184.19/28.95 | (1609) op(e3, all_48_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (557), (1402) imply: % 184.19/28.95 | (1610) op(e2, all_64_2) = e4 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (556), (1401) imply: % 184.19/28.95 | (1611) op(e2, all_10_2) = e3 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (555), (1400) imply: % 184.19/28.95 | (1612) op(e2, all_38_2) = e1 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (554), (881) imply: % 184.19/28.95 | (1613) op(e2, all_40_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (548), (1399) imply: % 184.19/28.95 | (1614) op(e1, all_16_2) = e4 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (547), (1398) imply: % 184.19/28.95 | (1615) op(e1, all_62_2) = e3 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (546), (1397) imply: % 184.19/28.95 | (1616) op(e1, all_4_2) = e2 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (545), (1103) imply: % 184.19/28.95 | (1617) op(e1, all_34_2) = e0 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (539), (1396) imply: % 184.19/28.95 | (1618) op(e0, all_12_2) = e4 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (538), (1072) imply: % 184.19/28.95 | (1619) op(e0, all_22_2) = e3 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (537), (1086) imply: % 184.19/28.95 | (1620) op(e0, all_28_2) = e2 % 184.19/28.95 | % 184.19/28.95 | REDUCE: (536), (1395) imply: % 184.19/28.95 | (1621) op(e0, all_20_2) = e1 % 184.19/28.95 | % 184.19/28.95 | BETA: splitting (138) gives: % 184.19/28.95 | % 184.19/28.95 | Case 1: % 184.19/28.95 | | % 184.19/28.95 | | (1622) ~ (all_4_2 = e0) % 184.19/28.95 | | % 184.19/28.95 | | BETA: splitting (141) gives: % 184.19/28.95 | | % 184.19/28.95 | | Case 1: % 184.19/28.95 | | | % 184.19/28.95 | | | (1623) ~ (all_6_2 = e0) % 184.19/28.95 | | | % 184.19/28.95 | | | BETA: splitting (144) gives: % 184.19/28.95 | | | % 184.19/28.95 | | | Case 1: % 184.19/28.95 | | | | % 184.19/28.95 | | | | (1624) ~ (all_8_2 = e0) % 184.19/28.95 | | | | % 184.19/28.95 | | | | BETA: splitting (147) gives: % 184.19/28.95 | | | | % 184.19/28.95 | | | | Case 1: % 184.19/28.95 | | | | | % 184.19/28.95 | | | | | (1625) ~ (all_10_2 = e1) % 184.19/28.95 | | | | | % 184.19/28.95 | | | | | BETA: splitting (150) gives: % 184.19/28.95 | | | | | % 184.19/28.95 | | | | | Case 1: % 184.19/28.95 | | | | | | % 184.19/28.95 | | | | | | (1626) ~ (all_12_2 = e3) % 184.19/28.95 | | | | | | % 184.19/28.95 | | | | | | BETA: splitting (153) gives: % 184.19/28.95 | | | | | | % 184.19/28.95 | | | | | | Case 1: % 184.19/28.95 | | | | | | | % 184.19/28.95 | | | | | | | (1627) ~ (all_14_2 = e1) % 184.19/28.95 | | | | | | | % 184.19/28.95 | | | | | | | REDUCE: (1356), (1627) imply: % 184.19/28.95 | | | | | | | (1628) ~ (all_12_2 = e1) % 184.19/28.95 | | | | | | | % 184.19/28.95 | | | | | | | BETA: splitting (156) gives: % 184.19/28.95 | | | | | | | % 184.19/28.95 | | | | | | | Case 1: % 184.19/28.95 | | | | | | | | % 184.19/28.96 | | | | | | | | (1629) ~ (all_16_2 = e3) % 184.19/28.96 | | | | | | | | % 184.19/28.96 | | | | | | | | BETA: splitting (159) gives: % 184.19/28.96 | | | | | | | | % 184.19/28.96 | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | % 184.19/28.96 | | | | | | | | | (1630) ~ (all_18_2 = e2) % 184.19/28.96 | | | | | | | | | % 184.19/28.96 | | | | | | | | | REDUCE: (1231), (1630) imply: % 184.19/28.96 | | | | | | | | | (1631) ~ (all_12_2 = e2) % 184.19/28.96 | | | | | | | | | % 184.19/28.96 | | | | | | | | | BETA: splitting (162) gives: % 184.19/28.96 | | | | | | | | | % 184.19/28.96 | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | (1632) ~ (all_20_2 = e3) % 184.19/28.96 | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | BETA: splitting (165) gives: % 184.19/28.96 | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | (1633) ~ (all_22_2 = e2) % 184.19/28.96 | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | BETA: splitting (168) gives: % 184.19/28.96 | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | (1634) ~ (all_24_2 = e2) % 184.19/28.96 | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | REDUCE: (1349), (1634) imply: % 184.19/28.96 | | | | | | | | | | | | (1635) ~ (all_16_2 = e2) % 184.19/28.96 | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | BETA: splitting (174) gives: % 184.19/28.96 | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | (1636) ~ (all_28_2 = e1) % 184.19/28.96 | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | BETA: splitting (177) gives: % 184.19/28.96 | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | (1637) ~ (all_30_2 = e3) % 184.19/28.96 | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | BETA: splitting (180) gives: % 184.19/28.96 | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | (1638) ~ (all_32_2 = e4) % 184.19/28.96 | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | REDUCE: (1352), (1638) imply: % 184.19/28.96 | | | | | | | | | | | | | | | (1639) ~ (all_20_2 = e4) % 184.19/28.96 | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 184.19/28.96 | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | (1640) ~ (all_34_2 = e4) % 184.19/28.96 | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | (1641) ~ (all_36_2 = e0) % 184.19/28.96 | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | (1642) ~ (all_38_2 = e0) % 184.19/28.96 | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | (1643) ~ (all_40_2 = e1) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | (1644) ~ (all_52_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | REDUCE: (1345), (1644) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | (1645) ~ (all_36_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | (1646) ~ (all_56_2 = e4) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1292), (1646) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | (1647) ~ (all_8_2 = e4) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | (1648) ~ (all_58_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1350), (1648) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | (1649) ~ (all_20_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1650) ~ (all_62_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (155), (182), (224), (231), (350), (393), % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (732), (733), (857), (1253), (1265), (1302), % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1428), (1460), (1587), (1591), (1603), (1612), % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1614), (1616), (1622), (1629), (1635), (1640), % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1650), (function-axioms) are inconsistent by % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #569. % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1651) all_62_2 = e2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1652) op(e2, e1) = all_62_1 & $i(all_62_1) & ( ~ % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (all_62_1 = e4) | ( ~ (all_62_0 = e0) & op(e1, % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | e4) = all_62_0 & $i(all_62_0))) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1652) implies: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1653) op(e2, e1) = all_62_1 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1326), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1654) all_112_2 = e2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1500), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1655) ~ (all_244_15 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1476), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1656) ~ (all_84_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1497), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1657) ~ (all_22_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1488), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1658) ~ (all_10_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1658) implies: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1659) ~ (all_10_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1498), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1660) ~ (all_4_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1660) implies: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1661) ~ (all_4_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1615), (1651) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | (1662) op(e1, e2) = e3 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1663) ~ (all_112_2 = e2) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1654), (1663) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1664) $false % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1664) is inconsistent. % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1665) op(e2, e1) = all_112_1 & $i(all_112_1) & ( ~ % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (all_112_1 = e0) | ( ~ (all_112_0 = e4) & op(e1, % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_112_0 & $i(all_112_0))) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1665) implies: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1666) op(e2, e1) = all_112_1 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (1662) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1667) all_4_2 = e3 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | all_112_1, e1, e2, simplifying with (188), (1666) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1668) all_112_1 = all_38_2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_1, % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | all_112_1, e1, e2, simplifying with (1653), (1666) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1669) all_112_1 = all_62_1 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1668), (1669) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1670) all_62_1 = all_38_2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1670) implies: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1671) all_62_1 = all_38_2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1265), (1667) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1672) all_150_2 = e3 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1363), (1667) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1673) all_160_2 = e3 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1535), (1667) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1674) ~ (all_34_2 = e3) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1531), (1667) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1675) ~ (all_28_2 = e3) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1591), (1667) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1676) op(e3, all_38_2) = e2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1616), (1667) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | (1677) op(e1, e3) = e2 % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (350) gives: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1678) ~ (all_150_2 = e3) % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1672), (1678) imply: % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | (1679) $false % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1679) is inconsistent. % 184.19/28.96 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1680) op(e3, e1) = all_150_1 & $i(all_150_1) & ( ~ % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | (all_150_1 = e0) | ( ~ (all_150_0 = e4) & op(e1, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_150_0 & $i(all_150_0))) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1680) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | (1681) op(e3, e1) = all_150_1 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1682) ~ (all_160_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1673), (1682) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1683) $false % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1683) is inconsistent. % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1684) op(e3, e1) = all_160_1 & $i(all_160_1) & ( ~ % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_160_1 = e4) | ( ~ (all_160_0 = e0) & op(e1, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_160_0 & $i(all_160_0))) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1684) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1685) op(e3, e1) = all_160_1 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | all_160_1, e1, e3, simplifying with (185), (1685) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1686) all_160_1 = all_36_2 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_150_1, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | all_160_1, e1, e3, simplifying with (1681), (1685) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1687) all_160_1 = all_150_1 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1686), (1687) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (1688) all_150_1 = all_36_2 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1689) ~ (all_64_2 = e0) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1690) ~ (all_66_2 = e0) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1302), (1690) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1691) ~ (all_16_2 = e0) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1692) ~ (all_76_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (1692) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693) ~ (all_40_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1694) ~ (all_78_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1336), (1694) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1695) ~ (all_10_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (284), (736), (1317), (1431), (1585), % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607), (1611), (1625), (1659), (1693), (1695), % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #565. % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1696) all_78_2 = e4 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1697) op(e4, e2) = all_78_1 & $i(all_78_1) & ( ~ % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_78_1 = e1) | ( ~ (all_78_0 = e0) & op(e2, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_78_0 & $i(all_78_0))) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1697) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1698) op(e4, e2) = all_78_1 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1336), (1696) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1699) all_10_2 = e4 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1699) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1700) all_10_2 = e4 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1361), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1701) all_138_2 = e4 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1481), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1702) ~ (all_244_3 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1475), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1703) ~ (all_84_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1454), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1704) ~ (all_64_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1494), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1705) ~ (all_38_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1490), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706) ~ (all_22_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1611), (1700) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1707) op(e2, e4) = e3 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1708) ~ (all_138_2 = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1701), (1708) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1709) $false % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1709) is inconsistent. % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1710) op(e4, e2) = all_138_1 & $i(all_138_1) & ( ~ % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_138_1 = e0) | ( ~ (all_138_0 = e1) & op(e2, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_138_0 & $i(all_138_0))) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1710) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1711) op(e4, e2) = all_138_1 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (787) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1712) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (498), (1702), (1703), (1712), % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #562. % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1713) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1713) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1714) all_252_7 = e4 & op(e2, e3) = e4 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1714) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1715) all_252_7 = e4 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e3, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (1707) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1716) all_64_2 = e3 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_138_1, e2, e4, simplifying with (140), (1711) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1717) all_138_1 = all_6_2 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_78_1, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_138_1, e2, e4, simplifying with (1698), (1711) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1718) all_138_1 = all_78_1 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1717), (1718) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1719) all_78_1 = all_6_2 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1309), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1720) all_120_2 = e3 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1297), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1721) all_134_2 = e3 % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1438), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722) ~ (all_244_0 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1444), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1723) ~ (all_100_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1456), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1724) ~ (all_40_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1455), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1725) ~ (all_38_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1725) implies: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1726) ~ (all_38_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1452), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1727) ~ (all_16_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1728) ~ (all_12_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1704), (1716) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1729) ~ (e4 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1730) ~ (all_120_2 = e3) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1720), (1730) imply: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1731) $false % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1731) is inconsistent. % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1732) op(e3, e2) = all_120_1 & $i(all_120_1) & ( ~ % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_120_1 = e1) | ( ~ (all_120_0 = e0) & op(e2, % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_120_0 & $i(all_120_0))) % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1732) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1733) op(e3, e2) = all_120_1 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1734) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (504), (1722), (1723), (1734), % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #559. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1735) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1735) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1736) all_252_6 = e3 & op(e2, e4) = e3 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1736) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1737) all_252_6 = e3 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1738) ~ (all_134_2 = e3) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1721), (1738) imply: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1739) $false % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1739) is inconsistent. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1740) op(e3, e2) = all_134_1 & $i(all_134_1) & ( ~ % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_134_1 = e0) | ( ~ (all_134_0 = e1) & op(e2, % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_134_0 & $i(all_134_0))) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1740) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1741) op(e3, e2) = all_134_1 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_134_1, e2, e3, simplifying with (143), (1741) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1742) all_134_1 = all_8_2 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_120_1, % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_134_1, e2, e3, simplifying with (1733), (1741) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1743) all_134_1 = all_120_1 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1742), (1743) imply: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_120_1 = all_8_2 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1744) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1745) all_120_1 = all_8_2 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1746) ~ (all_88_2 = e2) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1242), (1746) imply: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) ~ (all_26_2 = e2) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (1645), (1747), (1748), % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #556. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1749) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) all_252_11 = e2 & op(e2, e1) = e2 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1750) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) all_252_11 = e2 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (146), (1625), (1737), (1752), % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #553. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1753) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1753) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1754) all_252_8 = e1 & op(e2, e2) = e1 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1754) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755) all_252_8 = e1 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1756) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (1707), (1715), (1756), % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #551. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1757) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1757) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1758) all_252_8 = e0 & op(e2, e2) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1755), (1758) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #550. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1759) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1759) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1760) all_252_11 = e0 & op(e2, e1) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1760) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1761) op(e2, e1) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (1642), (1761), (function-axioms) are % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1762) all_252_18 = e0 & op(e2, e0) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1762) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1763) all_252_18 = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1764) op(e2, e0) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1765) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (1765), % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #546. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1766) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1767) all_252_8 = e0 & op(e2, e2) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1755), (1767) are inconsistent by sub-proof % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #550. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1768) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1768) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1769) all_252_14 = e0 & op(e1, e2) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1769) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1770) op(e1, e2) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (1770), (function-axioms) are % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1771) all_252_22 = e0 & op(e0, e2) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1771) implies: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1772) all_252_22 = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1773) op(e0, e2) = e0 % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1774) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (1631), (1633), (1774), % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1775) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1776) all_252_22 = e2 & op(e0, e2) = e2 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1772), (1776) are inconsistent by sub-proof % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #541. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1777) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1777) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1778) all_252_23 = e2 & op(e0, e1) = e2 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1649), (1778), (function-axioms) are % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1779) all_252_24 = e2 & op(e0, e0) = e2 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1779) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) all_252_24 = e2 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1781) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1781) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1782) all_252_20 = e4 & op(e0, e4) = e4 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1782) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1783) all_252_20 = e4 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1784) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1784) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1785) all_252_4 = e4 & op(e4, e2) = e4 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1785) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1786) all_252_4 = e4 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1787) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1787) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1788) all_252_16 = e3 & op(e4, e0) = e3 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1788) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1789) op(e4, e0) = e3 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (1637), (1789), (function-axioms) are % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1790) all_252_17 = e3 & op(e3, e0) = e3 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1790) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1791) all_252_17 = e3 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (757) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1792) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1792) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1793) all_252_16 = e4 & op(e4, e0) = e4 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1793) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1794) all_252_16 = e4 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (793) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1795) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1795) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1796) all_252_0 = e2 & op(e4, e4) = e2 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1796) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1797) all_252_0 = e2 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (754) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1798) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1799) all_252_16 = e1 & op(e4, e0) = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (1794), (1799) are inconsistent by sub-proof % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #538. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1800) all_252_17 = e1 & op(e3, e0) = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1800) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1801) all_252_17 = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (176), (182), (191), (756), (1637), % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674), (1693), (1780), (1801), (function-axioms) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #534. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1802) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1802) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1803) all_252_18 = e1 & op(e2, e0) = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1803) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804) op(e2, e0) = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (191), (1764), (1804), (function-axioms) are % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #533. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1805) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1805) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1806) all_252_19 = e1 & op(e1, e0) = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1806) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1807) all_252_19 = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1808) op(e1, e0) = e1 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1809) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1809) gives: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1810) all_252_0 = e0 & op(e4, e4) = e0 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1810) implies: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1811) all_252_0 = e0 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1797), (1811) imply: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1812) e2 = e0 % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (1812) imply: % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1813) $false % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1813) is inconsistent. % 184.19/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1814) all_252_2 = e0 & op(e3, e4) = e0 % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1814) implies: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1815) all_252_2 = e0 % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1816) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (155), (1677), (1691), (1816), % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #531. % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1817) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1817) gives: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/28.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) all_252_14 = e0 & op(e1, e2) = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1818) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) op(e1, e2) = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (1819), (function-axioms) are % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1820) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) all_252_15 = e0 & op(e1, e1) = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1821) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) all_252_15 = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (762) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_13 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e3) = e4) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1823) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_252_12 = e4 & op(e1, e4) = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1824) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) all_252_12 = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (790) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1826) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1826) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) all_252_0 = e1 & op(e4, e4) = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1827) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) all_252_0 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1797), (1828) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) e2 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1829) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1830) $false % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1830) is inconsistent. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1831) all_252_2 = e1 & op(e3, e4) = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1831) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1832) all_252_2 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1815), (1832) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1833) e1 = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1833) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1834) e1 = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1834) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1835) $false % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1835) is inconsistent. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1836) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 & % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1836) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1837) all_252_6 = e1 & op(e2, e4) = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1837) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) all_252_6 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1737), (1838) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1839) e3 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1839) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) e3 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1791), (1840) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) all_252_17 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (176), (182), (191), (756), (1637), % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674), (1693), (1780), (1841), (function-axioms) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #534. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1842) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) all_252_12 = e1 & op(e1, e4) = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1843) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) all_252_12 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1825), (1844) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) e4 = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (1845) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) $false % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1846) is inconsistent. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_252_20 = e1 & op(e0, e4) = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1847) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1848) op(e0, e4) = e1 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (1848), (function-axioms) are % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1849) all_252_13 = e4 & op(e1, e3) = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1849) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) op(e1, e3) = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1677), (1850), (function-axioms) are % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_15 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_19 = e4 & % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e4) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1851) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) all_252_14 = e4 & op(e1, e2) = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1852) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) op(e1, e2) = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1662), (1853), (function-axioms) are % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #528. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_19 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4) % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1854) gives: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) all_252_15 = e4 & op(e1, e1) = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1855) implies: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) all_252_15 = e4 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1822), (1856) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) e4 = e0 % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1857) imply: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) $false % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1858) is inconsistent. % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) all_252_19 = e4 & op(e1, e0) = e4 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1859) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) op(e1, e0) = e4 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (1808), (1860), (function-axioms) are % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #527. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) all_252_19 = e0 & op(e1, e0) = e0 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1861) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) all_252_19 = e0 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1807), (1862) are inconsistent by sub-proof % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #526. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1863) gives: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1864) all_252_6 = e0 & op(e2, e4) = e0 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1707), (1864), (function-axioms) are % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #552. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1865) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1865) gives: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1866) all_252_12 = e0 & op(e1, e4) = e0 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1691), (1866), (function-axioms) are % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #532. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1867) all_252_20 = e0 & op(e0, e4) = e0 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1867) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1868) all_252_20 = e0 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (1783), (1868) are inconsistent by sub-proof % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #525. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1869) all_252_24 = e1 & op(e0, e0) = e1 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1780), (1869) are inconsistent by sub-proof % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #524. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1870) all_252_1 = e2 & op(e4, e3) = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (1656), (1870), (function-axioms) are % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #523. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1871) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 & % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2) % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1871) gives: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1872) all_252_4 = e2 & op(e4, e2) = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1872) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1873) all_252_4 = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1786), (1873) imply: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1874) e4 = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (1874) imply: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1875) $false % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1875) is inconsistent. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1876) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 = % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2) % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1876) gives: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1877) all_252_9 = e2 & op(e4, e1) = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (1747), (1877), (function-axioms) are % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #558. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1878) all_252_16 = e2 & op(e4, e0) = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1878) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1879) all_252_16 = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1794), (1879) imply: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1880) e4 = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1880) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1881) e4 = e2 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (1881) imply: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1882) $false % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1882) is inconsistent. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1883) all_252_17 = e4 & op(e3, e0) = e4 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1883) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1884) all_252_17 = e4 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1791), (1884) imply: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1885) e4 = e3 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (1885) imply: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1886) $false % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1886) is inconsistent. % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1887) gives: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_252_18 = e4 & op(e2, e0) = e4 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1888) implies: % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) all_252_18 = e4 % 184.37/29.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1763), (1889) imply: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) e4 = e0 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1890) imply: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) $false % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1891) is inconsistent. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1892) gives: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) all_252_19 = e4 & op(e1, e0) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1893) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) op(e1, e0) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (1640), (1894), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) all_252_24 = e4 & op(e0, e0) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1780), (1895) are inconsistent by sub-proof % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #522. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (182), (191), (1674), (1693), (1780), % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1896), (function-axioms) are inconsistent by % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #535. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) all_252_5 = e4 & op(e3, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1897) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) op(e3, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (1647), (1898), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 & % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4) % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1899) gives: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) all_252_8 = e4 & op(e2, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1900) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) all_252_8 = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1755), (1901) imply: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1902) e4 = e1 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (1902) imply: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903) $false % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1903) is inconsistent. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1904) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4) % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1904) gives: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) all_252_14 = e4 & op(e1, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1905) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) op(e1, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (1662), (1906), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #528. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) all_252_22 = e4 & op(e0, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1907) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) op(e0, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (1773), (1908), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #520. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) all_252_21 = e4 & op(e0, e3) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1706), (1909), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1910) gives: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_252_22 = e4 & op(e0, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1911) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) op(e0, e2) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (1773), (1912), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #520. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1913) gives: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) all_252_23 = e4 & op(e0, e1) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1639), (1914), (function-axioms) are % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #518. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_252_24 = e4 & op(e0, e0) = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1915) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) all_252_24 = e4 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1780), (1916) imply: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) e4 = e2 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1917) implies: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) e4 = e2 % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (1918) imply: % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) $false % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1919) is inconsistent. % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1920) gives: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) all_252_11 = e1 & op(e2, e1) = e1 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1751), (1921) are inconsistent by sub-proof % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #517. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_252_18 = e1 & op(e2, e0) = e1 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1922) implies: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1923) op(e2, e0) = e1 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (1643), (1923), (function-axioms) are % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #516. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1924) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (486), (1649), (1655), (1924), % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #514. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925) all_88_2 = e2 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1242), (1925) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1926) all_26_2 = e2 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1542), (1926) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1927) ~ (all_38_2 = e2) % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (735) gives: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1928) all_250_13 = e4 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (1928) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1929) all_38_2 = e4 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1705), (1929) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1930) $false % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1930) is inconsistent. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1931) all_250_13 = e3 | all_250_13 = e2 | all_250_13 = % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_13 = e0 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1931) gives: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_250_13 = e3 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (1932) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1933) all_38_2 = e3 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1726), (1933) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1934) $false % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1934) is inconsistent. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1935) all_250_13 = e2 | all_250_13 = e1 | all_250_13 = % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1935) gives: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936) all_250_13 = e2 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (1936) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) all_38_2 = e2 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1927), (1937) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) $false % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1938) is inconsistent. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) all_250_13 = e1 | all_250_13 = e0 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1939) gives: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) all_250_13 = e1 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (1940) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_38_2 = e1 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1676), (1941) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) op(e3, e1) = e2 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (1645), (1942), (function-axioms) are % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #557. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) all_250_13 = e0 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (1943) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) all_38_2 = e0 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1642), (1944) imply: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) $false % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1945) is inconsistent. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (155), (1626), (1629), (1946), % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #511. % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1947) gives: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_252_13 = e4 & op(e1, e3) = e4 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1948) implies: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) op(e1, e3) = e4 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (1677), (1949), (function-axioms) are % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529. % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) all_252_21 = e4 & op(e0, e3) = e4 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1706), (1950), (function-axioms) are % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) all_76_2 = e3 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (1951) imply: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_40_2 = e3 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1952) implies: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1953) all_40_2 = e3 % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1578), (1953) imply: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1954) ~ (all_244_24 = e3) % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1496), (1953) imply: % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1955) ~ (all_10_2 = e3) % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.37/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1955) implies: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1956) ~ (all_10_2 = e3) % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1613), (1953) imply: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1957) op(e2, e3) = e0 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1958) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1958) gives: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959) all_252_20 = e3 & op(e0, e4) = e3 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1959) implies: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1960) op(e0, e4) = e3 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (1960), (function-axioms) are % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961) all_252_21 = e3 & op(e0, e3) = e3 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1961) implies: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1962) op(e0, e3) = e3 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_2, e3, % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (164), (1962) gives: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1963) all_22_2 = e3 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0, % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (1957) gives: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1964) all_10_2 = e0 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1956), (1964) imply: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1965) ~ (e3 = e0) % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1595), (1609), (1963), (function-axioms) are % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #510. % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1966) gives: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1967) all_252_22 = e3 & op(e0, e2) = e3 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1675), (1967), (function-axioms) are % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1968) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (480), (1632), (1954), (1968), % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506. % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.56/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1969) all_66_2 = e0 % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (1302), (1614), (1640), (1969), % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #570. % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1970) all_64_2 = e0 % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (1970) imply: % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1971) ~ (all_12_2 = e0) % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (730), (1427), (1593), (1604), (1626), (1628), % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631), (1971), (function-axioms) are inconsistent % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503. % 184.57/29.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1972) all_58_2 = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1350), (1621), (1636), (1972), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | #501. % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1973) all_56_2 = e4 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1292), (1973) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1974) all_8_2 = e4 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1526), (1974) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1975) ~ (all_48_2 = e4) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1586), (1974) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1976) op(e4, all_10_2) = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1607), (1974) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1977) op(e3, e4) = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2, % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | e2, e4, e3, simplifying with (280), (1977) gives: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1978) all_100_2 = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1437), (1978) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1979) ~ (all_244_0 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1451), (1978) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1980) ~ (all_48_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | SIMP: (1980) implies: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1981) ~ (all_48_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1445), (1978) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1982) ~ (all_16_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1983) ~ (all_62_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (155), (182), (224), (231), (350), (393), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (732), (733), (857), (1253), (1265), (1302), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1428), (1460), (1587), (1591), (1603), (1612), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1614), (1616), (1622), (1629), (1635), (1640), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1983), (function-axioms) are inconsistent by % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | sub-proof #569. % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1984) all_62_2 = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1488), (1984) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1985) ~ (all_10_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1985) implies: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1986) ~ (all_10_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (191), (246), (249), (284), (421), (504), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (736), (738), (1212), (1317), (1336), (1343), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1431), (1433), (1572), (1585), (1596), (1607), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1609), (1611), (1619), (1625), (1641), (1975), % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | (1976), (1979), (1981), (1986), (function-axioms) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #497. % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1987) all_52_2 = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1988) op(e2, e3) = all_52_1 & $i(all_52_1) & ( ~ % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (all_52_1 = e4) | ( ~ (all_52_0 = e0) & op(e3, % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | e4) = all_52_0 & $i(all_52_0))) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | ALPHA: (1988) implies: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1989) op(e2, e3) = all_52_1 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1345), (1987) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1990) all_36_2 = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1170), (1990) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1991) all_74_2 = e2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | REDUCE: (1485), (1990) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1992) ~ (all_244_3 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | REDUCE: (1590), (1990) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1993) op(e2, all_62_2) = e1 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | REDUCE: (1608), (1990) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | (1994) op(e3, e2) = e1 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1995) ~ (all_74_2 = e2) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1991), (1995) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1996) $false % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | CLOSE: (1996) is inconsistent. % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1997) op(e2, e3) = all_74_1 & $i(all_74_1) & ( ~ % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (all_74_1 = e0) | ( ~ (all_74_0 = e4) & op(e3, % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | e0) = all_74_0 & $i(all_74_0))) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1997) implies: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1998) op(e2, e3) = all_74_1 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | all_74_1, e3, e2, simplifying with (146), (1998) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | gives: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (1999) all_74_1 = all_10_2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | all_74_1, e3, e2, simplifying with (1989), (1998) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | gives: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (2000) all_74_1 = all_52_1 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e1, % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (1994) gives: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (2001) all_8_2 = e1 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1999), (2000) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (2002) all_52_1 = all_10_2 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (2001) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (2003) ~ (all_244_8 = e1) % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1585), (2001) imply: % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | (2004) op(all_10_2, e1) = e3 % 184.57/29.05 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1586), (2001) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | (2005) op(e1, all_10_2) = e2 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | (2006) ~ (all_62_2 = e2) % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | (2007) ~ (all_76_2 = e3) % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (2007) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | (2008) ~ (all_40_2 = e3) % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2009) ~ (all_78_2 = e4) % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1336), (2009) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2010) ~ (all_10_2 = e4) % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (146), (164), (188), (191), (224), (252), % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (257), (258), (284), (440), (492), (498), (736), % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (785), (972), (1251), (1317), (1431), (1475), % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (1529), (1585), (1601), (1602), (1607), (1611), % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (1625), (1633), (1992), (2004), (2006), (2008), % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2010), (function-axioms) are inconsistent by % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #492. % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2011) all_78_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1336), (2011) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2012) all_10_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2012) implies: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2013) all_10_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2005), (2013) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | (2014) op(e1, e4) = e2 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1635), (2014), (function-axioms) are % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #573. % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | (2015) all_76_2 = e3 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (2015) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | (2016) all_40_2 = e3 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2016) implies: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | (2017) all_40_2 = e3 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (161), (385), (1367), (1613), (1632), % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | (2004), (2017), (function-axioms) are inconsistent % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #491. % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | (2018) all_62_2 = e2 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1993), (2018) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | (2019) op(e2, e2) = e1 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (2003), (2019), (function-axioms) are % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | (2020) all_40_2 = e1 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | REDUCE: (1613), (2020) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | | (2021) op(e2, e1) = e0 % 184.57/29.06 | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (1642), (2021), (function-axioms) are % 184.57/29.06 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 184.57/29.06 | | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | (2022) all_38_2 = e0 % 184.57/29.06 | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | REDUCE: (1557), (2022) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | | (2023) ~ (all_20_2 = e0) % 184.57/29.06 | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | SIMP: (2023) implies: % 184.57/29.06 | | | | | | | | | | | | | | | | | | (2024) ~ (all_20_2 = e0) % 184.57/29.06 | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (219), (727), (1350), (1424), (1599), % 184.57/29.06 | | | | | | | | | | | | | | | | | | (1617), (1621), (1632), (1636), (1639), (2024), % 184.57/29.06 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.06 | | | | | | | | | | | | | | | | | | #484. % 184.57/29.06 | | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | (2025) all_36_2 = e0 % 184.57/29.06 | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | REDUCE: (1552), (2025) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | | (2026) ~ (all_20_2 = e0) % 184.57/29.06 | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | SIMP: (2026) implies: % 184.57/29.06 | | | | | | | | | | | | | | | | | (2027) ~ (all_20_2 = e0) % 184.57/29.06 | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (219), (727), (1350), (1424), (1599), % 184.57/29.06 | | | | | | | | | | | | | | | | | (1617), (1621), (1632), (1636), (1639), (2027), % 184.57/29.06 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.06 | | | | | | | | | | | | | | | | | #484. % 184.57/29.06 | | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | (2028) all_34_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | COMBINE_EQS: (1379), (2028) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | (2029) all_232_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | REDUCE: (1617), (2028) imply: % 184.57/29.06 | | | | | | | | | | | | | | | | (2030) op(e1, e4) = e0 % 184.57/29.06 | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | | REF_CLOSE: (155), (463), (730), (1427), (1457), (1593), % 184.57/29.06 | | | | | | | | | | | | | | | | (1604), (1626), (1628), (1631), (2029), (2030), % 184.57/29.06 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.06 | | | | | | | | | | | | | | | | #483. % 184.57/29.06 | | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | (2031) all_32_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | COMBINE_EQS: (1352), (2031) imply: % 184.57/29.06 | | | | | | | | | | | | | | | (2032) all_20_2 = e4 % 184.57/29.06 | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | REDUCE: (1621), (2032) imply: % 184.57/29.06 | | | | | | | | | | | | | | | (2033) op(e0, e4) = e1 % 184.57/29.06 | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (2033), (function-axioms) are % 184.57/29.06 | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 184.57/29.06 | | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | End of split % 184.57/29.06 | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | Case 2: % 184.57/29.06 | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | (2034) all_30_2 = e3 % 184.57/29.06 | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | COMBINE_EQS: (1200), (2034) imply: % 184.57/29.06 | | | | | | | | | | | | | | (2035) all_236_2 = e3 % 184.57/29.06 | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | REDUCE: (1571), (2034) imply: % 184.57/29.06 | | | | | | | | | | | | | | (2036) ~ (all_244_24 = e3) % 184.57/29.06 | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | REDUCE: (1604), (2034) imply: % 184.57/29.06 | | | | | | | | | | | | | | (2037) op(e4, e3) = e0 % 184.57/29.06 | | | | | | | | | | | | | | % 184.57/29.06 | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (164), (173), (255), (257), (469), % 184.57/29.06 | | | | | | | | | | | | | | (480), (752), (1332), (1477), (1595), (1609), % 184.57/29.06 | | | | | | | | | | | | | | (1620), (1626), (1632), (1633), (2035), (2036), % 184.57/29.06 | | | | | | | | | | | | | | (2037), (function-axioms) are inconsistent by % 184.57/29.06 | | | | | | | | | | | | | | sub-proof #480. % 184.57/29.07 | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | End of split % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | Case 2: % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | (2038) all_28_2 = e1 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (137), (140), (143), (149), (161), % 184.57/29.07 | | | | | | | | | | | | | (164), (480), (492), (521), (750), (773), (1468), % 184.57/29.07 | | | | | | | | | | | | | (1503), (1538), (1563), (1620), (1622), (1623), % 184.57/29.07 | | | | | | | | | | | | | (1624), (2038), (function-axioms) are inconsistent % 184.57/29.07 | | | | | | | | | | | | | by sub-proof #472. % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | End of split % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | Case 2: % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | (2039) all_24_2 = e2 % 184.57/29.07 | | | | | | | | | | | | (2040) op(e2, e1) = all_24_1 & $i(all_24_1) & ( ~ % 184.57/29.07 | | | | | | | | | | | | (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e1, % 184.57/29.07 | | | | | | | | | | | | e3) = all_24_0 & $i(all_24_0))) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | ALPHA: (2040) implies: % 184.57/29.07 | | | | | | | | | | | | (2041) op(e2, e1) = all_24_1 % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | COMBINE_EQS: (1349), (2039) imply: % 184.57/29.07 | | | | | | | | | | | | (2042) all_16_2 = e2 % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | COMBINE_EQS: (867), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2043) all_152_2 = e2 % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1462), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2044) ~ (all_244_15 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1445), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2045) ~ (all_100_2 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1452), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2046) ~ (all_64_2 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1459), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2047) ~ (all_62_2 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1457), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2048) ~ (all_12_2 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1460), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2049) ~ (all_4_2 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | SIMP: (2049) implies: % 184.57/29.07 | | | | | | | | | | | | (2050) ~ (all_4_2 = e2) % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1588), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2051) op(all_26_2, e2) = e1 % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | REDUCE: (1614), (2042) imply: % 184.57/29.07 | | | | | | | | | | | | (2052) op(e1, e2) = e4 % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | BETA: splitting (353) gives: % 184.57/29.07 | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | (2053) ~ (all_152_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | REDUCE: (2043), (2053) imply: % 184.57/29.07 | | | | | | | | | | | | | (2054) $false % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | CLOSE: (2054) is inconsistent. % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | Case 2: % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | (2055) op(e2, e1) = all_152_1 & $i(all_152_1) & ( ~ % 184.57/29.07 | | | | | | | | | | | | | (all_152_1 = e0) | ( ~ (all_152_0 = e3) & op(e1, % 184.57/29.07 | | | | | | | | | | | | | e0) = all_152_0 & $i(all_152_0))) % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | ALPHA: (2055) implies: % 184.57/29.07 | | | | | | | | | | | | | (2056) op(e2, e1) = all_152_1 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, % 184.57/29.07 | | | | | | | | | | | | | e2, e1, simplifying with (137), (2052) gives: % 184.57/29.07 | | | | | | | | | | | | | (2057) all_4_2 = e4 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, % 184.57/29.07 | | | | | | | | | | | | | all_152_1, e1, e2, simplifying with (188), (2056) % 184.57/29.07 | | | | | | | | | | | | | gives: % 184.57/29.07 | | | | | | | | | | | | | (2058) all_152_1 = all_38_2 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1, % 184.57/29.07 | | | | | | | | | | | | | all_152_1, e1, e2, simplifying with (2041), (2056) % 184.57/29.07 | | | | | | | | | | | | | gives: % 184.57/29.07 | | | | | | | | | | | | | (2059) all_152_1 = all_24_1 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | COMBINE_EQS: (2058), (2059) imply: % 184.57/29.07 | | | | | | | | | | | | | (2060) all_38_2 = all_24_1 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | SIMP: (2060) implies: % 184.57/29.07 | | | | | | | | | | | | | (2061) all_38_2 = all_24_1 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | REDUCE: (1533), (2057) imply: % 184.57/29.07 | | | | | | | | | | | | | (2062) ~ (all_244_15 = e4) % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | REDUCE: (1494), (2061) imply: % 184.57/29.07 | | | | | | | | | | | | | (2063) ~ (all_24_1 = all_10_2) % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | REDUCE: (1511), (2057) imply: % 184.57/29.07 | | | | | | | | | | | | | (2064) ~ (all_6_2 = e4) % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | REDUCE: (1592), (2057), (2061) imply: % 184.57/29.07 | | | | | | | | | | | | | (2065) op(all_24_1, e4) = e1 % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | BETA: splitting (174) gives: % 184.57/29.07 | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | (2066) ~ (all_28_2 = e1) % 184.57/29.07 | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | BETA: splitting (180) gives: % 184.57/29.07 | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | (2067) ~ (all_32_2 = e4) % 184.57/29.07 | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | REDUCE: (1352), (2067) imply: % 184.57/29.07 | | | | | | | | | | | | | | | (2068) ~ (all_20_2 = e4) % 184.57/29.07 | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 184.57/29.07 | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | (2069) ~ (all_38_2 = e0) % 184.57/29.07 | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | (2070) ~ (all_40_2 = e1) % 184.57/29.07 | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | BETA: splitting (204) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | (2071) ~ (all_48_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | (2072) ~ (all_52_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | REDUCE: (1345), (2072) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | (2073) ~ (all_36_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | (2074) ~ (all_58_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | REDUCE: (1350), (2074) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | (2075) ~ (all_20_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | (2076) ~ (all_64_2 = e0) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | (2077) ~ (all_76_2 = e3) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (2077) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | (2078) ~ (all_40_2 = e3) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | (2079) ~ (all_78_2 = e4) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1336), (2079) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | (2080) ~ (all_10_2 = e4) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | (2081) ~ (all_80_2 = e3) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (2081) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | (2082) ~ (all_6_2 = e3) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2083) ~ (all_88_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1242), (2083) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2084) ~ (all_26_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (2085) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (2073), (2084), (2085), % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | #556. % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (2086) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2086) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2087) all_252_11 = e2 & op(e2, e1) = e2 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2087) implies: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) op(e2, e1) = e2 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_24_1, e2, % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (2041), (2088) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2089) all_24_1 = e2 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2063), (2089) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090) ~ (all_10_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2090) implies: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2091) ~ (all_10_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (284), (736), (1317), (1431), (1585), % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607), (1611), (1625), (2078), (2080), (2091), % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | #565. % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2092) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (486), (2044), (2075), (2092), % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | #514. % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2093) all_88_2 = e2 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1242), (2093) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2094) all_26_2 = e2 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2094) implies: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2095) all_26_2 = e2 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1515), (2095) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2096) ~ (all_6_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2096) implies: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2097) ~ (all_6_2 = e2) % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2051), (2095) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | (2098) op(e2, e2) = e1 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (745) gives: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (2099) all_250_2 = e4 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1436), (2099) imply: % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) all_6_2 = e4 % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.07 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2100) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2101) all_6_2 = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2064), (2101) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2102) $false % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2102) is inconsistent. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2103) all_250_2 = e3 | all_250_2 = e2 | all_250_2 = e1 | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_2 = e0 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2103) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2104) all_250_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1436), (2104) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2105) all_6_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2105) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106) all_6_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2082), (2106) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2107) $false % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2107) is inconsistent. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2108) all_250_2 = e2 | all_250_2 = e1 | all_250_2 = e0 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2108) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2109) all_250_2 = e2 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1436), (2109) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2110) all_6_2 = e2 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2110) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2111) all_6_2 = e2 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2097), (2111) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2112) $false % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2112) is inconsistent. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2113) all_250_2 = e1 | all_250_2 = e0 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2113) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_250_2 = e1 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1436), (2114) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) all_6_2 = e1 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2115) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) all_6_2 = e1 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1510), (2116) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) ~ (all_244_8 = e1) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (2098), (2117), (function-axioms) are % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_250_2 = e0 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1436), (2118) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) all_6_2 = e0 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2119) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_6_2 = e0 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1623), (2120) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) $false % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2121) is inconsistent. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (2122) all_80_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1251), (2122) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (2123) all_6_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (257), (284), (440), (736), (972), (1317), % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (1431), (1475), (1585), (1602), (1607), (1611), % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (1625), (2078), (2080), (2123), (function-axioms) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #493. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2124) all_78_2 = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2125) op(e4, e2) = all_78_1 & $i(all_78_1) & ( ~ % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (all_78_1 = e1) | ( ~ (all_78_0 = e0) & op(e2, % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_78_0 & $i(all_78_0))) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2125) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2126) op(e4, e2) = all_78_1 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1336), (2124) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2127) all_10_2 = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2127) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2128) all_10_2 = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1361), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2129) all_138_2 = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1481), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2130) ~ (all_244_3 = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1475), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2131) ~ (all_84_2 = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1454), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2132) ~ (all_64_2 = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1488), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2133) ~ (all_62_2 = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1490), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2134) ~ (all_22_2 = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1586), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2135) op(all_8_2, e4) = e2 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1611), (2128) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | (2136) op(e2, e4) = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (335) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (2137) ~ (all_138_2 = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2129), (2137) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (2138) $false % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2138) is inconsistent. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (2139) op(e4, e2) = all_138_1 & $i(all_138_1) & ( ~ % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_138_1 = e0) | ( ~ (all_138_0 = e1) & op(e2, % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_138_0 & $i(all_138_0))) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2139) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | (2140) op(e4, e2) = all_138_1 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (787) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | (2141) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (498), (2130), (2131), (2141), % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | #562. % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | (2142) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2142) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) all_252_7 = e4 & op(e2, e3) = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2143) implies: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) all_252_7 = e4 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e3, % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (2136) gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) all_64_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | all_138_1, e2, e4, simplifying with (140), (2140) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) all_138_1 = all_6_2 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_78_1, % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | all_138_1, e2, e4, simplifying with (2126), (2140) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) all_138_1 = all_78_1 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2146), (2147) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_78_1 = all_6_2 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1309), (2145) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2149) all_120_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1297), (2145) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2150) all_134_2 = e3 % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1438), (2145) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2151) ~ (all_244_0 = e3) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1444), (2145) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2152) ~ (all_100_2 = e3) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (2145) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2153) ~ (all_12_2 = e3) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2132), (2145) imply: % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (2154) ~ (e4 = e3) % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1583), (2145) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (2155) op(e3, all_6_2) = e4 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (309) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2156) ~ (all_120_2 = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2149), (2156) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) $false % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2157) is inconsistent. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158) op(e3, e2) = all_120_1 & $i(all_120_1) & ( ~ % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_120_1 = e1) | ( ~ (all_120_0 = e0) & op(e2, % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_120_0 & $i(all_120_0))) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2158) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2159) op(e3, e2) = all_120_1 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2160) ~ (all_134_2 = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2150), (2160) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2161) $false % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2161) is inconsistent. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2162) op(e3, e2) = all_134_1 & $i(all_134_1) & ( ~ % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_134_1 = e0) | ( ~ (all_134_0 = e1) & op(e2, % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_134_0 & $i(all_134_0))) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2162) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2163) op(e3, e2) = all_134_1 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2164) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (504), (2151), (2152), (2164), % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #559. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2165) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2165) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2166) all_252_6 = e3 & op(e2, e4) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2166) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2167) all_252_6 = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_134_1, e2, e3, simplifying with (143), (2163) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2168) all_134_1 = all_8_2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_120_1, % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_134_1, e2, e3, simplifying with (2159), (2163) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2169) all_134_1 = all_120_1 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2168), (2169) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2170) all_120_1 = all_8_2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2170) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2171) all_120_1 = all_8_2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2172) ~ (all_80_2 = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (2172) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2173) ~ (all_6_2 = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2174) ~ (all_82_2 = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1332), (2174) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175) ~ (all_28_2 = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2176) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2176) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2177) all_252_4 = e3 & op(e4, e2) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2177) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2178) op(e4, e2) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (2173), (2178), (function-axioms) are % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2179) all_252_5 = e3 & op(e3, e2) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2179) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2180) all_252_5 = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2181) op(e3, e2) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2182) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2182) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2183) all_252_2 = e2 & op(e3, e4) = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2183) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2184) op(e3, e4) = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (2045), (2184), (function-axioms) are % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #471. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2185) all_252_3 = e2 & op(e3, e3) = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2185) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2186) op(e3, e3) = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e3, % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (2181) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2187) all_8_2 = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_3, % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, e3, simplifying with (498), (2186) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2188) all_244_3 = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1448), (2188) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2189) ~ (all_100_2 = e2) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2135), (2187) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2190) op(e3, e4) = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (2045), (2190), (function-axioms) are % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #471. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2191) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 & % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2191) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2192) all_252_5 = e2 & op(e3, e2) = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2192) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2193) all_252_5 = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2180), (2193) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2194) e3 = e2 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (2194) imply: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2195) $false % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2195) is inconsistent. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2196) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (203), (2071), (2073), (2196), % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #469. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2197) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2197) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2198) all_252_8 = e3 & op(e2, e2) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2198) implies: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2199) all_252_8 = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2200) op(e2, e2) = e3 % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2201) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (2136), (2144), (2201), % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #551. % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2202) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2202) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2203) all_252_8 = e0 & op(e2, e2) = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2203) implies: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2204) op(e2, e2) = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (2200), (2204), (function-axioms) are % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468. % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2205) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2205) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2206) all_252_11 = e0 & op(e2, e1) = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2206) implies: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2207) op(e2, e1) = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2069), (2207), (function-axioms) are % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2208) all_252_18 = e0 & op(e2, e0) = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2208) implies: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2209) all_252_18 = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210) op(e2, e0) = e0 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (770) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2211) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e3) = e2) % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2211) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2212) all_252_6 = e2 & op(e2, e4) = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (2046), (2212), (function-axioms) are % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #467. % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213) all_252_7 = e2 & op(e2, e3) = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2213) implies: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2214) all_252_7 = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2144), (2214) imply: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2215) e4 = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (2215) imply: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) $false % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2216) is inconsistent. % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 & % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2) % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2217) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) all_252_8 = e2 & op(e2, e2) = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2218) implies: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) all_252_8 = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2199), (2219) imply: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) e3 = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (2220) imply: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) $false % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2221) is inconsistent. % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2) % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2222) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) all_252_11 = e2 & op(e2, e1) = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2223) implies: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) all_252_11 = e2 % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 184.57/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (146), (1625), (2167), (2225), % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #553. % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2226) gives: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) all_252_8 = e1 & op(e2, e2) = e1 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2227) implies: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_252_8 = e1 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2199), (2228) imply: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) e3 = e1 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2229) imply: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) $false % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2230) is inconsistent. % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2231) gives: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) all_252_11 = e1 & op(e2, e1) = e1 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2224), (2232) are inconsistent by sub-proof % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #517. % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) all_252_18 = e1 & op(e2, e0) = e1 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2233) implies: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) op(e2, e0) = e1 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (191), (2210), (2234), (function-axioms) are % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #533. % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) all_252_18 = e2 & op(e2, e0) = e2 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2235) implies: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) all_252_18 = e2 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2209), (2236) imply: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) e2 = e0 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2237) implies: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) e2 = e0 % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2238) imply: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) $false % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2239) is inconsistent. % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2240) gives: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) all_252_14 = e3 & op(e1, e2) = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2241) implies: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) op(e1, e2) = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2052), (2242), (function-axioms) are % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #528. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) all_252_22 = e3 & op(e0, e2) = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2175), (2243), (function-axioms) are % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) all_82_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1332), (1620), (1633), (2244), % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #466. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) all_80_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1251), (2245) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2246) all_6_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2246) implies: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2247) all_6_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2155), (2247) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2248) op(e3, e3) = e4 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (2130), (2248), (function-axioms) are % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #563. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2249) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (155), (1626), (1629), (2249), % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #511. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (2250) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2250) gives: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2251) all_252_13 = e4 & op(e1, e3) = e4 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2251) implies: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2252) op(e1, e3) = e4 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e4, % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (224), (2252) gives: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2253) all_62_2 = e4 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2133), (2253) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2254) $false % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2254) is inconsistent. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2255) all_252_21 = e4 & op(e0, e3) = e4 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2134), (2255), (function-axioms) are % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2256) all_76_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (2256) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2257) all_40_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | SIMP: (2257) implies: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2258) all_40_2 = e3 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1578), (2258) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2259) ~ (all_244_24 = e3) % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1613), (2258) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2260) op(e2, e3) = e0 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0, % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (2260) gives: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2261) all_10_2 = e0 % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1490), (2261) imply: % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (2262) ~ (all_22_2 = e0) % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (164), (173), (255), (480), (752), % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (1332), (1595), (1609), (1620), (1626), (1632), % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | (1633), (2259), (2262), (function-axioms) are % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #481. % 184.80/29.11 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | (2263) all_64_2 = e0 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (2263) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | (2264) ~ (all_12_2 = e0) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (730), (1427), (1593), (1604), (1626), (1628), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | (1631), (2264), (function-axioms) are inconsistent % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | by sub-proof #503. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | (2265) all_58_2 = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1350), (1621), (2066), (2265), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | #501. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2266) all_52_2 = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2267) op(e2, e3) = all_52_1 & $i(all_52_1) & ( ~ % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (all_52_1 = e4) | ( ~ (all_52_0 = e0) & op(e3, % 184.80/29.12 | | | | | | | | | | | | | | | | | | | e4) = all_52_0 & $i(all_52_0))) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | ALPHA: (2267) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2268) op(e2, e3) = all_52_1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1345), (2266) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2269) all_36_2 = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | SIMP: (2269) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2270) all_36_2 = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1170), (2270) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2271) all_74_2 = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1485), (2270) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2272) ~ (all_244_3 = e2) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | REDUCE: (1608), (2270) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | (2273) op(e3, e2) = e1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | (2274) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (498), (2045), (2272), (2274), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | #465. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | (2275) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 & % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2275) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | (2276) all_252_5 = e2 & op(e3, e2) = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2276) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | (2277) op(e3, e2) = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (143), (2273), (2277), (function-axioms) are % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #464. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | (2278) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2278) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | (2279) all_252_10 = e2 & op(e3, e1) = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2279) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | (2280) all_252_10 = e2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2281) ~ (all_74_2 = e2) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2271), (2281) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2282) $false % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2282) is inconsistent. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2283) op(e2, e3) = all_74_1 & $i(all_74_1) & ( ~ % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (all_74_1 = e0) | ( ~ (all_74_0 = e4) & op(e3, % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_74_0 & $i(all_74_0))) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2283) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2284) op(e2, e3) = all_74_1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | all_74_1, e3, e2, simplifying with (146), (2284) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2285) all_74_1 = all_10_2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | all_74_1, e3, e2, simplifying with (2268), (2284) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2286) all_74_1 = all_52_1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e1, % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (2273) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2287) all_8_2 = e1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2285), (2286) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2288) all_52_1 = all_10_2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2288) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2289) all_52_1 = all_10_2 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (2287) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2290) ~ (all_244_8 = e1) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1585), (2287) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | (2291) op(all_10_2, e1) = e3 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | (2292) ~ (all_76_2 = e3) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (2292) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | (2293) ~ (all_40_2 = e3) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2294) ~ (all_78_2 = e4) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1336), (2294) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2295) ~ (all_10_2 = e4) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (146), (164), (188), (191), (224), (252), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (257), (258), (284), (440), (492), (498), (736), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (785), (972), (1251), (1317), (1431), (1475), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1529), (1585), (1601), (1602), (1607), (1611), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1625), (1633), (2047), (2272), (2291), (2293), % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2295), (function-axioms) are inconsistent by % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #492. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2296) all_78_2 = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1336), (2296) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2297) all_10_2 = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2297) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2298) all_10_2 = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2291), (2298) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2299) op(e4, e1) = e3 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1611), (2298) imply: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | (2300) op(e2, e4) = e3 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2301) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2301) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2302) all_252_9 = e4 & op(e4, e1) = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2302) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2303) op(e4, e1) = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (170), (2299), (2303), (function-axioms) are % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #463. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2304) all_252_10 = e4 & op(e3, e1) = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2280), (2304) are inconsistent by sub-proof % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | #462. % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (2305) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2305) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2306) all_252_11 = e4 & op(e2, e1) = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2306) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2307) all_252_11 = e4 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2308) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2308) gives: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2309) all_252_6 = e1 & op(e2, e4) = e1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2309) implies: % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2310) op(e2, e4) = e1 % 184.80/29.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e1, % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (2310) gives: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311) all_64_2 = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e3, % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (2300) gives: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2312) all_64_2 = e3 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2311), (2312) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313) e3 = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2313) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2314) $false % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2314) is inconsistent. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315) all_252_7 = e1 & op(e2, e3) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2315) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2316) op(e2, e3) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1625), (2316), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2317) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2317) gives: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2318) all_252_8 = e1 & op(e2, e2) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2318) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2319) op(e2, e2) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (2290), (2319), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2320) gives: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2321) all_252_11 = e1 & op(e2, e1) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2321) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2322) all_252_11 = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2307), (2322) are inconsistent by sub-proof % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #461. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323) all_252_18 = e1 & op(e2, e0) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2323) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2324) op(e2, e0) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (2070), (2324), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #516. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2325) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2325) gives: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2326) all_252_15 = e4 & op(e1, e1) = e4 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2326) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2327) op(e1, e1) = e4 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2062), (2327), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2328) all_252_23 = e4 & op(e0, e1) = e4 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2068), (2328), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #518. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | (2329) all_76_2 = e3 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (2329) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | (2330) all_40_2 = e3 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (161), (385), (1367), (1613), (1632), % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | (2291), (2330), (function-axioms) are inconsistent % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #491. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | (2331) all_252_17 = e2 & op(e3, e0) = e2 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2331) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | (2332) op(e3, e0) = e2 % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (2071), (2332), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #470. % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | (2333) all_48_2 = e2 % 184.80/29.13 | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | REDUCE: (1609), (2333) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | | | (2334) op(e3, e2) = e0 % 184.80/29.13 | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (1624), (2334), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 184.80/29.13 | | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | (2335) all_40_2 = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | REDUCE: (1613), (2335) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | | (2336) op(e2, e1) = e0 % 184.80/29.13 | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2069), (2336), (function-axioms) are % 184.80/29.13 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 184.80/29.13 | | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | End of split % 184.80/29.13 | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | Case 2: % 184.80/29.13 | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | (2337) all_38_2 = e0 % 184.80/29.13 | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2337) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | (2338) all_24_1 = e0 % 184.80/29.13 | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | SIMP: (2338) implies: % 184.80/29.13 | | | | | | | | | | | | | | | | (2339) all_24_1 = e0 % 184.80/29.13 | | | | | | | | | | | | | | | | % 184.80/29.13 | | | | | | | | | | | | | | | | REDUCE: (2065), (2339) imply: % 184.80/29.13 | | | | | | | | | | | | | | | | (2340) op(e0, e4) = e1 % 184.80/29.13 | | | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (2340), (function-axioms) are % 184.80/29.14 | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 184.80/29.14 | | | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | | (2341) all_32_2 = e4 % 184.80/29.14 | | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | | REF_CLOSE: (149), (1352), (1621), (1628), (2341), % 184.80/29.14 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.14 | | | | | | | | | | | | | | | #459. % 184.80/29.14 | | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | (2342) all_28_2 = e1 % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (137), (140), (143), (149), (161), % 184.80/29.14 | | | | | | | | | | | | | | (164), (480), (492), (521), (750), (773), (1468), % 184.80/29.14 | | | | | | | | | | | | | | (1503), (1538), (1563), (1620), (1622), (1623), % 184.80/29.14 | | | | | | | | | | | | | | (1624), (2342), (function-axioms) are inconsistent % 184.80/29.14 | | | | | | | | | | | | | | by sub-proof #472. % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | (2343) all_22_2 = e2 % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1483), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2344) ~ (all_244_3 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1506), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2345) ~ (all_244_24 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1477), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2346) ~ (all_84_2 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1497), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2347) ~ (all_62_2 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1503), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2348) ~ (all_28_2 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1490), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2349) ~ (all_10_2 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | SIMP: (2349) implies: % 184.80/29.14 | | | | | | | | | | | (2350) ~ (all_10_2 = e2) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (1619), (2343) imply: % 184.80/29.14 | | | | | | | | | | | (2351) op(e0, e2) = e3 % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | BETA: splitting (785) gives: % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | Case 1: % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | (2352) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 184.80/29.14 | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | BETA: splitting (2352) gives: % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | Case 1: % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | (2353) all_252_1 = e2 & op(e4, e3) = e2 % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | REF_CLOSE: (257), (2346), (2353), (function-axioms) are % 184.80/29.14 | | | | | | | | | | | | | inconsistent by sub-proof #523. % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | (2354) all_252_3 = e2 & op(e3, e3) = e2 % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | REF_CLOSE: (498), (2344), (2354), (function-axioms) are % 184.80/29.14 | | | | | | | | | | | | | inconsistent by sub-proof #496. % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | (2355) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 184.80/29.14 | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 184.80/29.14 | | | | | | | | | | | | op(e0, e3) = e2) % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | BETA: splitting (2355) gives: % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | Case 1: % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | (2356) all_252_7 = e2 & op(e2, e3) = e2 % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | REF_CLOSE: (146), (2350), (2356), (function-axioms) are % 184.80/29.14 | | | | | | | | | | | | | inconsistent by sub-proof #458. % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | (2357) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 184.80/29.14 | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | BETA: splitting (2357) gives: % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | Case 1: % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | (2358) all_252_13 = e2 & op(e1, e3) = e2 % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | ALPHA: (2358) implies: % 184.80/29.14 | | | | | | | | | | | | | | (2359) op(e1, e3) = e2 % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | REF_CLOSE: (224), (2347), (2359), (function-axioms) are % 184.80/29.14 | | | | | | | | | | | | | | inconsistent by sub-proof #572. % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | (2360) all_252_21 = e2 & op(e0, e3) = e2 % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | ALPHA: (2360) implies: % 184.80/29.14 | | | | | | | | | | | | | | (2361) all_252_21 = e2 % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | | REF_CLOSE: (8), (137), (140), (143), (149), (161), (173), % 184.80/29.14 | | | | | | | | | | | | | | (362), (480), (492), (521), (752), (773), (1362), % 184.80/29.14 | | | | | | | | | | | | | | (1468), (1536), (1538), (1622), (1623), (1624), % 184.80/29.14 | | | | | | | | | | | | | | (2345), (2348), (2351), (2361), (function-axioms) % 184.80/29.14 | | | | | | | | | | | | | | are inconsistent by sub-proof #455. % 184.80/29.14 | | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | End of split % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | (2362) all_20_2 = e3 % 184.80/29.14 | | | | | | | | | | (2363) op(e3, e0) = all_20_1 & $i(all_20_1) & ( ~ % 184.80/29.14 | | | | | | | | | | (all_20_1 = e4) | ( ~ (all_20_0 = e2) & op(e0, % 184.80/29.14 | | | | | | | | | | e4) = all_20_0 & $i(all_20_0))) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | ALPHA: (2363) implies: % 184.80/29.14 | | | | | | | | | | (2364) op(e3, e0) = all_20_1 % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | COMBINE_EQS: (1378), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2365) all_230_2 = e3 % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1560), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2366) ~ (all_244_15 = e3) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1563), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2367) ~ (all_244_24 = e3) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1536), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2368) ~ (all_28_2 = e3) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1545), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2369) ~ (all_26_2 = e3) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1504), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2370) ~ (all_22_2 = e3) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1470), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2371) ~ (all_12_2 = e3) % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | REDUCE: (1621), (2362) imply: % 184.80/29.14 | | | | | | | | | | (2372) op(e0, e3) = e1 % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | BETA: splitting (460) gives: % 184.80/29.14 | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | Case 1: % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | (2373) ~ (all_230_2 = e3) % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | REDUCE: (2365), (2373) imply: % 184.80/29.14 | | | | | | | | | | | (2374) $false % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | | CLOSE: (2374) is inconsistent. % 184.80/29.14 | | | | | | | | | | | % 184.80/29.14 | | | | | | | | | | Case 2: % 184.80/29.14 | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | (2375) op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ % 184.80/29.15 | | | | | | | | | | | (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, % 184.80/29.15 | | | | | | | | | | | e2) = all_230_0 & $i(all_230_0))) % 184.80/29.15 | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | ALPHA: (2375) implies: % 184.80/29.15 | | | | | | | | | | | (2376) op(e3, e0) = all_230_1 % 184.80/29.15 | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | BETA: splitting (752) gives: % 184.80/29.15 | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | (2377) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 184.80/29.15 | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 184.80/29.15 | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | REF_CLOSE: (9), (149), (164), (1626), (2372), (2377), % 184.80/29.15 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 184.80/29.15 | | | | | | | | | | | | #453. % 184.80/29.15 | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | (2378) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 184.80/29.15 | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 184.80/29.15 | | | | | | | | | | | | op(e0, e0) = e3) % 184.80/29.15 | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | BETA: splitting (2378) gives: % 184.80/29.15 | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | (2379) all_252_22 = e3 & op(e0, e2) = e3 % 184.80/29.15 | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | REF_CLOSE: (173), (2368), (2379), (function-axioms) are % 184.80/29.15 | | | | | | | | | | | | | inconsistent by sub-proof #509. % 184.80/29.15 | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | (2380) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 184.80/29.15 | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 184.80/29.15 | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | BETA: splitting (2380) gives: % 184.80/29.15 | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | (2381) all_252_23 = e3 & op(e0, e1) = e3 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | ALPHA: (2381) implies: % 184.80/29.15 | | | | | | | | | | | | | | (2382) all_252_23 = e3 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_2, e1, % 184.80/29.15 | | | | | | | | | | | | | | e3, e0, simplifying with (164), (2372) gives: % 184.80/29.15 | | | | | | | | | | | | | | (2383) all_22_2 = e1 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_2, % 184.80/29.15 | | | | | | | | | | | | | | all_230_1, e0, e3, simplifying with (203), (2376) % 184.80/29.15 | | | | | | | | | | | | | | gives: % 184.80/29.15 | | | | | | | | | | | | | | (2384) all_230_1 = all_48_2 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1, % 184.80/29.15 | | | | | | | | | | | | | | all_230_1, e0, e3, simplifying with (2364), (2376) % 184.80/29.15 | | | | | | | | | | | | | | gives: % 184.80/29.15 | | | | | | | | | | | | | | (2385) all_230_1 = all_20_1 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | COMBINE_EQS: (2384), (2385) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2386) all_48_2 = all_20_1 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | COMBINE_EQS: (1181), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2387) all_104_2 = e1 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | COMBINE_EQS: (1359), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2388) all_118_2 = e1 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (1506), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2389) ~ (all_244_24 = e1) % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (1503), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2390) ~ (all_28_2 = e1) % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (1466), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2391) ~ (all_12_2 = e1) % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (1490), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2392) ~ (all_10_2 = e1) % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (2370), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2393) ~ (e3 = e1) % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (1595), (2383), (2386) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2394) op(e1, all_20_1) = e3 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | REDUCE: (1619), (2383) imply: % 184.80/29.15 | | | | | | | | | | | | | | (2395) op(e0, e1) = e3 % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | BETA: splitting (750) gives: % 184.80/29.15 | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | (2396) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 184.80/29.15 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 184.80/29.15 | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | BETA: splitting (2396) gives: % 184.80/29.15 | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | (2397) all_252_20 = e1 & op(e0, e4) = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | ALPHA: (2397) implies: % 184.80/29.15 | | | | | | | | | | | | | | | | (2398) op(e0, e4) = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (2398), (function-axioms) are % 184.80/29.15 | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | (2399) all_252_21 = e1 & op(e0, e3) = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | ALPHA: (2399) implies: % 184.80/29.15 | | | | | | | | | | | | | | | | (2400) all_252_21 = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | (2401) ~ (all_104_2 = e1) % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | REDUCE: (2387), (2401) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | (2402) $false % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | CLOSE: (2402) is inconsistent. % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | (2403) op(e1, e0) = all_104_1 & $i(all_104_1) & ( ~ % 184.80/29.15 | | | | | | | | | | | | | | | | | (all_104_1 = e4) | ( ~ (all_104_0 = e2) & op(e0, % 184.80/29.15 | | | | | | | | | | | | | | | | | e4) = all_104_0 & $i(all_104_0))) % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | ALPHA: (2403) implies: % 184.80/29.15 | | | | | | | | | | | | | | | | | (2404) op(e1, e0) = all_104_1 % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2405) ~ (all_118_2 = e1) % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | REDUCE: (2388), (2405) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2406) $false % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | CLOSE: (2406) is inconsistent. % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2407) op(e1, e0) = all_118_1 & $i(all_118_1) & ( ~ % 184.80/29.15 | | | | | | | | | | | | | | | | | | (all_118_1 = e2) | ( ~ (all_118_0 = e4) & op(e0, % 184.80/29.15 | | | | | | | | | | | | | | | | | | e2) = all_118_0 & $i(all_118_0))) % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | ALPHA: (2407) implies: % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2408) op(e1, e0) = all_118_1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, % 184.80/29.15 | | | | | | | | | | | | | | | | | | all_118_1, e0, e1, simplifying with (182), (2408) % 184.80/29.15 | | | | | | | | | | | | | | | | | | gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2409) all_118_1 = all_34_2 % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_104_1, % 184.80/29.15 | | | | | | | | | | | | | | | | | | all_118_1, e0, e1, simplifying with (2404), (2408) % 184.80/29.15 | | | | | | | | | | | | | | | | | | gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2410) all_118_1 = all_104_1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2409), (2410) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | (2411) all_104_1 = all_34_2 % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | (2412) ~ (all_24_2 = e2) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | REDUCE: (1349), (2412) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | (2413) ~ (all_16_2 = e2) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2414) ~ (all_26_2 = e0) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (137), (140), (143), (149), % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (170), (173), (185), (186), (188), (189), (191), % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (201), (404), (480), (486), (492), (514), (749), % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (751), (763), (773), (1255), (1353), (1529), % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (1597), (1608), (1612), (1622), (1623), (1624), % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (1631), (2364), (2366), (2367), (2389), (2394), % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2395), (2400), (2414), (function-axioms) are % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2415) all_26_2 = e0 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1341), (2415) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2416) all_44_2 = e0 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (1544), (2415) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2417) ~ (all_244_15 = e0) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (2369), (2415) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2418) ~ (e3 = e0) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (1588), (2415) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2419) op(e0, all_16_2) = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | REDUCE: (1603), (2415) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | (2420) op(e4, e0) = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | (2421) ~ (all_44_2 = e0) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2416), (2421) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | (2422) $false % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2422) is inconsistent. % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (2420) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | (2423) all_30_2 = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1316), (2423) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | (2424) all_54_2 = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1202), (2423) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | (2425) all_132_2 = e1 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1604), (2423) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | (2426) op(e4, e1) = e0 % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | (2427) ~ (all_132_2 = e1) % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2425), (2427) imply: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | (2428) $false % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2428) is inconsistent. % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 184.80/29.15 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | (2429) op(e1, e4) = all_132_1 & $i(all_132_1) & ( ~ % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | (all_132_1 = e3) | ( ~ (all_132_0 = e2) & op(e4, % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | e3) = all_132_0 & $i(all_132_0))) % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2429) implies: % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | (2430) op(e1, e4) = all_132_1 % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | (2431) ~ (all_54_2 = e1) % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2424), (2431) imply: % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | (2432) $false % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2432) is inconsistent. % 185.04/29.15 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | (2433) op(e1, e4) = all_54_1 & $i(all_54_1) & ( ~ % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | (all_54_1 = e2) | ( ~ (all_54_0 = e3) & op(e4, % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_54_0 & $i(all_54_0))) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2433) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | (2434) op(e1, e4) = all_54_1 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | all_132_1, e4, e1, simplifying with (155), (2430) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | (2435) all_132_1 = all_16_2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_54_1, % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | all_132_1, e4, e1, simplifying with (2430), (2434) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | (2436) all_132_1 = all_54_1 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2435), (2436) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | (2437) all_54_1 = all_16_2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | (2438) ~ (all_34_2 = e4) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2439) ~ (all_52_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1345), (2439) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | (2440) ~ (all_36_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) ~ (all_62_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (155), (182), (224), (231), (350), (393), % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (732), (733), (857), (1253), (1265), (1302), % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (1428), (1460), (1587), (1591), (1603), (1612), % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (1614), (1616), (1622), (1629), (2413), (2438), % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2441), (function-axioms) are inconsistent by % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #569. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2442) all_62_2 = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) op(e2, e1) = all_62_1 & $i(all_62_1) & ( ~ % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_62_1 = e4) | ( ~ (all_62_0 = e0) & op(e1, % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_62_0 & $i(all_62_0))) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2443) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) op(e2, e1) = all_62_1 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1326), (2442) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) all_112_2 = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1500), (2442) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2446) ~ (all_244_15 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1501), (2442) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2447) ~ (all_34_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2447) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2448) ~ (all_34_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1459), (2442) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2449) ~ (all_16_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1615), (2442) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2450) op(e1, e2) = e3 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (2442) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (2451) op(e1, e3) = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2452) ~ (all_66_2 = e0) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1302), (2452) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2453) ~ (all_16_2 = e0) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2454) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (185), (2426), (2440), (2454), % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #441. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2455) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2455) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2456) all_252_11 = e2 & op(e2, e1) = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2456) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2457) op(e2, e1) = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2458) ~ (all_112_2 = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2445), (2458) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2459) $false % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2459) is inconsistent. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2460) op(e2, e1) = all_112_1 & $i(all_112_1) & ( ~ % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_112_1 = e0) | ( ~ (all_112_0 = e4) & op(e1, % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_112_0 & $i(all_112_0))) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2460) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2461) op(e2, e1) = all_112_1 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2462) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (155), (2451), (2453), (2462), % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #531. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2463) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2463) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2464) all_252_14 = e0 & op(e1, e2) = e0 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465) op(e1, e2) = e0 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (2465), (function-axioms) are % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2466) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2466) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2467) all_252_15 = e0 & op(e1, e1) = e0 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2467) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2468) op(e1, e1) = e0 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2417), (2468), (function-axioms) are % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2469) all_252_19 = e0 & op(e1, e0) = e0 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2469) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2470) all_252_19 = e0 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (761) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2471) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2471) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2472) all_252_12 = e3 & op(e1, e4) = e3 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (1629), (2472), (function-axioms) are % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #513. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2473) all_252_13 = e3 & op(e1, e3) = e3 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2473) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2474) all_252_13 = e3 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2475) gives: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2476) all_252_12 = e2 & op(e1, e4) = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2476) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2477) op(e1, e4) = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (2413), (2477), (function-axioms) are % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #573. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478) all_252_13 = e2 & op(e1, e3) = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2478) implies: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479) all_252_13 = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2474), (2479) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2480) e3 = e2 % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (2480) imply: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2481) $false % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2481) is inconsistent. % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2482) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2483) all_252_14 = e2 & op(e1, e2) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2483) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2484) op(e1, e2) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (137), (2450), (2484), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #439. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2485) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2485) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2486) all_252_15 = e2 & op(e1, e1) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2486) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2487) op(e1, e1) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2446), (2487), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2488) all_252_19 = e2 & op(e1, e0) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (2448), (2488), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2489) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2489) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2490) all_252_14 = e3 & op(e1, e2) = e3 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (2450) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2491) all_4_2 = e3 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_62_1, % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (2444), (2457) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2492) all_62_1 = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_112_1, e1, e2, simplifying with (188), (2461) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2493) all_112_1 = all_38_2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_1, % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_112_1, e1, e2, simplifying with (2444), (2461) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2494) all_112_1 = all_62_1 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2493), (2494) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2495) all_62_1 = all_38_2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2495) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2496) all_62_1 = all_38_2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2492), (2496) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) all_38_2 = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2497) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) all_38_2 = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1592), (2491), (2498) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2499) op(e2, e3) = e1 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1625), (2499), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) all_252_15 = e3 & op(e1, e1) = e3 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2501) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) op(e1, e1) = e3 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2366), (2502), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) all_252_19 = e3 & op(e1, e0) = e3 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2503) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) all_252_19 = e3 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2470), (2504) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) e3 = e0 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2505) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) $false % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2506) is inconsistent. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2507) gives: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) all_252_15 = e2 & op(e1, e1) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2508) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) op(e1, e1) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2446), (2509), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) all_252_23 = e2 & op(e0, e1) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2510) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2511) op(e0, e1) = e2 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2395), (2511), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #446. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2512) all_66_2 = e0 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1302), (2512) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2513) all_16_2 = e0 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2513) implies: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2514) all_16_2 = e0 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2419), (2514) imply: % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) op(e0, e0) = e1 % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (2389), (2515), (function-axioms) are % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #474. % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.17 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | (2516) all_52_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1345), (2516) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | (2517) all_36_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2517) implies: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | (2518) all_36_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1590), (2518) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | (2519) op(e2, all_62_2) = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1608), (2518) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | (2520) op(e3, e2) = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (431) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e1, % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (143), (2520) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) all_8_2 = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1290), (2521) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_154_2 = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1116), (2521) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) all_220_2 = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1519), (2521) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2524) ~ (all_244_8 = e1) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (356) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2525) ~ (all_154_2 = e1) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2522), (2525) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526) $false % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2526) is inconsistent. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2527) op(e1, e3) = all_154_1 & $i(all_154_1) & ( ~ % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_154_1 = e4) | ( ~ (all_154_0 = e0) & op(e3, % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_154_0 & $i(all_154_0))) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2527) implies: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528) op(e1, e3) = all_154_1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (447) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2529) ~ (all_220_2 = e1) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2523), (2529) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2530) $false % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2530) is inconsistent. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2531) op(e1, e3) = all_220_1 & $i(all_220_1) & ( ~ % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_220_1 = e0) | ( ~ (all_220_0 = e4) & op(e3, % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_220_0 & $i(all_220_0))) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2531) implies: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2532) op(e1, e3) = all_220_1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_220_1, e3, e1, simplifying with (224), (2532) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2533) all_220_1 = all_62_2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_154_1, % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_220_1, e3, e1, simplifying with (2528), (2532) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2534) all_220_1 = all_154_1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2533), (2534) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_154_1 = all_62_2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) ~ (all_62_2 = e2) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (155), (182), (224), (231), (350), (393), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732), (733), (857), (1253), (1265), (1302), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428), (1460), (1587), (1591), (1603), (1612), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614), (1616), (1622), (1629), (2413), (2438), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2536), (function-axioms) are inconsistent by % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #569. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) all_62_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2519), (2537) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) op(e2, e2) = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (2524), (2538), (function-axioms) are % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) all_208_2 = e0 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1373), (2539) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) all_100_2 = e0 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (2540) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) ~ (all_12_2 = e0) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (730), (1427), (1593), (1604), (1626), (1628), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (1631), (2541), (function-axioms) are inconsistent % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | (2542) all_34_2 = e4 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (463), (730), (1379), (1427), (1457), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | (1593), (1604), (1617), (1626), (1628), (1631), % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | (2542), (function-axioms) are inconsistent by % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #437. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2543) all_24_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1349), (2543) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2544) all_16_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | SIMP: (2544) implies: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2545) all_16_2 = e2 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1457), (2545) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2546) ~ (all_12_2 = e2) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1629), (2545) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2547) ~ (e3 = e2) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1588), (2545) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2548) op(all_26_2, e2) = e1 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | REDUCE: (1614), (2545) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2549) op(e1, e2) = e4 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, % 185.04/29.18 | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (2549) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2550) all_4_2 = e4 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1253), (2550) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2551) all_180_2 = e4 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1032), (2550) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | (2552) all_192_2 = e4 % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | (2553) ~ (all_180_2 = e4) % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | REDUCE: (2551), (2553) imply: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | (2554) $false % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | CLOSE: (2554) is inconsistent. % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | % 185.04/29.18 | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.18 | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | (2555) op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | e0) = all_180_0 & $i(all_180_0))) % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | ALPHA: (2555) implies: % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | (2556) op(e4, e1) = all_180_1 % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | (2557) ~ (all_192_2 = e4) % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2552), (2557) imply: % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | (2558) $false % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | CLOSE: (2558) is inconsistent. % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | (2559) op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | e3) = all_192_0 & $i(all_192_0))) % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2559) implies: % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | (2560) op(e4, e1) = all_192_1 % 185.04/29.19 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | all_192_1, e1, e4, simplifying with (170), (2560) % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | (2561) all_192_1 = all_26_2 % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_180_1, % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | all_192_1, e1, e4, simplifying with (2556), (2560) % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | (2562) all_192_1 = all_180_1 % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2561), (2562) imply: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | (2563) all_180_1 = all_26_2 % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (2564) ~ (all_26_2 = e0) % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (137), (140), (143), (149), % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (170), (173), (185), (186), (188), (189), (191), % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (201), (404), (480), (486), (492), (514), (749), % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (751), (763), (773), (1255), (1353), (1529), % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (1597), (1608), (1612), (1622), (1623), (1624), % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (1631), (2364), (2366), (2367), (2389), (2394), % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (2395), (2400), (2564), (function-axioms) are % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #442. % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (2565) all_26_2 = e0 % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2548), (2565) imply: % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | (2566) op(e0, e2) = e1 % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2390), (2566), (function-axioms) are % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.20 | | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.20 | | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | | End of split % 185.04/29.20 | | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | | End of split % 185.04/29.20 | | | | | | | | | | | | | | | | | % 185.04/29.20 | | | | | | | | | | | | | | | | End of split % 185.04/29.20 | | | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | Case 2: % 185.04/29.21 | | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | | (2567) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 185.04/29.21 | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 185.04/29.21 | | | | | | | | | | | | | | | op(e0, e0) = e1) % 185.04/29.21 | | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | | REF_CLOSE: (9), (173), (480), (2382), (2389), (2390), (2567), % 185.04/29.21 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.21 | | | | | | | | | | | | | | | #435. % 185.04/29.21 | | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | Case 2: % 185.04/29.21 | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | (2568) all_252_24 = e3 & op(e0, e0) = e3 % 185.04/29.21 | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | | REF_CLOSE: (480), (2367), (2568), (function-axioms) are % 185.04/29.21 | | | | | | | | | | | | | | inconsistent by sub-proof #507. % 185.04/29.21 | | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | | | % 185.04/29.21 | | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | | % 185.04/29.21 | | | | | | | | | End of split % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | Case 2: % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | | (2569) all_18_2 = e2 % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | | REF_CLOSE: (11), (137), (140), (143), (173), (428), (434), % 185.04/29.21 | | | | | | | | | (480), (492), (521), (773), (828), (1231), (1372), % 185.04/29.21 | | | | | | | | | (1472), (1618), (1622), (1623), (1624), (2569), % 185.04/29.21 | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.21 | | | | | | | | | #433. % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | End of split % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | Case 2: % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | (2570) all_16_2 = e3 % 185.04/29.21 | | | | | | | | (2571) op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = % 185.04/29.21 | | | | | | | | e2) | ( ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 % 185.04/29.21 | | | | | | | | & $i(all_16_0))) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | ALPHA: (2571) implies: % 185.04/29.21 | | | | | | | | (2572) op(e3, e1) = all_16_1 % 185.04/29.21 | | | | | | | | (2573) ~ (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, e2) % 185.04/29.21 | | | | | | | | = all_16_0 & $i(all_16_0)) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | COMBINE_EQS: (1294), (2570) imply: % 185.04/29.21 | | | | | | | | (2574) all_144_2 = e3 % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1439), (2570) imply: % 185.04/29.21 | | | | | | | | (2575) ~ (all_244_0 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1445), (2570) imply: % 185.04/29.21 | | | | | | | | (2576) ~ (all_100_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1452), (2570) imply: % 185.04/29.21 | | | | | | | | (2577) ~ (all_64_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1459), (2570) imply: % 185.04/29.21 | | | | | | | | (2578) ~ (all_62_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1464), (2570) imply: % 185.04/29.21 | | | | | | | | (2579) ~ (all_34_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1457), (2570) imply: % 185.04/29.21 | | | | | | | | (2580) ~ (all_12_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1460), (2570) imply: % 185.04/29.21 | | | | | | | | (2581) ~ (all_4_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | SIMP: (2581) implies: % 185.04/29.21 | | | | | | | | (2582) ~ (all_4_2 = e3) % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1588), (2570) imply: % 185.04/29.21 | | | | | | | | (2583) op(all_26_2, e3) = e1 % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1587), (2570) imply: % 185.04/29.21 | | | | | | | | (2584) op(e3, all_26_2) = e4 % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | REDUCE: (1614), (2570) imply: % 185.04/29.21 | | | | | | | | (2585) op(e1, e3) = e4 % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | BETA: splitting (343) gives: % 185.04/29.21 | | | | | | | | % 185.04/29.21 | | | | | | | | Case 1: % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | | (2586) ~ (all_144_2 = e3) % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | | REDUCE: (2574), (2586) imply: % 185.04/29.21 | | | | | | | | | (2587) $false % 185.04/29.21 | | | | | | | | | % 185.04/29.21 | | | | | | | | | CLOSE: (2587) is inconsistent. % 185.04/29.21 | | | | | | | | | % 185.04/29.22 | | | | | | | | Case 2: % 185.04/29.22 | | | | | | | | | % 185.04/29.22 | | | | | | | | | (2588) op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ % 185.04/29.22 | | | | | | | | | (all_144_1 = e0) | ( ~ (all_144_0 = e2) & op(e1, % 185.04/29.22 | | | | | | | | | e0) = all_144_0 & $i(all_144_0))) % 185.04/29.22 | | | | | | | | | % 185.04/29.22 | | | | | | | | | ALPHA: (2588) implies: % 185.04/29.22 | | | | | | | | | (2589) op(e3, e1) = all_144_1 % 185.04/29.22 | | | | | | | | | % 185.04/29.22 | | | | | | | | | BETA: splitting (794) gives: % 185.04/29.22 | | | | | | | | | % 185.04/29.22 | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | (2590) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 185.04/29.22 | | | | | | | | | | e3 & op(e3, e4) = e3) % 185.04/29.22 | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | REF_CLOSE: (280), (504), (2575), (2576), (2590), % 185.04/29.22 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.22 | | | | | | | | | | #559. % 185.04/29.22 | | | | | | | | | | % 185.04/29.22 | | | | | | | | | Case 2: % 185.04/29.22 | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | (2591) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 185.04/29.22 | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 185.04/29.22 | | | | | | | | | | op(e0, e4) = e3) % 185.04/29.22 | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | BETA: splitting (2591) gives: % 185.04/29.22 | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | (2592) all_252_6 = e3 & op(e2, e4) = e3 % 185.04/29.22 | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | REF_CLOSE: (227), (2577), (2592), (function-axioms) are % 185.04/29.22 | | | | | | | | | | | inconsistent by sub-proof #432. % 185.04/29.22 | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | Case 2: % 185.04/29.22 | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | (2593) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 185.04/29.22 | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 185.04/29.22 | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | BETA: splitting (2593) gives: % 185.04/29.22 | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | (2594) all_252_12 = e3 & op(e1, e4) = e3 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | ALPHA: (2594) implies: % 185.04/29.22 | | | | | | | | | | | | (2595) all_252_12 = e3 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e4, % 185.04/29.22 | | | | | | | | | | | | e3, e1, simplifying with (224), (2585) gives: % 185.04/29.22 | | | | | | | | | | | | (2596) all_62_2 = e4 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, % 185.04/29.22 | | | | | | | | | | | | all_144_1, e1, e3, simplifying with (185), (2589) % 185.04/29.22 | | | | | | | | | | | | gives: % 185.04/29.22 | | | | | | | | | | | | (2597) all_144_1 = all_36_2 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1, % 185.04/29.22 | | | | | | | | | | | | all_144_1, e1, e3, simplifying with (2572), (2589) % 185.04/29.22 | | | | | | | | | | | | gives: % 185.04/29.22 | | | | | | | | | | | | (2598) all_144_1 = all_16_1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | COMBINE_EQS: (2597), (2598) imply: % 185.04/29.22 | | | | | | | | | | | | (2599) all_36_2 = all_16_1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | SIMP: (2599) implies: % 185.04/29.22 | | | | | | | | | | | | (2600) all_36_2 = all_16_1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | COMBINE_EQS: (1345), (2600) imply: % 185.04/29.22 | | | | | | | | | | | | (2601) all_52_2 = all_16_1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | COMBINE_EQS: (1170), (2600) imply: % 185.04/29.22 | | | | | | | | | | | | (2602) all_74_2 = all_16_1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | COMBINE_EQS: (1314), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2603) all_114_2 = e4 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | COMBINE_EQS: (1360), (2600) imply: % 185.04/29.22 | | | | | | | | | | | | (2604) all_122_2 = all_16_1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | COMBINE_EQS: (860), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2605) all_130_2 = e4 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1500), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2606) ~ (all_244_15 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1476), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2607) ~ (all_84_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1497), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2608) ~ (all_22_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | SIMP: (2608) implies: % 185.04/29.22 | | | | | | | | | | | | (2609) ~ (all_22_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1488), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2610) ~ (all_10_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | SIMP: (2610) implies: % 185.04/29.22 | | | | | | | | | | | | (2611) ~ (all_10_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1498), (2596) imply: % 185.04/29.22 | | | | | | | | | | | | (2612) ~ (all_4_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | SIMP: (2612) implies: % 185.04/29.22 | | | | | | | | | | | | (2613) ~ (all_4_2 = e4) % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1589), (2596), (2600) imply: % 185.04/29.22 | | | | | | | | | | | | (2614) op(e4, all_16_1) = e3 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1590), (2596), (2600) imply: % 185.04/29.22 | | | | | | | | | | | | (2615) op(all_16_1, e4) = e1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | REDUCE: (1608), (2600) imply: % 185.04/29.22 | | | | | | | | | | | | (2616) op(e3, all_16_1) = e1 % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | BETA: splitting (323) gives: % 185.04/29.22 | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | (2617) ~ (all_130_2 = e4) % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | REDUCE: (2605), (2617) imply: % 185.04/29.22 | | | | | | | | | | | | | (2618) $false % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | CLOSE: (2618) is inconsistent. % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | Case 2: % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | (2619) op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ % 185.04/29.22 | | | | | | | | | | | | | (all_130_1 = e2) | ( ~ (all_130_0 = e0) & op(e1, % 185.04/29.22 | | | | | | | | | | | | | e2) = all_130_0 & $i(all_130_0))) % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | ALPHA: (2619) implies: % 185.04/29.22 | | | | | | | | | | | | | (2620) op(e4, e1) = all_130_1 % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | BETA: splitting (301) gives: % 185.04/29.22 | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | (2621) ~ (all_114_2 = e4) % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | REDUCE: (2603), (2621) imply: % 185.04/29.22 | | | | | | | | | | | | | | (2622) $false % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | CLOSE: (2622) is inconsistent. % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | Case 2: % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | (2623) op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ % 185.04/29.22 | | | | | | | | | | | | | | (all_114_1 = e0) | ( ~ (all_114_0 = e2) & op(e1, % 185.04/29.22 | | | | | | | | | | | | | | e0) = all_114_0 & $i(all_114_0))) % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | ALPHA: (2623) implies: % 185.04/29.22 | | | | | | | | | | | | | | (2624) op(e4, e1) = all_114_1 % 185.04/29.22 | | | | | | | | | | | | | | (2625) ~ (all_114_1 = e0) | ( ~ (all_114_0 = e2) & % 185.04/29.22 | | | | | | | | | | | | | | op(e1, e0) = all_114_0 & $i(all_114_0)) % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 185.04/29.22 | | | | | | | | | | | | | | all_130_1, e1, e4, simplifying with (170), (2620) % 185.04/29.22 | | | | | | | | | | | | | | gives: % 185.04/29.22 | | | | | | | | | | | | | | (2626) all_130_1 = all_26_2 % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_114_1, % 185.04/29.22 | | | | | | | | | | | | | | all_130_1, e1, e4, simplifying with (2620), (2624) % 185.04/29.22 | | | | | | | | | | | | | | gives: % 185.04/29.22 | | | | | | | | | | | | | | (2627) all_130_1 = all_114_1 % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | COMBINE_EQS: (2626), (2627) imply: % 185.04/29.22 | | | | | | | | | | | | | | (2628) all_114_1 = all_26_2 % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | BETA: splitting (159) gives: % 185.04/29.22 | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | (2629) ~ (all_18_2 = e2) % 185.04/29.22 | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | REDUCE: (1231), (2629) imply: % 185.04/29.22 | | | | | | | | | | | | | | | (2630) ~ (all_12_2 = e2) % 185.04/29.22 | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 185.04/29.22 | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | (2631) ~ (all_20_2 = e3) % 185.04/29.22 | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | (2632) ~ (all_22_2 = e2) % 185.04/29.22 | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | (2633) ~ (all_26_2 = e0) % 185.04/29.22 | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | (2634) ~ (all_28_2 = e1) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | (2635) ~ (all_30_2 = e3) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | (2636) ~ (all_32_2 = e4) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1352), (2636) imply: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | (2637) ~ (all_20_2 = e4) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | (2638) ~ (all_36_2 = e0) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | (2639) ~ (all_38_2 = e0) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | (2640) ~ (all_40_2 = e1) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | | (2641) ~ (all_52_2 = e2) % 185.04/29.22 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2601), (2641) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | (2642) ~ (all_16_1 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (2643) ~ (all_56_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1292), (2643) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | (2644) ~ (all_8_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2645) ~ (all_58_2 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1350), (2645) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2646) ~ (all_20_2 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2647) ~ (all_76_2 = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (2647) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2648) ~ (all_40_2 = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2649) ~ (all_80_2 = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (2649) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2650) ~ (all_6_2 = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2651) ~ (all_82_2 = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1332), (2651) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2652) ~ (all_28_2 = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2653) ~ (all_88_2 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1242), (2653) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2654) ~ (all_26_2 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2655) ~ (all_94_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1333), (2655) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2656) ~ (all_38_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2657) ~ (all_96_2 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1330), (2657) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658) ~ (all_34_2 = e2) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2659) ~ (all_100_2 = e1) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2660) ~ (all_102_2 = e0) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1317), (2660) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2661) ~ (all_10_2 = e0) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2662) ~ (all_104_2 = e1) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1181), (2662) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2663) ~ (all_22_2 = e1) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664) ~ (all_108_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1284), (2664) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2665) ~ (all_28_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) ~ (all_122_2 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2604), (2666) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) ~ (all_16_1 = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2668) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) all_252_9 = e4 & op(e4, e1) = e4 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2669) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) all_252_9 = e4 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) op(e4, e1) = e4 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2672) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) all_252_0 = e3 & op(e4, e4) = e3 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2673) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) op(e4, e4) = e3 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (2575), (2674), (function-axioms) are % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #561. % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_252_1 = e3 & op(e4, e3) = e3 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2675) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) all_252_1 = e3 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) op(e4, e3) = e3 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2678) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) all_252_1 = e1 & op(e4, e3) = e1 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2679) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) all_252_1 = e1 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2676), (2680) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) e3 = e1 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2681) imply: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) $false % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2682) is inconsistent. % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) all_252_3 = e1 & op(e3, e3) = e1 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2683) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) all_252_3 = e1 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2685) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_252_1 = e0 & op(e4, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2686) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) op(e4, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (257), (2677), (2687), (function-axioms) are % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #431. % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) all_252_3 = e0 & op(e3, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2684), (2688) are inconsistent by sub-proof % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #430. % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 & % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2689) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) all_252_7 = e0 & op(e2, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (2661), (2690), (function-axioms) are % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2691) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) all_252_13 = e0 & op(e1, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2585), (2692), (function-axioms) are % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) all_252_21 = e0 & op(e0, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2693) implies: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_252_21 = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) op(e0, e3) = e0 % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2696) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) all_252_20 = e3 & op(e0, e4) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2697) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) op(e0, e4) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (2698), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) all_252_21 = e3 & op(e0, e3) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2699) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) all_252_21 = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2694), (2700) imply: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) e3 = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (2701) imply: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) $false % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2702) is inconsistent. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2703) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) all_252_22 = e3 & op(e0, e2) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2652), (2704), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2705) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) all_252_23 = e3 & op(e0, e1) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2706) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) op(e0, e1) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2631), (2707), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) all_252_24 = e3 & op(e0, e0) = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2708) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) all_252_24 = e3 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (1628), (2663), (2710), % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #478. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2711) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) all_252_22 = e1 & op(e0, e2) = e1 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2712) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) op(e0, e2) = e1 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2634), (2713), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2714) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) all_252_23 = e1 & op(e0, e1) = e1 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2715) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) all_252_23 = e1 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) op(e0, e1) = e1 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2718) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) all_252_20 = e4 & op(e0, e4) = e4 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2719) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) op(e0, e4) = e4 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2721) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) all_252_9 = e0 & op(e4, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2722) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) op(e4, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2671), (2723), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #427. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) all_252_10 = e0 & op(e3, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2724) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) op(e3, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2638), (2725), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2726) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) all_252_11 = e0 & op(e2, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2727) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) op(e2, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (2728), (function-axioms) are % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2729) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) all_252_15 = e0 & op(e1, e1) = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2730) implies: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) all_252_15 = e0 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2732) gives: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_252_20 = e2 & op(e0, e4) = e2 % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2733) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) op(e0, e4) = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2720), (2734), (function-axioms) are % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #426. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_252_21 = e2 & op(e0, e3) = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2735) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) op(e0, e3) = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2632), (2736), (function-axioms) are % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #543. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2737) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2738) all_252_22 = e2 & op(e0, e2) = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2738) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2739) all_252_22 = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2740) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (2585), (2595), (2740), % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2741) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2741) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2742) all_252_14 = e2 & op(e1, e2) = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2742) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2743) op(e1, e2) = e2 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2744) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (2744), % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #546. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2745) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2745) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2746) all_252_8 = e0 & op(e2, e2) = e0 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2746) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2747) all_252_8 = e0 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2748) op(e2, e2) = e0 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2749) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2749) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2750) all_252_12 = e1 & op(e1, e4) = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2595), (2750) are inconsistent by sub-proof % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #424. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2751) all_252_13 = e1 & op(e1, e3) = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2585), (2751), (function-axioms) are % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #423. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2752) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2752) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2753) all_252_14 = e1 & op(e1, e2) = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (13), (182), (760), (2585), % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595), (2658), (2731), (2753), (function-axioms) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #420. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2754) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2754) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2755) all_252_15 = e1 & op(e1, e1) = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2731), (2755) are inconsistent by sub-proof % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #419. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_252_19 = e1 & op(e1, e0) = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2756) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757) all_252_19 = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2758) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2758) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2759) all_252_4 = e3 & op(e4, e2) = e3 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2759) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2760) op(e4, e2) = e3 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (2650), (2760), (function-axioms) are % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2761) all_252_5 = e3 & op(e3, e2) = e3 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2761) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2762) all_252_5 = e3 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2763) op(e3, e2) = e3 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (774) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2764) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) all_252_4 = e1 & op(e4, e2) = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2765) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) all_252_4 = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4) % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2767) gives: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) all_252_4 = e4 & op(e4, e2) = e4 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2768) implies: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_252_4 = e4 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2766), (2769) imply: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) e4 = e1 % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (2770) imply: % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) $false % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2771) is inconsistent. % 185.04/29.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) all_252_5 = e4 & op(e3, e2) = e4 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2772) implies: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) op(e3, e2) = e4 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e4, e2, % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (2763), (2773) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) e4 = e3 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (2774) imply: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) $false % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2775) is inconsistent. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 & % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2776) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) all_252_8 = e4 & op(e2, e2) = e4 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2747), (2777) are inconsistent by sub-proof % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #418. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2778) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_252_14 = e4 & op(e1, e2) = e4 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (758), (759), (760), (2585), (2595), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658), (2779), (function-axioms) are inconsistent % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #412. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) all_252_22 = e4 & op(e0, e2) = e4 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2665), (2780), (function-axioms) are % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_252_5 = e1 & op(e3, e2) = e1 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2781) implies: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) all_252_5 = e1 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2762), (2782) imply: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) e3 = e1 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2783) implies: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) e3 = e1 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2784) imply: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) $false % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2785) is inconsistent. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2786) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) all_252_8 = e1 & op(e2, e2) = e1 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2787) implies: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_252_8 = e1 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2747), (2788) imply: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) e1 = e0 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2757), (2789) imply: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) all_252_19 = e0 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (12), (13), (182), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759), (760), (2585), (2595), (2658), (2731), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790), (function-axioms) are inconsistent by % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #409. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (13), (173), (182), (760), (2585), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595), (2634), (2658), (2731), (2791), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #408. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2792) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) all_252_8 = e3 & op(e2, e2) = e3 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2793) implies: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) op(e2, e2) = e3 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (2748), (2794), (function-axioms) are % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2795) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_252_14 = e3 & op(e1, e2) = e3 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2796) implies: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) op(e1, e2) = e3 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (137), (2743), (2797), (function-axioms) are % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #439. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_252_22 = e3 & op(e0, e2) = e3 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2652), (2798), (function-axioms) are % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (137), (1622), (2739), (2799), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #406. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (182), (2658), (2731), (2800), % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #404. % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2801) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2801) gives: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2802) all_252_23 = e2 & op(e0, e1) = e2 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2802) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2803) op(e0, e1) = e2 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (161), (2717), (2803), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #475. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2804) all_252_24 = e2 & op(e0, e0) = e2 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2804) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2805) all_252_24 = e2 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2709), (2805) imply: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2806) e3 = e2 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (2806) imply: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2807) $false % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2807) is inconsistent. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2808) all_252_23 = e0 & op(e0, e1) = e0 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2716), (2808) are inconsistent by sub-proof % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #403. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2809) all_252_21 = e4 & op(e0, e3) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2809) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2810) op(e0, e3) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2695), (2810), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #402. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2811) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2811) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2812) all_252_22 = e4 & op(e0, e2) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2665), (2812), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2813) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (161), (2709), (2717), (2813), % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #400. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2814) all_252_24 = e1 & op(e0, e0) = e1 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2709), (2814) are inconsistent by sub-proof % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #399. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2815) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2815) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2816) all_252_7 = e1 & op(e2, e3) = e1 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2816) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2817) op(e2, e3) = e1 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1625), (2817), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2818) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2818) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2819) all_252_13 = e1 & op(e1, e3) = e1 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2585), (2819), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #423. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2820) all_252_21 = e1 & op(e0, e3) = e1 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2820) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2821) op(e0, e3) = e1 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2663), (2821), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #479. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2822) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2822) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2823) all_252_4 = e3 & op(e4, e2) = e3 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2823) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2824) op(e4, e2) = e3 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (2650), (2824), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2825) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2825) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2826) all_252_9 = e3 & op(e4, e1) = e3 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (2670), (2826) are inconsistent by sub-proof % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #398. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2827) all_252_16 = e3 & op(e4, e0) = e3 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2827) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2828) op(e4, e0) = e3 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (2635), (2828), (function-axioms) are % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2829) all_252_10 = e4 & op(e3, e1) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2829) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2830) op(e3, e1) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1, e4, % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (2572), (2830) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2831) all_16_1 = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2667), (2831) imply: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2832) $false % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2832) is inconsistent. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2833) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2833) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2834) all_252_11 = e4 & op(e2, e1) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2834) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2835) op(e2, e1) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, e4, % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (188), (2835) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2836) all_38_2 = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2656), (2836) imply: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2837) $false % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2837) is inconsistent. % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2838) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2838) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2839) all_252_15 = e4 & op(e1, e1) = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2839) implies: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2840) all_252_15 = e4 % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 185.04/29.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2841) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2841) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2842) all_252_12 = e0 & op(e1, e4) = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2595), (2842) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2843) all_252_13 = e0 & op(e1, e3) = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2585), (2843), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2844) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2844) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2845) all_252_14 = e0 & op(e1, e2) = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2845) implies: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2846) all_252_14 = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2847) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (2585), (2595), (2847), % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2848) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2848) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2849) all_252_14 = e2 & op(e1, e2) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2846), (2849) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #397. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2850) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2850) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2851) all_252_15 = e2 & op(e1, e1) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2840), (2851) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #396. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2852) all_252_19 = e2 & op(e1, e0) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (2658), (2852), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2853) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2853) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2854) all_252_15 = e0 & op(e1, e1) = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2854) implies: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2855) all_252_15 = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2840), (2855) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2856) e4 = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (2856) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2857) $false % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2857) is inconsistent. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2858) all_252_19 = e0 & op(e1, e0) = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2858) implies: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2859) all_252_19 = e0 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2860) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (2585), (2595), (2860), % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2861) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2861) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2862) all_252_14 = e2 & op(e1, e2) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2862) implies: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2863) all_252_14 = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2864) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2864) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2865) all_252_12 = e1 & op(e1, e4) = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2595), (2865) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #424. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2866) all_252_13 = e1 & op(e1, e3) = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2585), (2866), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #423. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2867) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2867) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2868) all_252_14 = e1 & op(e1, e2) = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2863), (2868) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #395. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2869) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2869) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2870) all_252_15 = e1 & op(e1, e1) = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2840), (2870) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #394. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2871) all_252_19 = e1 & op(e1, e0) = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2871) implies: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2872) all_252_19 = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2859), (2872) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #526. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2873) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2873) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2874) all_252_15 = e2 & op(e1, e1) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2840), (2874) are inconsistent by sub-proof % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #396. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2875) all_252_19 = e2 & op(e1, e0) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (2658), (2875), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2876) all_252_23 = e4 & op(e0, e1) = e4 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2637), (2876), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #518. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2877) all_122_2 = e4 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2604), (2877) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2878) all_16_1 = e4 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2616), (2878) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2879) op(e3, e4) = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2, % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e4, e3, simplifying with (280), (2879) gives: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2880) all_100_2 = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2659), (2880) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2881) $false % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2881) is inconsistent. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2882) all_108_2 = e4 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1284), (2882) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2883) all_28_2 = e4 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (2883) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2884) op(e0, e4) = e2 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (2630), (2884), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #544. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2885) all_104_2 = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1181), (2885) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2886) all_22_2 = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2886) implies: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2887) all_22_2 = e1 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (2887) imply: % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2888) op(e0, e1) = e3 % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2631), (2888), (function-axioms) are % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 185.04/29.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2889) all_102_2 = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (2889) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2890) all_10_2 = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1611), (2890) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2891) op(e2, e0) = e3 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (2648), (2891), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #566. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2892) all_100_2 = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1605), (2892) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2893) op(e3, e1) = e4 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1, e4, % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (2572), (2893) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2894) all_16_1 = e4 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2614), (2894) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2895) op(e4, e4) = e3 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (2575), (2895), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #561. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2896) all_96_2 = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1330), (2896) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2897) all_34_2 = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (2897) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2898) op(e1, e2) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (2898), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2899) all_94_2 = e4 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1333), (2899) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2900) all_38_2 = e4 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2900) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2901) all_38_2 = e4 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1612), (2901) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2902) op(e2, e4) = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (2901) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2903) op(e2, e1) = e4 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2904) ~ (all_110_2 = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1282), (2904) imply: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2905) ~ (all_34_2 = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2906) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2572), (2642), (2654), (2906), % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #393. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2907) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2907) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2908) all_252_11 = e2 & op(e2, e1) = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2908) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2909) op(e2, e1) = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2903), (2909), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #392. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2910) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2910) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2911) all_252_15 = e2 & op(e1, e1) = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2911) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2912) all_252_15 = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2913) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2913) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2914) all_252_12 = e0 & op(e1, e4) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2595), (2914) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2915) all_252_13 = e0 & op(e1, e3) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2585), (2915), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2916) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2916) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2917) all_252_14 = e0 & op(e1, e2) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2917) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2918) op(e1, e2) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (2918), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2919) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) all_252_15 = e0 & op(e1, e1) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2912), (2920) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #416. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) all_252_19 = e0 & op(e1, e0) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2921) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) all_252_19 = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (2633), (2638), (2923), % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2924) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2925) all_252_11 = e0 & op(e2, e1) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2925) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) op(e2, e1) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (2926), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2927) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) all_252_15 = e0 & op(e1, e1) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2928) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929) all_252_15 = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (12), (13), (182), % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759), (760), (2585), (2595), (2905), (2922), % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929), (function-axioms) are inconsistent by % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #409. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2930) all_252_23 = e0 & op(e0, e1) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2930) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2931) op(e0, e1) = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (759) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2932) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2932) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2933) all_252_12 = e1 & op(e1, e4) = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2595), (2933) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #424. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2934) all_252_13 = e1 & op(e1, e3) = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2585), (2934), (function-axioms) are % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #423. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2935) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2935) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_252_14 = e1 & op(e1, e2) = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2936) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2937) all_252_14 = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2938) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (13), (2585), (2595), (2938), % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #425. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2939) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2939) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) all_252_14 = e2 & op(e1, e2) = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2940) implies: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2941) all_252_14 = e2 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2937), (2941) are inconsistent by sub-proof % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #391. % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2942) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2942) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, e0, % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (161), (2931) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2943) all_20_2 = e0 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e1, % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (2902) gives: % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2944) all_64_2 = e1 % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (2944) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2945) ~ (all_12_2 = e1) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1470), (2943) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2946) ~ (all_12_2 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (730), (1427), (1593), (1604), (1626), (1628), % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2630), (2946), (function-axioms) are inconsistent % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #503. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2947) all_252_19 = e2 & op(e1, e0) = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (2905), (2947), (function-axioms) are % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2948) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2948) gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2949) all_252_15 = e1 & op(e1, e1) = e1 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2912), (2949) are inconsistent by sub-proof % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #415. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2950) all_252_19 = e1 & op(e1, e0) = e1 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2922), (2950) are inconsistent by sub-proof % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #414. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2951) all_252_23 = e2 & op(e0, e1) = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2646), (2951), (function-axioms) are % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2952) all_110_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1282), (2952) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2953) all_34_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2953) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2954) all_34_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (2954) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2955) op(e1, e2) = e0 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (2955), (function-axioms) are % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2956) all_88_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1242), (2956) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2957) all_26_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2957) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2958) all_26_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2584), (2958) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2959) op(e3, e2) = e4 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (2644), (2959), (function-axioms) are % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2960) all_82_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1332), (2960) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2961) all_28_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (2961) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2962) op(e0, e3) = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2632), (2962), (function-axioms) are % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #543. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2963) all_80_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1251), (2963) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2964) all_6_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2964) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2965) all_6_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1602), (2965) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2966) op(e4, e3) = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e2, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (2966) gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2967) all_84_2 = e2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1475), (2967) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2968) ~ (all_10_2 = e2) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2968) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2969) ~ (all_10_2 = e2) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (284), (736), (1317), (1431), (1585), % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607), (1611), (1625), (2611), (2648), (2969), % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #565. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2970) all_76_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2971) op(e3, e2) = all_76_1 & $i(all_76_1) & ( ~ % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_76_1 = e4) | ( ~ (all_76_0 = e1) & op(e2, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_76_0 & $i(all_76_0))) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2971) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2972) op(e3, e2) = all_76_1 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (2970) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2973) all_40_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2973) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2974) all_40_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1367), (2974) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2975) all_174_2 = e3 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1578), (2974) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2976) ~ (all_244_24 = e3) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1496), (2974) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2977) ~ (all_10_2 = e3) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2977) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2978) ~ (all_10_2 = e3) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1613), (2974) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2979) op(e2, e3) = e0 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (385) gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980) ~ (all_174_2 = e3) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2975), (2980) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2981) $false % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2981) is inconsistent. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2982) op(e3, e2) = all_174_1 & $i(all_174_1) & ( ~ % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_174_1 = e1) | ( ~ (all_174_0 = e4) & op(e2, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_174_0 & $i(all_174_0))) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2982) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2983) op(e3, e2) = all_174_1 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (2979) gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2984) all_10_2 = e0 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_174_1, e2, e3, simplifying with (143), (2983) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2985) all_174_1 = all_8_2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_76_1, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_174_1, e2, e3, simplifying with (2972), (2983) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2986) all_174_1 = all_76_1 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2985), (2986) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2987) all_76_1 = all_8_2 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1317), (2984) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2988) all_102_2 = e0 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1366), (2984) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2989) all_172_2 = e0 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1492), (2984) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2990) ~ (all_244_8 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2611), (2984) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2991) ~ (e4 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2978), (2984) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2992) ~ (e3 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1625), (2984) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2993) ~ (e1 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (382) gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2994) ~ (all_172_2 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2989), (2994) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2995) $false % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2995) is inconsistent. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2996) op(e0, e2) = all_172_1 & $i(all_172_1) & ( ~ % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_172_1 = e1) | ( ~ (all_172_0 = e4) & op(e2, % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_172_0 & $i(all_172_0))) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2996) implies: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2997) op(e0, e2) = all_172_1 % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2998) ~ (all_102_2 = e0) % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2988), (2998) imply: % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2999) $false % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2999) is inconsistent. % 185.04/29.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3000) op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4) = all_102_0 & $i(all_102_0))) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3000) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3001) op(e0, e2) = all_102_1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3002) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (3002), % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #546. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3003) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3003) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3004) all_252_8 = e0 & op(e2, e2) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3004) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3005) op(e2, e2) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (2990), (3005), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #448. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3006) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3006) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3007) all_252_14 = e0 & op(e1, e2) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3007) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3008) op(e1, e2) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (3008), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3009) all_252_22 = e0 & op(e0, e2) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3009) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3010) all_252_22 = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3011) op(e0, e2) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3012) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (2630), (2632), (3012), % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3013) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3013) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3014) all_252_22 = e2 & op(e0, e2) = e2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3010), (3014) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #541. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3015) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3015) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3016) all_252_23 = e2 & op(e0, e1) = e2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2646), (3016), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3017) all_252_24 = e2 & op(e0, e0) = e2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3017) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3018) all_252_24 = e2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3019) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3019) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3020) all_252_20 = e3 & op(e0, e4) = e3 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3020) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3021) op(e0, e4) = e3 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (3021), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3022) all_252_21 = e3 & op(e0, e3) = e3 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3022) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3023) op(e0, e3) = e3 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3024) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3024) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3025) all_252_20 = e4 & op(e0, e4) = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3025) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3026) op(e0, e4) = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3027) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (149), (164), (1628), (3023), (3027), % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3028) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3028) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3029) all_252_22 = e1 & op(e0, e2) = e1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3029) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3030) op(e0, e2) = e1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2634), (3030), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3031) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3031) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3032) all_252_23 = e1 & op(e0, e1) = e1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3032) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3033) all_252_23 = e1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3034) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (2633), (2638), (3034), % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3035) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3035) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3036) all_252_11 = e0 & op(e2, e1) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3036) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3037) op(e2, e1) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (3037), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3038) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3038) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_102_1, e2, e0, simplifying with (3001), (3011) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3039) all_102_1 = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_172_1, e2, e0, simplifying with (173), (2997) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3040) all_172_1 = all_28_2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_102_1, % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_172_1, e2, e0, simplifying with (2997), (3001) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3041) all_172_1 = all_102_1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, e4, % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e0, simplifying with (149), (3026) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3042) all_12_2 = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3040), (3041) imply: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3043) all_102_1 = all_28_2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3043) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044) all_102_1 = all_28_2 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3039), (3044) imply: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3045) all_28_2 = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (1593), (1604), (3042), (function-axioms) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #505. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3046) all_252_23 = e0 & op(e0, e1) = e0 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3033), (3046) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #403. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3047) all_252_24 = e1 & op(e0, e0) = e1 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3018), (3047) are inconsistent by sub-proof % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #524. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3048) all_252_21 = e4 & op(e0, e3) = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2609), (3048), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3049) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3049) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3050) all_252_22 = e4 & op(e0, e2) = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3050) implies: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3051) op(e0, e2) = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (3011), (3051), (function-axioms) are % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #520. % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3052) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3052) gives: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3053) all_252_23 = e4 & op(e0, e1) = e4 % 185.04/29.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2637), (3053), (function-axioms) are % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #518. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3054) all_252_24 = e4 & op(e0, e0) = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3018), (3054) are inconsistent by sub-proof % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #522. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3055) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3055) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3056) all_252_22 = e3 & op(e0, e2) = e3 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3056) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3057) all_252_22 = e3 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3010), (3057) are inconsistent by sub-proof % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #389. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3058) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (480), (2631), (2976), (3058), % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3059) all_58_2 = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1350), (1621), (2634), (3059), % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | #501. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3060) all_56_2 = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3061) op(e4, e3) = all_56_1 & $i(all_56_1) & ( ~ % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e0) | ( ~ (all_56_0 = e1) & op(e3, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_0 & $i(all_56_0))) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3061) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3062) op(e4, e3) = all_56_1 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1292), (3060) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3063) all_8_2 = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3063) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3064) all_8_2 = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1380), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3065) all_234_2 = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1449), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3066) ~ (all_100_2 = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1526), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3067) ~ (all_48_2 = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1522), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3068) ~ (all_28_2 = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1508), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3069) ~ (all_6_2 = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3069) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3070) ~ (all_6_2 = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1607), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3071) op(e3, e4) = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3064) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (3072) op(e3, e2) = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3073) ~ (all_234_2 = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3065), (3073) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3074) $false % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3074) is inconsistent. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3075) op(e4, e3) = all_234_1 & $i(all_234_1) & ( ~ % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_234_1 = e1) | ( ~ (all_234_0 = e0) & op(e3, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_234_0 & $i(all_234_0))) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3075) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3076) op(e4, e3) = all_234_1 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3077) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3077) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3078) all_252_4 = e4 & op(e4, e2) = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (3070), (3078), (function-axioms) are % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #388. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3079) all_252_5 = e4 & op(e3, e2) = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3079) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3080) all_252_5 = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e4, e3, simplifying with (280), (3071) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3081) all_100_2 = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_234_1, e3, e4, simplifying with (257), (3076) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3082) all_234_1 = all_84_2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_56_1, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_234_1, e3, e4, simplifying with (3062), (3076) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3083) all_234_1 = all_56_1 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3082), (3083) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3084) all_84_2 = all_56_1 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1300), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3085) all_136_2 = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1368), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086) all_176_2 = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1437), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3087) ~ (all_244_0 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1448), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3088) ~ (all_244_3 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1444), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3089) ~ (all_64_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3089) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3090) ~ (all_64_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1451), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3091) ~ (all_48_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3091) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3092) ~ (all_48_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3093) ~ (all_12_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3066), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3094) ~ (e4 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2576), (3081) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) ~ (e3 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1581), (3081), (3084) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) op(e2, all_56_1) = e4 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1582), (3081), (3084) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3097) op(all_56_1, e2) = e3 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3098) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3098) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099) all_252_2 = e2 & op(e3, e4) = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3099) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3100) all_252_2 = e2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (388) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3101) ~ (all_176_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3086), (3101) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102) $false % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3102) is inconsistent. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3103) op(e2, e3) = all_176_1 & $i(all_176_1) & ( ~ % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_176_1 = e1) | ( ~ (all_176_0 = e0) & op(e3, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_176_0 & $i(all_176_0))) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3103) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3104) op(e2, e3) = all_176_1 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (475) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3105) ~ (all_240_2 = e1) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1381), (3105) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106) ~ (all_48_2 = e1) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3107) ~ (all_136_2 = e2) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3085), (3107) imply: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3108) $false % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3108) is inconsistent. % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3109) op(e2, e3) = all_136_1 & $i(all_136_1) & ( ~ % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_136_1 = e0) | ( ~ (all_136_0 = e1) & op(e3, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_136_0 & $i(all_136_0))) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3109) implies: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3110) op(e2, e3) = all_136_1 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_176_1, e3, e2, simplifying with (146), (3104) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3111) all_176_1 = all_10_2 % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_136_1, % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_176_1, e3, e2, simplifying with (3104), (3110) % 185.04/29.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3112) all_176_1 = all_136_1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3111), (3112) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3113) all_136_1 = all_10_2 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3114) ~ (all_58_2 = e2) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1350), (3114) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3115) ~ (all_20_2 = e2) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3116) ~ (all_64_2 = e0) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3117) ~ (all_76_2 = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1343), (3117) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3118) ~ (all_40_2 = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3119) ~ (all_80_2 = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (3119) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120) ~ (all_6_2 = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3121) ~ (all_82_2 = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1332), (3121) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3122) ~ (all_28_2 = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3123) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3123) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) all_252_4 = e3 & op(e4, e2) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3124) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) op(e4, e2) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (3120), (3125), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_252_5 = e3 & op(e3, e2) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3126) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) all_252_5 = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3080), (3127) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) e4 = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (3128) imply: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) $false % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3129) is inconsistent. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3130) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) all_252_8 = e3 & op(e2, e2) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3131) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_252_8 = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) op(e2, e2) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (3134), % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #546. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3135) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_252_8 = e0 & op(e2, e2) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3136) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) op(e2, e2) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (3133), (3137), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3138) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) all_252_14 = e0 & op(e1, e2) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3139) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) op(e1, e2) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (3140), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) all_252_22 = e0 & op(e0, e2) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3141) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) all_252_22 = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) op(e0, e2) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (2630), (2632), (3144), % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3145) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3145) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3146) all_252_22 = e2 & op(e0, e2) = e2 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3142), (3146) are inconsistent by sub-proof % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #541. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3147) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3147) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3148) all_252_23 = e2 & op(e0, e1) = e2 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3115), (3148), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3149) all_252_24 = e2 & op(e0, e0) = e2 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3149) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3150) all_252_24 = e2 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (754) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3151) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3151) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3152) all_252_16 = e1 & op(e4, e0) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3152) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3153) all_252_16 = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3154) op(e4, e0) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3155) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3155) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3156) all_252_20 = e3 & op(e0, e4) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3156) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3157) op(e0, e4) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (3157), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3158) all_252_21 = e3 & op(e0, e3) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3158) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3159) op(e0, e3) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3160) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3160) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161) all_252_16 = e3 & op(e4, e0) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3161) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3162) op(e4, e0) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3154), (3162), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #387. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_252_17 = e3 & op(e3, e0) = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3163) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3164) all_252_17 = e3 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3165) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (149), (164), (1628), (3159), (3165), % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3166) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3166) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167) all_252_22 = e1 & op(e0, e2) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3167) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168) op(e0, e2) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2634), (3168), (function-axioms) are % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3169) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) all_252_23 = e1 & op(e0, e1) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3170) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) op(e0, e1) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3172) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) all_252_2 = e0 & op(e3, e4) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3100), (3173) are inconsistent by sub-proof % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #386. % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) all_252_3 = e0 & op(e3, e3) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3174) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) all_252_3 = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3176) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) all_252_20 = e4 & op(e0, e4) = e4 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3177) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) all_252_20 = e4 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3179) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_252_1 = e1 & op(e4, e3) = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3180) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3181) all_252_1 = e1 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3182) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3182) gives: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3183) all_252_0 = e0 & op(e4, e4) = e0 % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3183) implies: % 185.04/29.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3184) all_252_0 = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (797) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3185) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3185) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3186) all_252_0 = e4 & op(e4, e4) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (3184), (3186) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3187) all_252_1 = e4 & op(e4, e3) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (2607), (3187), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #564. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3188) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 & % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3188) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3189) all_252_4 = e4 & op(e4, e2) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (3070), (3189), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #388. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3190) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3190) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3191) all_252_9 = e4 & op(e4, e1) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3191) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3192) all_252_9 = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3193) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3193) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194) all_252_0 = e3 & op(e4, e4) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3194) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3195) op(e4, e4) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (2575), (3195), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #561. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3196) all_252_1 = e3 & op(e4, e3) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3196) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3197) all_252_1 = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3181), (3197) imply: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3198) e3 = e1 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3198) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3199) e3 = e1 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3199) imply: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3200) $false % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3200) is inconsistent. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3201) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3201) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202) all_252_4 = e3 & op(e4, e2) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3202) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3203) op(e4, e2) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (3120), (3203), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3204) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3204) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3205) all_252_9 = e3 & op(e4, e1) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3205) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3206) all_252_9 = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3192), (3206) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #384. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207) all_252_16 = e3 & op(e4, e0) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3207) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3208) op(e4, e0) = e3 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3154), (3208), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #387. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3209) all_252_16 = e4 & op(e4, e0) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (3153), (3209) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3210) all_252_2 = e0 & op(e3, e4) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3100), (3210) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #386. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3211) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3211) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3212) all_252_6 = e0 & op(e2, e4) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3212) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3213) op(e2, e4) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (3116), (3213), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3214) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3214) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3215) all_252_12 = e0 & op(e1, e4) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3215) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3216) all_252_12 = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2595), (3216) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #381. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3217) all_252_20 = e0 & op(e0, e4) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3217) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3218) all_252_20 = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (3178), (3218) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #525. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3219) all_252_3 = e1 & op(e3, e3) = e1 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3175), (3219) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #380. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3220) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (146), (164), (1625), (2585), (3159), % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3220), (function-axioms) are inconsistent by % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #379. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3221) all_252_21 = e4 & op(e0, e3) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2609), (3221), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #519. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3222) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3222) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3223) all_252_22 = e4 & op(e0, e2) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3223) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3224) op(e0, e2) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (3143), (3224), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #520. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3225) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3225) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3226) all_252_23 = e4 & op(e0, e1) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3226) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3227) op(e0, e1) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (161), (3171), (3227), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3228) all_252_24 = e4 & op(e0, e0) = e4 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3150), (3228) are inconsistent by sub-proof % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #522. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3229) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0) % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3229) gives: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3230) all_252_5 = e0 & op(e3, e2) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3230) implies: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3231) op(e3, e2) = e0 % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (1624), (3231), (function-axioms) are % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547. % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3232) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3232) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3233) all_252_10 = e0 & op(e3, e1) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3233) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234) op(e3, e1) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2638), (3234), (function-axioms) are % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3235) all_252_17 = e0 & op(e3, e0) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3164), (3235) are inconsistent by sub-proof % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #378. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3236) all_252_24 = e1 & op(e0, e0) = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3150), (3236) are inconsistent by sub-proof % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3237) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (182), (191), (2579), (3118), (3150), % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3237), (function-axioms) are inconsistent by % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #535. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3238) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (161), (173), (2631), (3122), (3150), % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3238), (function-axioms) are inconsistent by % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #375. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3239) all_252_17 = e1 & op(e3, e0) = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3239) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3240) all_252_17 = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (176), (182), (191), (756), (2579), % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2635), (3118), (3150), (3240), (function-axioms) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #534. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3241) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3241) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3242) all_252_18 = e1 & op(e2, e0) = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3242) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3243) op(e2, e0) = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3244) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3244) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3245) all_252_20 = e3 & op(e0, e4) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3245) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3246) op(e0, e4) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (3246), (function-axioms) are % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3247) all_252_21 = e3 & op(e0, e3) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3247) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3248) op(e0, e3) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3249) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3249) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3250) all_252_6 = e0 & op(e2, e4) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3250) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3251) op(e2, e4) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (3116), (3251), (function-axioms) are % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3252) all_252_7 = e0 & op(e2, e3) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3252) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3253) all_252_7 = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3254) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3254) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3255) all_252_16 = e3 & op(e4, e0) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3255) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3256) op(e4, e0) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (2635), (3256), (function-axioms) are % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3257) all_252_17 = e3 & op(e3, e0) = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3257) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3258) all_252_17 = e3 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3259) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3259) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3260) all_252_2 = e0 & op(e3, e4) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3100), (3260) are inconsistent by sub-proof % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #386. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3261) all_252_3 = e0 & op(e3, e3) = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3261) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3262) all_252_3 = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3263) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3263) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3264) all_252_1 = e1 & op(e4, e3) = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3264) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3265) all_252_1 = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3266) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3266) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3267) all_252_1 = e2 & op(e4, e3) = e2 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3265), (3267) are inconsistent by sub-proof % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #374. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3268) all_252_3 = e2 & op(e3, e3) = e2 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (3088), (3268), (function-axioms) are % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #496. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3269) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3269) gives: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3270) all_252_7 = e2 & op(e2, e3) = e2 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3270) implies: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3271) all_252_7 = e2 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3253), (3271) imply: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3272) e2 = e0 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3272) imply: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3273) $false % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3273) is inconsistent. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3274) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (164), (2585), (2632), (3274), % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #373. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3275) all_252_3 = e1 & op(e3, e3) = e1 % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3262), (3275) are inconsistent by sub-proof % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #380. % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3276) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 185.04/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (146), (164), (1625), (2585), (3248), % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3276), (function-axioms) are inconsistent by % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #379. % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3277) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0) % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (143), (185), (1624), (2638), (3258), (3277), % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372. % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3278) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (182), (191), (2579), (3118), (3150), % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3278), (function-axioms) are inconsistent by % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #535. % 185.87/29.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3279) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3279) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3280) all_252_8 = e0 & op(e2, e2) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3280) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3281) op(e2, e2) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (3133), (3281), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3282) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3282) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3283) all_252_11 = e0 & op(e2, e1) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3283) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3284) op(e2, e1) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (3284), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3285) all_252_18 = e0 & op(e2, e0) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3285) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3286) op(e2, e0) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (191), (3243), (3286), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #533. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3287) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (161), (173), (2631), (3122), (3150), % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3287), (function-axioms) are inconsistent by % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #375. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3288) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3288) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3289) all_252_19 = e1 & op(e1, e0) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3289) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3290) all_252_19 = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3291) op(e1, e0) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3292) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3292) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3293) all_252_20 = e3 & op(e0, e4) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3293) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3294) op(e0, e4) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (3294), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3295) all_252_21 = e3 & op(e0, e3) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3295) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3296) op(e0, e3) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3297) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3297) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3298) all_252_16 = e3 & op(e4, e0) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3298) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3299) op(e4, e0) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (2635), (3299), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3300) all_252_17 = e3 & op(e3, e0) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3300) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3301) all_252_17 = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3302) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (149), (164), (1628), (3296), (3302), % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3303) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3303) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3304) all_252_22 = e1 & op(e0, e2) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3304) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3305) op(e0, e2) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2634), (3305), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3306) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3306) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3307) all_252_23 = e1 & op(e0, e1) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3307) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3308) all_252_23 = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3309) op(e0, e1) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3310) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (2633), (2638), (3310), % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3311) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3311) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3312) all_252_11 = e0 & op(e2, e1) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3312) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3313) op(e2, e1) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (3313), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3314) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3314) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3315) all_252_15 = e0 & op(e1, e1) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3315) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3316) all_252_15 = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3317) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3317) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3318) all_252_2 = e0 & op(e3, e4) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3100), (3318) are inconsistent by sub-proof % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #386. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3319) all_252_3 = e0 & op(e3, e3) = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3319) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3320) all_252_3 = e0 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3321) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3321) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3322) all_252_12 = e2 & op(e1, e4) = e2 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2595), (3322) are inconsistent by sub-proof % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #371. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3323) all_252_13 = e2 & op(e1, e3) = e2 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3323) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3324) op(e1, e3) = e2 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2585), (3324), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3325) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3325) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3326) all_252_14 = e2 & op(e1, e2) = e2 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3326) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327) all_252_14 = e2 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3328) op(e1, e2) = e2 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3329) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3329) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3330) all_252_1 = e1 & op(e4, e3) = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3330) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3331) all_252_1 = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3332) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3332) gives: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3333) all_252_0 = e3 & op(e4, e4) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3333) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3334) op(e4, e4) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (2575), (3334), (function-axioms) are % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #561. % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3335) all_252_1 = e3 & op(e4, e3) = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3335) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3336) all_252_1 = e3 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3331), (3336) imply: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3337) e3 = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3337) implies: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3338) e3 = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3132), (3338) imply: % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3339) all_252_8 = e1 % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (14), (137), (140), (143), % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773), (776), (1622), (1623), (1624), (3080), % 185.87/29.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120), (3328), (3339), (function-axioms) are % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #368. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3340) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3340) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3341) all_252_4 = e3 & op(e4, e2) = e3 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3341) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3342) op(e4, e2) = e3 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (3120), (3342), (function-axioms) are % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3343) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3343) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3344) all_252_9 = e3 & op(e4, e1) = e3 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3344) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3345) all_252_9 = e3 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3346) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3346) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3347) all_252_9 = e2 & op(e4, e1) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3347) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3348) all_252_9 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (3345), (3348) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #367. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3349) all_252_10 = e2 & op(e3, e1) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3349) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3350) all_252_10 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (14), (143), % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (203), (280), (778), (779), (781), (1624), % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576), (2638), (3080), (3100), (3350), % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #361. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3351) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3351) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3352) all_252_11 = e2 & op(e2, e1) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3352) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3353) all_252_11 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3354) op(e2, e1) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3355) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3355) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3356) all_252_6 = e1 & op(e2, e4) = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3356) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3357) all_252_6 = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3358) op(e2, e4) = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (774) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3359) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3359) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3360) all_252_4 = e1 & op(e4, e2) = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3360) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3361) op(e4, e2) = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (793) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3362) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3362) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3363) all_252_0 = e2 & op(e4, e4) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3363) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3364) op(e4, e4) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (3087), (3364), (function-axioms) are % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #500. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3365) all_252_1 = e2 & op(e4, e3) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3331), (3365) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #374. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3366) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 & % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3366) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3367) all_252_4 = e2 & op(e4, e2) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3367) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3368) op(e4, e2) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e1, % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e4, simplifying with (140), (3361) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3369) all_6_2 = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2, % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e4, simplifying with (140), (3368) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3370) all_6_2 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3369), (3370) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3371) e2 = e1 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3371) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3372) $false % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3372) is inconsistent. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3373) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3373) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3374) all_252_9 = e2 & op(e4, e1) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3374) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3375) all_252_9 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3345), (3375) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3376) e3 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (3376) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3377) $false % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3377) is inconsistent. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3378) all_252_16 = e2 & op(e4, e0) = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3378) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3379) all_252_16 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3380) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3380) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3381) all_252_9 = e4 & op(e4, e1) = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3381) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3382) all_252_9 = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3345), (3382) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #384. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3383) all_252_10 = e4 & op(e3, e1) = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3383) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3384) all_252_10 = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3385) all_252_24 = e0 & op(e0, e0) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3385) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3386) all_252_24 = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3150), (3386) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3387) e2 = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3387) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3388) e2 = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3388) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3389) $false % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3389) is inconsistent. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3390) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3390) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3391) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (757) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3392) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3392) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3393) all_252_16 = e4 & op(e4, e0) = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3393) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3394) all_252_16 = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3379), (3394) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) e4 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3384), (3395) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) all_252_10 = e2 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (14), (143), % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (203), (280), (778), (779), (781), (1624), % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576), (2638), (3080), (3100), (3396), % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #361. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) all_252_17 = e4 & op(e3, e0) = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3397) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) all_252_17 = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3301), (3398) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) e4 = e3 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3399) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) e4 = e3 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (3400) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) $false % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3401) is inconsistent. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3402) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) all_252_18 = e4 & op(e2, e0) = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3403) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) all_252_18 = e4 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3405) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) all_252_6 = e0 & op(e2, e4) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3406) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) op(e2, e4) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3358), (3407), (function-axioms) are % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #360. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) all_252_7 = e0 & op(e2, e3) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3408) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) all_252_7 = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3391) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3410) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) all_252_16 = e0 & op(e4, e0) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3411) implies: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) all_252_16 = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3379), (3412) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) e2 = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3413) imply: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3414) $false % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3414) is inconsistent. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3415) all_252_17 = e0 & op(e3, e0) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3301), (3415) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #378. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3416) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3416) gives: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3417) all_252_18 = e0 & op(e2, e0) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (3404), (3417) are inconsistent by sub-proof % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #359. % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3418) all_252_19 = e0 & op(e1, e0) = e0 % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3418) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3419) all_252_19 = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3290), (3419) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3420) e1 = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3357), (3420) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3421) all_252_6 = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (771) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3422) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = e3) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3422) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) all_252_6 = e3 & op(e2, e4) = e3 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (2577), (3423), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #432. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) all_252_7 = e3 & op(e2, e3) = e3 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3409), (3424) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #358. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 & % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e3) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3425) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3355) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3420) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) $false % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3426) is inconsistent. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) all_252_7 = e1 & op(e2, e3) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3427) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) all_252_7 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3409), (3428) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3429) e1 = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3420) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3430) $false % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3430) is inconsistent. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3431) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3432) all_252_8 = e1 & op(e2, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3432) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3433) all_252_8 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3132), (3433) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #369. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3434) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3434) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3435) all_252_11 = e1 & op(e2, e1) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3353), (3435) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #357. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3436) all_252_18 = e1 & op(e2, e0) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3436) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3437) all_252_18 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3404), (3437) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3438) e4 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3438) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439) e4 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (3439) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3440) $false % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3440) is inconsistent. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3441) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3441) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3442) all_252_11 = e3 & op(e2, e1) = e3 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (3353), (3442) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #356. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3443) all_252_18 = e3 & op(e2, e0) = e3 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3404), (3443) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3444) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3444) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3445) all_252_8 = e0 & op(e2, e2) = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3445) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3446) op(e2, e2) = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (3133), (3446), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3447) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3447) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3448) all_252_11 = e0 & op(e2, e1) = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3448) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3449) op(e2, e1) = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (3449), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) all_252_18 = e0 & op(e2, e0) = e0 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (3404), (3450) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #359. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3451) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) all_252_19 = e4 & op(e1, e0) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3452) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) all_252_19 = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (12), (759), (2585), (2595), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3316), (3327), (3453), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #353. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) all_252_24 = e4 & op(e0, e0) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3454) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3455) all_252_24 = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3150), (3455) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3456) e4 = e2 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3384), (3456) imply: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3457) all_252_10 = e2 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (14), (143), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (203), (280), (778), (779), (781), (1624), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576), (2638), (3080), (3100), (3457), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #361. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3458) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3458) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3459) all_252_11 = e4 & op(e2, e1) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3459) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3460) op(e2, e1) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (3354), (3460), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #392. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3461) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3461) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3462) all_252_15 = e4 & op(e1, e1) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3462) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3463) op(e1, e1) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2606), (3463), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3464) all_252_23 = e4 & op(e0, e1) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3464) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3465) op(e0, e1) = e4 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (161), (3309), (3465), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3466) all_252_5 = e1 & op(e3, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (3080), (3466) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #364. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3467) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3467) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3468) all_252_8 = e1 & op(e2, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3468) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3469) all_252_8 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (14), (137), (140), (143), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773), (776), (1622), (1623), (1624), (3080), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120), (3328), (3469), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #368. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3470) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3470) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471) all_252_14 = e1 & op(e1, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3471) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3472) all_252_14 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3327), (3472) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #391. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3473) all_252_22 = e1 & op(e0, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3473) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3474) op(e0, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2634), (3474), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3475) all_252_7 = e1 & op(e2, e3) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3475) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3476) op(e2, e3) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1625), (3476), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3477) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3477) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3478) all_252_8 = e1 & op(e2, e2) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3478) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3479) all_252_8 = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (14), (137), (140), (143), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773), (776), (1622), (1623), (1624), (3080), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120), (3328), (3479), (function-axioms) are % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #368. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3480) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3480) gives: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3481) all_252_11 = e1 & op(e2, e1) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3353), (3481) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #357. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3482) all_252_18 = e1 & op(e2, e0) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3482) implies: % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3483) op(e2, e0) = e1 % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (191), (1576), (3291), (3483), % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #352. % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3484) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3484) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3485) all_252_15 = e2 & op(e1, e1) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3316), (3485) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #421. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3486) all_252_23 = e2 & op(e0, e1) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3486) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3487) op(e0, e1) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (161), (3309), (3487), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #475. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3488) all_252_16 = e3 & op(e4, e0) = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3488) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3489) op(e4, e0) = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (2635), (3489), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3490) all_252_3 = e1 & op(e3, e3) = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3320), (3490) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #380. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3491) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (146), (164), (1625), (2585), (3296), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3491), (function-axioms) are inconsistent by % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #379. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3492) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3492) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3493) all_252_15 = e2 & op(e1, e1) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3316), (3493) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #421. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3494) all_252_19 = e2 & op(e1, e0) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3494) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3495) all_252_19 = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3290), (3495) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3496) e2 = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3496) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3497) $false % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3497) is inconsistent. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3498) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (143), (185), (1624), (2638), (3301), (3498), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #372. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3499) all_252_23 = e0 & op(e0, e1) = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3499) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3500) all_252_23 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3308), (3500) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3501) all_252_24 = e1 & op(e0, e0) = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3150), (3501) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3502) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (182), (191), (2579), (3118), (3150), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3502), (function-axioms) are inconsistent by % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #535. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3503) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (161), (173), (2631), (3122), (3150), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3503), (function-axioms) are inconsistent by % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #375. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3504) all_252_24 = e1 & op(e0, e0) = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3150), (3504) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #524. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3505) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3505) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3506) all_252_14 = e3 & op(e1, e2) = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (2582), (3506), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3507) all_252_22 = e3 & op(e0, e2) = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (3122), (3507), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3508) all_82_2 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1332), (1620), (2632), (3508), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #466. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3509) all_80_2 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1251), (3509) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3510) all_6_2 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3070), (3510) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3511) ~ (e4 = e3) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1602), (3510) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3512) op(e4, e3) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_56_1, e2, % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (3062), (3512) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3513) all_56_1 = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3097), (3513) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3514) op(e2, e2) = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3096), (3513) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3515) op(e2, e2) = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (492), (3514), (3515), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3516) all_76_2 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1343), (3516) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3517) all_40_2 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (3517) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3518) ~ (all_48_2 = e3) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (738), (1433), (1596), (1619), (3067), (3092), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106), (3518), (function-axioms) are inconsistent % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #499. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3519) all_64_2 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1438), (3519) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3520) ~ (all_244_0 = e0) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (3519) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3521) ~ (all_12_2 = e0) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3521) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3522) ~ (all_12_2 = e0) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3523) all_250_20 = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1427), (3523) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3524) all_12_2 = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3524) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3525) all_12_2 = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1440), (3525) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3526) ~ (all_244_0 = e4) % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (747) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3527) all_250_0 = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (992), (3527) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3528) all_244_0 = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3528) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3529) all_244_0 = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3526), (3529) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3530) $false % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3530) is inconsistent. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3531) all_250_0 = e3 | all_250_0 = e2 | all_250_0 = e1 | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_0 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3531) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3532) all_250_0 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (992), (3532) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3533) all_244_0 = e3 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2575), (3533) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3534) $false % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3534) is inconsistent. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3535) all_250_0 = e2 | all_250_0 = e1 | all_250_0 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3535) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3536) all_250_0 = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (992), (3536) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3537) all_244_0 = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3087), (3537) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3538) $false % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3538) is inconsistent. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3539) all_250_0 = e1 | all_250_0 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3539) gives: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3540) all_250_0 = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (992), (3540) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3541) all_244_0 = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (529), (3541) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3542) op(e1, e1) = e4 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (2606), (3542), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3543) all_250_0 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (992), (3543) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3544) all_244_0 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3520), (3544) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3545) $false % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3545) is inconsistent. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3546) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_20 = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1427), (1626), (1628), (2630), (3522), (3546) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #504. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3547) all_58_2 = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1350), (1621), (2634), (3547), % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3548) all_240_2 = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1381), (3548) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3549) all_48_2 = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3549) implies: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3550) all_48_2 = e1 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1609), (3550) imply: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3551) op(e3, e1) = e0 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (2638), (3551), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3552) all_252_3 = e2 & op(e3, e3) = e2 % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (3088), (3552), (function-axioms) are % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #496. % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3553) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 & % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2) % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3553) gives: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3554) all_252_5 = e2 & op(e3, e2) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3554) implies: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3555) all_252_5 = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3080), (3555) imply: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3556) e4 = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (3556) imply: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3557) $false % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3557) is inconsistent. % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3558) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2) % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3558) gives: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3559) all_252_10 = e2 & op(e3, e1) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3559) implies: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3560) all_252_10 = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (792) gives: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3561) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2) % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3561) gives: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3562) all_252_0 = e2 & op(e4, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3562) implies: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3563) op(e4, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (3087), (3563), (function-axioms) are % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #500. % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3564) all_252_2 = e2 & op(e3, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3564) implies: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3565) all_252_2 = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12), (14), (143), % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (203), (280), (778), (779), (781), (1624), % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576), (2638), (3080), (3560), (3565), % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #361. % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3566) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 & % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e2) % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3566) gives: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3567) all_252_6 = e2 & op(e2, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (3090), (3567), (function-axioms) are % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #467. % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3568) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2) % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3568) gives: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3569) all_252_12 = e2 & op(e1, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (2595), (3569) are inconsistent by sub-proof % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #371. % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3570) all_252_20 = e2 & op(e0, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3570) implies: % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3571) op(e0, e4) = e2 % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (2630), (3571), (function-axioms) are % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #544. % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 185.87/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3572) all_252_17 = e2 & op(e3, e0) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3572) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3573) op(e3, e0) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (3092), (3573), (function-axioms) are % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #470. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3574) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 & % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3574) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3575) all_252_8 = e4 & op(e2, e2) = e4 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3575) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3576) all_252_8 = e4 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3577) op(e2, e2) = e4 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3578) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (3578), % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #546. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3579) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3579) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3580) all_252_8 = e0 & op(e2, e2) = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3580) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3581) all_252_8 = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3576), (3581) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3582) e4 = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (3582) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3583) $false % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3583) is inconsistent. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3584) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3584) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3585) all_252_14 = e0 & op(e1, e2) = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3585) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3586) op(e1, e2) = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (3586), (function-axioms) are % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3587) all_252_22 = e0 & op(e0, e2) = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3587) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3588) all_252_22 = e0 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3589) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3589) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590) all_252_4 = e3 & op(e4, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3590) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3591) all_252_4 = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (774) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3592) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3592) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593) all_252_4 = e1 & op(e4, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3591), (3593) are inconsistent by sub-proof % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #348. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3594) all_252_5 = e1 & op(e3, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3594) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3595) op(e3, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e4, e2, % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (3072), (3595) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3596) e4 = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (3596) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3597) $false % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3597) is inconsistent. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3598) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3598) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3599) all_252_8 = e1 & op(e2, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3599) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3600) all_252_8 = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3576), (3600) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3601) e4 = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (3601) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3602) $false % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3602) is inconsistent. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3603) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3603) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3604) all_252_14 = e1 & op(e1, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3604) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3605) all_252_14 = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (775) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3606) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3606) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3607) all_252_4 = e2 & op(e4, e2) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (3591), (3607) are inconsistent by sub-proof % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #347. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3608) all_252_5 = e2 & op(e3, e2) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3608) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3609) op(e3, e2) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e4, e2, % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (3072), (3609) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3610) e4 = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (3610) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3611) $false % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3611) is inconsistent. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 & % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3612) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3613) all_252_8 = e2 & op(e2, e2) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3613) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3614) all_252_8 = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3576), (3614) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3615) e4 = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (3615) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3616) $false % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3616) is inconsistent. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3617) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3617) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3618) all_252_14 = e2 & op(e1, e2) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3605), (3618) are inconsistent by sub-proof % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #422. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3619) all_252_22 = e2 & op(e0, e2) = e2 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3588), (3619) are inconsistent by sub-proof % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #447. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3620) all_252_22 = e1 & op(e0, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3620) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3621) op(e0, e2) = e1 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (2634), (3621), (function-axioms) are % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3622) all_252_5 = e3 & op(e3, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3622) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3623) op(e3, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, e4, e2, % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (3072), (3623) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3624) e4 = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (3624) imply: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3625) $false % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3625) is inconsistent. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3626) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3626) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3627) all_252_8 = e3 & op(e2, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3627) implies: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3628) op(e2, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (492), (3577), (3628), (function-axioms) are % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3629) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3629) gives: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3630) all_252_14 = e3 & op(e1, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (2582), (3630), (function-axioms) are % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3631) all_252_22 = e3 & op(e0, e2) = e3 % 186.06/29.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3631) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3632) all_252_22 = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3588), (3632) are inconsistent by sub-proof % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #389. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3633) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3633) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3634) all_252_14 = e4 & op(e1, e2) = e4 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3634) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635) op(e1, e2) = e4 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (3635) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3636) all_4_2 = e4 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2613), (3636) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3637) $false % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3637) is inconsistent. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3638) all_252_22 = e4 & op(e0, e2) = e4 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (3068), (3638), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #411. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3639) all_52_2 = e2 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2601), (3639) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3640) all_16_1 = e2 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (140), (143), (243), (732), (857), (1511), % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (1520), (1591), (1612), (2573), (2602), (2613), % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (2614), (2616), (3640), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3641) all_40_2 = e1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1613), (3641) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3642) op(e2, e1) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (2639), (3642), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3643) all_38_2 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3644) op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | e4) = all_38_0 & $i(all_38_0))) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3644) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3645) op(e0, e2) = all_38_1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1255), (3643) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3646) all_188_2 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1529), (3643) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3647) ~ (all_244_8 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1556), (3643) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3648) ~ (all_244_15 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3649) ~ (all_188_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3646), (3649) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3650) $false % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3650) is inconsistent. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3651) op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_188_0 & $i(all_188_0))) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3651) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3652) op(e0, e2) = all_188_1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3653) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (3653), % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | #546. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3654) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3654) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3655) all_252_8 = e0 & op(e2, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3655) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3656) op(e2, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (3647), (3656), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #448. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3657) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3657) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3658) all_252_14 = e0 & op(e1, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3658) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3659) op(e1, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (3659), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3660) all_252_22 = e0 & op(e0, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3660) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3661) op(e0, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3662) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3662) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3663) all_252_12 = e0 & op(e1, e4) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2595), (3663) are inconsistent by sub-proof % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3664) all_252_13 = e0 & op(e1, e3) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2585), (3664), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3665) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3665) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3666) all_252_14 = e0 & op(e1, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3666) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3667) op(e1, e2) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (3667), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3668) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3668) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3669) all_252_15 = e0 & op(e1, e1) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3669) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3670) op(e1, e1) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (3648), (3670), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3671) all_252_19 = e0 & op(e1, e0) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3671) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3672) op(e1, e0) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, e2, e0, simplifying with (173), (3645) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3673) all_38_1 = all_28_2 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_1, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_188_1, e2, e0, simplifying with (3645), (3652) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3674) all_188_1 = all_38_1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_188_1, e2, e0, simplifying with (3652), (3661) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3675) all_188_1 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, e0, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (182), (3672) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3676) all_34_2 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3674), (3675) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3677) all_38_1 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3677) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3678) all_38_1 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3673), (3678) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3679) all_28_2 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2634), (3679) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3680) ~ (e1 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1600), (1621), (3676), (3680), (function-axioms) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #345. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | (3681) all_36_2 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (2600), (2614), (2635), (3681), % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | #344. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | (3682) all_32_2 = e4 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1352), (1621), (1628), (3682), % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | #459. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3683) all_30_2 = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1571), (3683) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3684) ~ (all_244_24 = e3) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1480), (3683) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3685) ~ (all_84_2 = e3) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1604), (3683) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3686) op(e4, e3) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e0, % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (3686) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3687) all_84_2 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1441), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3688) ~ (all_244_0 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1474), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3689) ~ (all_244_3 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1479), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3690) ~ (all_26_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1477), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3691) ~ (all_22_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | SIMP: (3691) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3692) ~ (all_22_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1475), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3693) ~ (all_10_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | SIMP: (3693) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3694) ~ (all_10_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1478), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3695) ~ (all_6_2 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (2607), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3696) ~ (e4 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (3685), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3697) ~ (e3 = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | REDUCE: (1601), (3687) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | (3698) op(e4, e0) = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | (3699) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3699) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | (3700) all_252_1 = e0 & op(e4, e3) = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3700) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | (3701) all_252_1 = e0 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3702) ~ (all_82_2 = e3) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1332), (3702) imply: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | (3703) ~ (all_28_2 = e3) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | (3704) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3704) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3705) all_252_20 = e3 & op(e0, e4) = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3705) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3706) op(e0, e4) = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1626), (3706), (function-axioms) are % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3707) all_252_21 = e3 & op(e0, e3) = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3707) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | (3708) op(e0, e3) = e3 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | (3709) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3709) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3710) all_252_1 = e1 & op(e4, e3) = e1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3710) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3711) all_252_1 = e1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (140), (170), (504), (789), (1623), % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2633), (3688), (3698), (3711), (function-axioms) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #340. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3712) all_252_3 = e1 & op(e3, e3) = e1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3712) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3713) all_252_3 = e1 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3714) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (3701), (3713), (3714) are inconsistent % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #339. % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3715) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3715) gives: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3716) all_252_7 = e2 & op(e2, e3) = e2 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3716) implies: % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3717) all_252_7 = e2 % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3718) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (257), (3686), (3713), (3718), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #338. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3719) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3719) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3720) all_252_7 = e3 & op(e2, e3) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (3717), (3720) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #337. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3721) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3721) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3722) all_252_13 = e3 & op(e1, e3) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (224), (2585), (3722), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #336. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1595), (1609), (3692), (3707), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #482. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3723) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (164), (2585), (2632), (3723), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #373. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3724) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (146), (164), (1625), (2585), (3708), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3724), (function-axioms) are inconsistent by % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #379. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | (3725) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3725) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3726) all_252_22 = e3 & op(e0, e2) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (3703), (3726), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3727) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (480), (2631), (3684), (3727), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | #506. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | (3728) all_82_2 = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1332), (1620), (2632), (3728), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | #466. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | (3729) all_252_3 = e0 & op(e3, e3) = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (3689), (3729), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #335. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | (3730) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3730) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | (3731) all_252_7 = e0 & op(e2, e3) = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (3694), (3731), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #429. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | (3732) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3732) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | (3733) all_252_13 = e0 & op(e1, e3) = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2585), (3733), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | (3734) all_252_21 = e0 & op(e0, e3) = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3734) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | (3735) all_252_21 = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | (3736) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3736) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3737) all_252_1 = e1 & op(e4, e3) = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3737) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3738) all_252_1 = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (140), (170), (504), (789), (1623), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2633), (3688), (3698), (3738), (function-axioms) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #340. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3739) all_252_3 = e1 & op(e3, e3) = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3739) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3740) all_252_3 = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (789) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e3) = e0) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3741) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) all_252_0 = e0 & op(e4, e4) = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (3688), (3742), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #343. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) all_252_1 = e0 & op(e4, e3) = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3743) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) all_252_1 = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (3740), (3744), (3745) are inconsistent % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #339. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3746) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) all_252_7 = e2 & op(e2, e3) = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3747) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) all_252_7 = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (257), (3686), (3740), (3749), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #338. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3750) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) all_252_7 = e3 & op(e2, e3) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (3748), (3751) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #337. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3752) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) all_252_13 = e3 & op(e1, e3) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (224), (2585), (3753), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #336. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) all_252_21 = e3 & op(e0, e3) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3754) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) all_252_21 = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3735), (3755) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #334. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (164), (2585), (2632), (3756), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #373. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e1) = e0) | (all_252_16 = e0 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e0) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (140), (170), (1623), (2633), (3698), (3757), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | #341. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | (3758) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3758) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3759) all_252_7 = e1 & op(e2, e3) = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3759) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3760) op(e2, e3) = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1625), (3760), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | (3761) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3761) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) all_252_13 = e1 & op(e1, e3) = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (2585), (3762), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #423. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) all_252_21 = e1 & op(e0, e3) = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3763) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (3764) all_252_21 = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3735), (3764) are inconsistent by sub-proof % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | #333. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3765) all_28_2 = e1 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | REDUCE: (1531), (3765) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3766) ~ (all_4_2 = e1) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | SIMP: (3766) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3767) ~ (all_4_2 = e1) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (732), (857), (1591), (1612), (1622), (2582), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (2613), (3767), (function-axioms) are inconsistent % 186.06/29.42 | | | | | | | | | | | | | | | | | | | by sub-proof #575. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | (3768) all_26_2 = e0 % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (164), (1619), (2583), (2625), (2628), % 186.06/29.42 | | | | | | | | | | | | | | | | | | (2631), (3768), (function-axioms) are inconsistent % 186.06/29.42 | | | | | | | | | | | | | | | | | | by sub-proof #332. % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | (3769) all_22_2 = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1483), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3770) ~ (all_244_3 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1506), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3771) ~ (all_244_24 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1477), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3772) ~ (all_84_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1503), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3773) ~ (all_28_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1504), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3774) ~ (all_20_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | SIMP: (3774) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3775) ~ (all_20_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1466), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3776) ~ (all_12_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1490), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3777) ~ (all_10_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | SIMP: (3777) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3778) ~ (all_10_2 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (2609), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3779) ~ (e4 = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | REDUCE: (1619), (3769) imply: % 186.06/29.42 | | | | | | | | | | | | | | | | | (3780) op(e0, e2) = e3 % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | (3781) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 186.06/29.42 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | BETA: splitting (3781) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3782) all_252_20 = e2 & op(e0, e4) = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | ALPHA: (3782) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3783) op(e0, e4) = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (2630), (3783), (function-axioms) are % 186.06/29.42 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #544. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3784) all_252_21 = e2 & op(e0, e3) = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | ALPHA: (3784) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3785) all_252_21 = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (137), (140), (143), (149), (161), (173), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (362), (480), (492), (521), (752), (773), (1362), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (1468), (1536), (1538), (1622), (1623), (1624), % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3771), (3773), (3780), (3785), (function-axioms) % 186.06/29.42 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #455. % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | End of split % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | (3786) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 186.06/29.42 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 186.06/29.42 | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | BETA: splitting (3786) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3787) all_252_22 = e2 & op(e0, e2) = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | ALPHA: (3787) implies: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | (3788) all_252_22 = e2 % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | (3789) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 186.06/29.42 | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3789) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | (3790) all_252_1 = e2 & op(e4, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (3772), (3790), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #523. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | (3791) all_252_3 = e2 & op(e3, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (3770), (3791), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #496. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | (3792) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3792) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | (3793) all_252_7 = e2 & op(e2, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (3778), (3793), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #458. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | (3794) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3794) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | (3795) all_252_13 = e2 & op(e1, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3795) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | (3796) op(e1, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (2585), (3796), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | (3797) all_252_21 = e2 & op(e0, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3797) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | (3798) all_252_21 = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | (3799) op(e0, e3) = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | (3800) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (149), (1626), (3798), (3800), % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | #457. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | (3801) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3801) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | (3802) all_252_22 = e3 & op(e0, e2) = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3802) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | (3803) all_252_22 = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3788), (3803) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | (3804) e3 = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3804) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | (3805) e3 = e2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (3805) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | (3806) $false % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3806) is inconsistent. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | (3807) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3807) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | (3808) all_252_23 = e3 & op(e0, e1) = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3808) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | (3809) op(e0, e1) = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2631), (3809), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | (3810) all_252_24 = e3 & op(e0, e0) = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3810) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | (3811) all_252_24 = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (3812) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3812) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3813) all_252_20 = e1 & op(e0, e4) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3813) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3814) op(e0, e4) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (3814), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3815) all_252_21 = e1 & op(e0, e3) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3815) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3816) all_252_21 = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3798), (3816) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3817) e2 = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3817) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3818) $false % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3818) is inconsistent. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (3819) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3819) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3820) all_252_22 = e1 & op(e0, e2) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3820) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3821) all_252_22 = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3788), (3821) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3822) e2 = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (3822) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3823) $false % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3823) is inconsistent. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3824) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3824) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3825) all_252_23 = e1 & op(e0, e1) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3825) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3826) all_252_23 = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827) op(e0, e1) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3828) all_252_24 = e0 & op(e0, e0) = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3828) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3829) all_252_24 = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3811), (3829) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #331. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3830) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3830) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3831) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3831) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3832) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3832) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3833) all_252_20 = e0 & op(e0, e4) = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3833) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3834) all_252_20 = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3835) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (13), (3799), (3834), (3835), % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #329. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3836) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3836) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3837) all_252_22 = e4 & op(e0, e2) = e4 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3837) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3838) op(e0, e2) = e4 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (3780), (3838), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3839) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (161), (3811), (3827), (3839), % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #400. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3840) all_252_21 = e0 & op(e0, e3) = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3840) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3841) all_252_21 = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3798), (3841) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3842) e2 = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (3842) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3843) $false % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3843) is inconsistent. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3844) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3844) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3845) all_252_22 = e0 & op(e0, e2) = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3788), (3845) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #407. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3846) all_252_23 = e0 & op(e0, e1) = e0 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3826), (3846) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #403. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3847) all_252_24 = e1 & op(e0, e0) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3811), (3847) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #399. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | (3848) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (480), (3771), (3775), (3848), % 186.06/29.43 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | | #327. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | End of split % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | (3849) all_20_2 = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | (3850) op(e3, e0) = all_20_1 & $i(all_20_1) & ( ~ % 186.06/29.43 | | | | | | | | | | | | | | | | (all_20_1 = e4) | ( ~ (all_20_0 = e2) & op(e0, % 186.06/29.43 | | | | | | | | | | | | | | | | e4) = all_20_0 & $i(all_20_0))) % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | ALPHA: (3850) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | (3851) op(e3, e0) = all_20_1 % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | COMBINE_EQS: (1378), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3852) all_230_2 = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | REDUCE: (1563), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3853) ~ (all_244_24 = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | REDUCE: (1536), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3854) ~ (all_28_2 = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | REDUCE: (1545), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3855) ~ (all_26_2 = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | REDUCE: (1504), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3856) ~ (all_22_2 = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | REDUCE: (1599), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3857) op(e3, all_34_2) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | REDUCE: (1621), (3849) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | (3858) op(e0, e3) = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | (3859) ~ (all_230_2 = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | REDUCE: (3852), (3859) imply: % 186.06/29.43 | | | | | | | | | | | | | | | | | (3860) $false % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | CLOSE: (3860) is inconsistent. % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | (3861) op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ % 186.06/29.43 | | | | | | | | | | | | | | | | | (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, % 186.06/29.43 | | | | | | | | | | | | | | | | | e2) = all_230_0 & $i(all_230_0))) % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | ALPHA: (3861) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | (3862) op(e3, e0) = all_230_1 % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | (3863) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 186.06/29.43 | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (149), (164), (1626), (3858), (3863), % 186.06/29.43 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.06/29.43 | | | | | | | | | | | | | | | | | | #453. % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | (3864) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 186.06/29.43 | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 186.06/29.43 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | BETA: splitting (3864) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | (3865) all_252_22 = e3 & op(e0, e2) = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (3854), (3865), (function-axioms) are % 186.06/29.43 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | (3866) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (3866) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | (3867) all_252_23 = e3 & op(e0, e1) = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | ALPHA: (3867) implies: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | (3868) all_252_23 = e3 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_2, e1, % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (164), (3858) gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | (3869) all_22_2 = e1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_2, % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | all_230_1, e0, e3, simplifying with (203), (3862) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | (3870) all_230_1 = all_48_2 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1, % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | all_230_1, e0, e3, simplifying with (3851), (3862) % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | (3871) all_230_1 = all_20_1 % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | % 186.06/29.43 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3870), (3871) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3872) all_48_2 = all_20_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1181), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3873) all_104_2 = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1359), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3874) all_118_2 = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (1575), (3872) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3875) ~ (all_244_24 = all_20_1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (1506), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3876) ~ (all_244_24 = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (1572), (3872) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3877) ~ (all_40_2 = all_20_1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | SIMP: (3877) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3878) ~ (all_40_2 = all_20_1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (1503), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3879) ~ (all_28_2 = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (1466), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3880) ~ (all_12_2 = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (3856), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3881) ~ (e3 = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (3869) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | (3882) op(e0, e1) = e3 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | (3883) ~ (all_104_2 = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3873), (3883) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | (3884) $false % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3884) is inconsistent. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | (3885) op(e1, e0) = all_104_1 & $i(all_104_1) & ( ~ % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | (all_104_1 = e4) | ( ~ (all_104_0 = e2) & op(e0, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | e4) = all_104_0 & $i(all_104_0))) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3885) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | (3886) op(e1, e0) = all_104_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | (3887) ~ (all_118_2 = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3874), (3887) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | (3888) $false % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3888) is inconsistent. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | (3889) op(e1, e0) = all_118_1 & $i(all_118_1) & ( ~ % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | (all_118_1 = e2) | ( ~ (all_118_0 = e4) & op(e0, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | e2) = all_118_0 & $i(all_118_0))) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3889) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | (3890) op(e1, e0) = all_118_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | (3891) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3891) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3892) all_252_20 = e1 & op(e0, e4) = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3892) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3893) op(e0, e4) = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (3893), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3894) all_252_21 = e1 & op(e0, e3) = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3894) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3895) all_252_21 = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | all_118_1, e0, e1, simplifying with (182), (3890) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3896) all_118_1 = all_34_2 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_104_1, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | all_118_1, e0, e1, simplifying with (3886), (3890) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3897) all_118_1 = all_104_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3896), (3897) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | (3898) all_104_1 = all_34_2 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3899) ~ (all_26_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3900) ~ (all_30_2 = e3) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3901) ~ (all_36_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (137), (140), (143), (149), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (173), (185), (188), (189), (191), (404), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (486), (492), (514), (749), (751), (763), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (773), (1255), (1529), (1597), (1612), (1622), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623), (1624), (2630), (3853), (3876), (3882), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3895), (3899), (3901), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3902) all_36_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2600), (3902) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3903) all_16_1 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2614), (3903) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3904) op(e4, e0) = e3 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (3900), (3904), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3905) all_30_2 = e3 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1480), (3905) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3906) ~ (all_84_2 = e3) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1604), (3905) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3907) op(e4, e3) = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e0, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (3907) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3908) all_84_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1306), (3908) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_98_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1149), (3908) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3910) all_184_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1479), (3908) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3911) ~ (all_26_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1478), (3908) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3912) ~ (all_6_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3906), (3908) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3913) ~ (e3 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3914) ~ (all_98_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3909), (3914) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3915) $false % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3915) is inconsistent. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3916) op(e0, e4) = all_98_1 & $i(all_98_1) & ( ~ % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_98_1 = e1) | ( ~ (all_98_0 = e2) & op(e4, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_98_0 & $i(all_98_0))) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3916) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3917) op(e0, e4) = all_98_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3918) ~ (all_184_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3910), (3918) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3919) $false % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3919) is inconsistent. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3920) op(e0, e4) = all_184_1 & $i(all_184_1) & ( ~ % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_184_1 = e2) | ( ~ (all_184_0 = e1) & op(e4, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_184_0 & $i(all_184_0))) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3920) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3921) op(e0, e4) = all_184_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_184_1, e4, e0, simplifying with (149), (3921) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3922) all_184_1 = all_12_2 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_98_1, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_184_1, e4, e0, simplifying with (3917), (3921) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3923) all_184_1 = all_98_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3922), (3923) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3924) all_98_1 = all_12_2 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3925) ~ (all_36_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (10), (137), (140), (143), (149), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (173), (185), (188), (189), (191), (404), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (486), (492), (514), (749), (751), (763), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773), (1255), (1529), (1597), (1612), (1622), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623), (1624), (2630), (3853), (3876), (3882), % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3895), (3899), (3925), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #444. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3926) all_36_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2600), (3926) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3927) all_16_1 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3927) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3928) all_16_1 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2615), (3928) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3929) op(e0, e4) = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1628), (3929), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3930) all_26_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3931) op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3931) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3932) op(e0, e4) = all_26_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1341), (3930) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3933) all_44_2 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2628), (3930) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3934) all_114_1 = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1544), (3930) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3935) ~ (all_244_15 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3855), (3930) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3936) ~ (e3 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1603), (3930) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3937) op(e4, e0) = e1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2584), (3930) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | (3938) op(e3, e0) = e4 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3939) ~ (all_44_2 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3933), (3939) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3940) $false % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3940) is inconsistent. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3941) op(e0, e4) = all_44_1 & $i(all_44_1) & ( ~ % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_44_1 = e2) | ( ~ (all_44_0 = e3) & op(e4, % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0))) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3941) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (3942) op(e0, e4) = all_44_1 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2625) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3943) ~ (all_114_1 = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3934), (3943) imply: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944) $false % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3944) is inconsistent. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3945) ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 & % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_114_0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3945) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) op(e1, e0) = all_114_0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3947) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) all_252_12 = e0 & op(e1, e4) = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2595), (3948) are inconsistent by sub-proof % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) all_252_13 = e0 & op(e1, e3) = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (2585), (3949), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3950) gives: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) all_252_14 = e0 & op(e1, e2) = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3951) implies: % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) op(e1, e2) = e0 % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (3952), (function-axioms) are % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.06/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3953) gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) all_252_15 = e0 & op(e1, e1) = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3954) implies: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) op(e1, e1) = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (3935), (3955), (function-axioms) are % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) all_252_19 = e0 & op(e1, e0) = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3956) implies: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) op(e1, e0) = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (149), (3942) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) all_44_1 = all_12_2 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1, % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (3932), (3942) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) all_44_1 = all_26_1 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_114_0, e0, e1, simplifying with (182), (3946) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) all_114_0 = all_34_2 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_114_0, e0, e1, simplifying with (3946), (3957) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) all_114_0 = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1, e4, % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (3851), (3938) gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) all_20_1 = e4 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (3937) gives: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) all_30_2 = e1 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3960), (3961) imply: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) all_34_2 = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3964) implies: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) all_34_2 = e0 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3958), (3959) imply: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) all_26_1 = all_12_2 % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1580), (3965) imply: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) ~ (all_244_24 = e0) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3875), (3962) imply: % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) ~ (all_244_24 = e4) % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1576), (3965) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) ~ (all_40_2 = e0) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1567), (3963) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) ~ (all_40_2 = e1) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3878), (3962) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) ~ (all_40_2 = e4) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3857), (3965) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) op(e3, e0) = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) ~ (all_108_2 = e4) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1284), (3973) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) ~ (all_28_2 = e4) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) all_250_24 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (3975) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) all_244_24 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3976) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) all_244_24 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3968), (3977) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3978) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) all_250_24 = e3 | all_250_24 = e2 | all_250_24 = % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_24 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3979) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) all_250_24 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (3980) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) all_244_24 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3981) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3982) all_244_24 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3853), (3982) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3983) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3983) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3984) all_250_24 = e2 | all_250_24 = e1 | all_250_24 = % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3984) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_250_24 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (3985) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3986) all_244_24 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3986) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3987) all_244_24 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1578), (3987) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3988) ~ (all_40_2 = e2) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3988) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3989) ~ (all_40_2 = e2) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1538), (3987) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) ~ (all_28_2 = e2) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3990) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) ~ (all_28_2 = e2) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (734) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) all_250_14 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1429), (3992) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) all_40_2 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3993) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) all_40_2 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3971), (3994) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3995) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) all_250_14 = e3 | all_250_14 = e2 | all_250_14 = % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_14 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3996) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) all_250_14 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1429), (3997) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) all_40_2 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3998) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) all_40_2 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (191), (3999) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) op(e2, e0) = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (728) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_250_22 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1425), (4001) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) all_28_2 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3974), (4002) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4003) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4004) all_250_22 = e3 | all_250_22 = e2 | all_250_22 = % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_22 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4004) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4005) all_250_22 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1425), (4005) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4006) all_28_2 = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3854), (4006) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4007) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4007) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4008) all_250_22 = e2 | all_250_22 = e1 | all_250_22 = % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3996) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1598), (3999) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4009) op(e3, all_28_2) = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4008) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4010) all_250_22 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1425), (4010) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011) all_28_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3991), (4011) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4012) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4013) all_250_22 = e1 | all_250_22 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4013) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4014) all_250_22 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1425), (4014) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4015) all_28_2 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3879), (4015) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4016) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4016) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4017) all_250_22 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1425), (4017) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4018) all_28_2 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3879), (4018) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4019) ~ (e1 = e0) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4009), (4018) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4020) op(e3, e0) = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (203), (3972), (4020), (function-axioms) are % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #362. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4021) ~ (all_250_14 = e3) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1429), (4021) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4022) ~ (all_40_2 = e3) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (4000), (4022), (function-axioms) are % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #566. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4023) all_250_14 = e2 | all_250_14 = e1 | all_250_14 = % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4023) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4024) all_250_14 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1429), (4024) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4025) all_40_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4025) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4026) all_40_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3989), (4026) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4027) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4027) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4028) all_250_14 = e1 | all_250_14 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4028) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4029) all_250_14 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1429), (4029) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4030) all_40_2 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4030) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4031) all_40_2 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3970), (4031) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4032) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4032) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4033) all_250_14 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1429), (4033) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4034) all_40_2 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4034) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4035) all_40_2 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3969), (4035) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4036) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4036) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4037) all_250_24 = e1 | all_250_24 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4037) gives: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4038) all_250_24 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (4038) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4039) all_244_24 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4039) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4040) all_244_24 = e1 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3876), (4040) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4041) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4041) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4042) all_250_24 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (800), (4042) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4043) all_244_24 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4043) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4044) all_244_24 = e0 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3967), (4044) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4045) $false % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4045) is inconsistent. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4046) all_108_2 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1284), (4046) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4047) all_28_2 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4047) implies: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4048) all_28_2 = e4 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (4048) imply: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4049) op(e0, e4) = e2 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (2630), (4049), (function-axioms) are % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #544. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | (4050) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (173), (480), (3868), (3876), (3879), (4050), % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | #435. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | (4051) all_252_24 = e3 & op(e0, e0) = e3 % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (3853), (4051), (function-axioms) are % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #507. % 186.24/29.45 | | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | (4052) all_18_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | COMBINE_EQS: (1231), (4052) imply: % 186.24/29.45 | | | | | | | | | | | | | | | (4053) all_12_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | SIMP: (4053) implies: % 186.24/29.45 | | | | | | | | | | | | | | | (4054) all_12_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | COMBINE_EQS: (828), (4054) imply: % 186.24/29.45 | | | | | | | | | | | | | | | (4055) all_210_2 = e2 % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | REDUCE: (1472), (4054) imply: % 186.24/29.45 | | | | | | | | | | | | | | | (4056) ~ (all_244_24 = e2) % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | REDUCE: (1618), (4054) imply: % 186.24/29.45 | | | | | | | | | | | | | | | (4057) op(e0, e2) = e4 % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | | REF_CLOSE: (11), (137), (140), (143), (173), (428), (434), % 186.24/29.45 | | | | | | | | | | | | | | | (480), (492), (521), (773), (1372), (1622), % 186.24/29.45 | | | | | | | | | | | | | | | (1623), (1624), (4055), (4056), (4057), % 186.24/29.45 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.45 | | | | | | | | | | | | | | | #434. % 186.24/29.45 | | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | Case 2: % 186.24/29.45 | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | (4058) all_252_20 = e3 & op(e0, e4) = e3 % 186.24/29.45 | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | ALPHA: (4058) implies: % 186.24/29.45 | | | | | | | | | | | | (4059) op(e0, e4) = e3 % 186.24/29.45 | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | | REF_CLOSE: (149), (1626), (4059), (function-axioms) are % 186.24/29.45 | | | | | | | | | | | | inconsistent by sub-proof #512. % 186.24/29.45 | | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | | % 186.24/29.45 | | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | | % 186.24/29.45 | | | | | | | | | End of split % 186.24/29.45 | | | | | | | | | % 186.24/29.45 | | | | | | | | End of split % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | End of split % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | Case 2: % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | (4060) all_14_2 = e1 % 186.24/29.46 | | | | | | | (4061) op(e1, e0) = all_14_1 & $i(all_14_1) & ( ~ (all_14_1 = % 186.24/29.46 | | | | | | | e2) | ( ~ (all_14_0 = e3) & op(e0, e2) = all_14_0 & % 186.24/29.46 | | | | | | | $i(all_14_0))) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | ALPHA: (4061) implies: % 186.24/29.46 | | | | | | | (4062) op(e1, e0) = all_14_1 % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | COMBINE_EQS: (1356), (4060) imply: % 186.24/29.46 | | | | | | | (4063) all_12_2 = e1 % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | SIMP: (4063) implies: % 186.24/29.46 | | | | | | | (4064) all_12_2 = e1 % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | COMBINE_EQS: (1357), (4064) imply: % 186.24/29.46 | | | | | | | (4065) all_42_2 = e1 % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (1440), (4064) imply: % 186.24/29.46 | | | | | | | (4066) ~ (all_244_0 = e1) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (1472), (4064) imply: % 186.24/29.46 | | | | | | | (4067) ~ (all_244_24 = e1) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (1468), (4064) imply: % 186.24/29.46 | | | | | | | (4068) ~ (all_28_2 = e1) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (1466), (4064) imply: % 186.24/29.46 | | | | | | | (4069) ~ (all_22_2 = e1) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (1457), (4064) imply: % 186.24/29.46 | | | | | | | (4070) ~ (all_16_2 = e1) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (1618), (4064) imply: % 186.24/29.46 | | | | | | | (4071) op(e0, e1) = e4 % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (137), (140), (143), (146), % 186.24/29.46 | | | | | | | (149), (156), (161), (164), (165), (168), (170), (171), % 186.24/29.46 | | | | | | | (173), (176), (177), (180), (182), (183), (185), (186), % 186.24/29.46 | | | | | | | (188), (189), (191), (195), (203), (224), (227), (231), % 186.24/29.46 | | | | | | | (257), (269), (280), (301), (323), (343), (362), (373), % 186.24/29.46 | | | | | | | (393), (404), (410), (480), (486), (492), (498), (504), % 186.24/29.46 | | | | | | | (514), (521), (729), (733), (749), (751), (752), (758), % 186.24/29.46 | | | | | | | (763), (773), (785), (792), (860), (1032), (1253), % 186.24/29.46 | | | | | | | (1255), (1294), (1302), (1314), (1349), (1352), (1358), % 186.24/29.46 | | | | | | | (1362), (1364), (1426), (1428), (1439), (1445), (1452), % 186.24/29.46 | | | | | | | (1477), (1483), (1490), (1497), (1503), (1504), (1506), % 186.24/29.46 | | | | | | | (1529), (1536), (1538), (1551), (1554), (1563), (1587), % 186.24/29.46 | | | | | | | (1588), (1589), (1595), (1597), (1599), (1600), (1603), % 186.24/29.46 | | | | | | | (1604), (1608), (1609), (1612), (1614), (1619), (1621), % 186.24/29.46 | | | | | | | (1622), (1623), (1624), (1626), (4062), (4065), (4066), % 186.24/29.46 | | | | | | | (4067), (4068), (4069), (4070), (4071), % 186.24/29.46 | | | | | | | (function-axioms) are inconsistent by sub-proof #314. % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | End of split % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | Case 2: % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | (4072) all_12_2 = e3 % 186.24/29.46 | | | | | | (4073) op(e3, e0) = all_12_1 & $i(all_12_1) & ( ~ (all_12_1 = e2) % 186.24/29.46 | | | | | | | ( ~ (all_12_0 = e1) & op(e0, e2) = all_12_0 & % 186.24/29.46 | | | | | | $i(all_12_0))) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | ALPHA: (4073) implies: % 186.24/29.46 | | | | | | (4074) op(e3, e0) = all_12_1 % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | COMBINE_EQS: (1374), (4072) imply: % 186.24/29.46 | | | | | | (4075) all_212_2 = e3 % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1440), (4072) imply: % 186.24/29.46 | | | | | | (4076) ~ (all_244_0 = e3) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1446), (4072) imply: % 186.24/29.46 | | | | | | (4077) ~ (all_100_2 = e3) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1453), (4072) imply: % 186.24/29.46 | | | | | | (4078) ~ (all_64_2 = e3) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1468), (4072) imply: % 186.24/29.46 | | | | | | (4079) ~ (all_28_2 = e3) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1470), (4072) imply: % 186.24/29.46 | | | | | | (4080) ~ (all_20_2 = e3) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1457), (4072) imply: % 186.24/29.46 | | | | | | (4081) ~ (all_16_2 = e3) % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1594), (4072) imply: % 186.24/29.46 | | | | | | (4082) op(all_30_2, e3) = e0 % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1593), (4072) imply: % 186.24/29.46 | | | | | | (4083) op(e3, all_30_2) = e4 % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | REDUCE: (1618), (4072) imply: % 186.24/29.46 | | | | | | (4084) op(e0, e3) = e4 % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | BETA: splitting (437) gives: % 186.24/29.46 | | | | | | % 186.24/29.46 | | | | | | Case 1: % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | (4085) ~ (all_212_2 = e3) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | REDUCE: (4075), (4085) imply: % 186.24/29.46 | | | | | | | (4086) $false % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | CLOSE: (4086) is inconsistent. % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | Case 2: % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | (4087) op(e3, e0) = all_212_1 & $i(all_212_1) & ( ~ (all_212_1 % 186.24/29.46 | | | | | | | = e1) | ( ~ (all_212_0 = e2) & op(e0, e1) = % 186.24/29.46 | | | | | | | all_212_0 & $i(all_212_0))) % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | ALPHA: (4087) implies: % 186.24/29.46 | | | | | | | (4088) op(e3, e0) = all_212_1 % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | BETA: splitting (794) gives: % 186.24/29.46 | | | | | | | % 186.24/29.46 | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | | (4089) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & % 186.24/29.46 | | | | | | | | op(e3, e4) = e3) % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | | REF_CLOSE: (280), (504), (4076), (4077), (4089), % 186.24/29.46 | | | | | | | | (function-axioms) are inconsistent by sub-proof #559. % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | Case 2: % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | | (4090) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 % 186.24/29.46 | | | | | | | | & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = % 186.24/29.46 | | | | | | | | e3) % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | | BETA: splitting (4090) gives: % 186.24/29.46 | | | | | | | | % 186.24/29.46 | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | % 186.24/29.46 | | | | | | | | | (4091) all_252_6 = e3 & op(e2, e4) = e3 % 186.24/29.46 | | | | | | | | | % 186.24/29.46 | | | | | | | | | REF_CLOSE: (227), (4078), (4091), (function-axioms) are % 186.24/29.46 | | | | | | | | | inconsistent by sub-proof #432. % 186.24/29.46 | | | | | | | | | % 186.24/29.46 | | | | | | | | Case 2: % 186.24/29.46 | | | | | | | | | % 186.24/29.46 | | | | | | | | | (4092) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = % 186.24/29.46 | | | | | | | | | e3 & op(e0, e4) = e3) % 186.24/29.46 | | | | | | | | | % 186.24/29.46 | | | | | | | | | BETA: splitting (4092) gives: % 186.24/29.46 | | | | | | | | | % 186.24/29.46 | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | (4093) all_252_12 = e3 & op(e1, e4) = e3 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REF_CLOSE: (155), (4081), (4093), (function-axioms) are % 186.24/29.46 | | | | | | | | | | inconsistent by sub-proof #513. % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | Case 2: % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | (4094) all_252_20 = e3 & op(e0, e4) = e3 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | ALPHA: (4094) implies: % 186.24/29.46 | | | | | | | | | | (4095) all_252_20 = e3 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_2, e4, % 186.24/29.46 | | | | | | | | | | e3, e0, simplifying with (164), (4084) gives: % 186.24/29.46 | | | | | | | | | | (4096) all_22_2 = e4 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_2, % 186.24/29.46 | | | | | | | | | | all_212_1, e0, e3, simplifying with (203), (4088) % 186.24/29.46 | | | | | | | | | | gives: % 186.24/29.46 | | | | | | | | | | (4097) all_212_1 = all_48_2 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1, % 186.24/29.46 | | | | | | | | | | all_212_1, e0, e3, simplifying with (4074), (4088) % 186.24/29.46 | | | | | | | | | | gives: % 186.24/29.46 | | | | | | | | | | (4098) all_212_1 = all_12_1 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | COMBINE_EQS: (4097), (4098) imply: % 186.24/29.46 | | | | | | | | | | (4099) all_48_2 = all_12_1 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | COMBINE_EQS: (1340), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4100) all_72_2 = e4 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1506), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4101) ~ (all_244_24 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1477), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4102) ~ (all_84_2 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1503), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4103) ~ (all_28_2 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1504), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4104) ~ (all_20_2 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | SIMP: (4104) implies: % 186.24/29.46 | | | | | | | | | | (4105) ~ (all_20_2 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1490), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4106) ~ (all_10_2 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | SIMP: (4106) implies: % 186.24/29.46 | | | | | | | | | | (4107) ~ (all_10_2 = e4) % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1596), (4096), (4099) imply: % 186.24/29.46 | | | | | | | | | | (4108) op(all_12_1, e4) = e0 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1609), (4099) imply: % 186.24/29.46 | | | | | | | | | | (4109) op(e3, all_12_1) = e0 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | REDUCE: (1619), (4096) imply: % 186.24/29.46 | | | | | | | | | | (4110) op(e0, e4) = e3 % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | BETA: splitting (240) gives: % 186.24/29.46 | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | (4111) ~ (all_72_2 = e4) % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | REDUCE: (4100), (4111) imply: % 186.24/29.46 | | | | | | | | | | | (4112) $false % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | CLOSE: (4112) is inconsistent. % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | Case 2: % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | (4113) op(e4, e0) = all_72_1 & $i(all_72_1) & ( ~ % 186.24/29.46 | | | | | | | | | | | (all_72_1 = e1) | ( ~ (all_72_0 = e2) & op(e0, % 186.24/29.46 | | | | | | | | | | | e1) = all_72_0 & $i(all_72_0))) % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | ALPHA: (4113) implies: % 186.24/29.46 | | | | | | | | | | | (4114) op(e4, e0) = all_72_1 % 186.24/29.46 | | | | | | | | | | | (4115) ~ (all_72_1 = e1) | ( ~ (all_72_0 = e2) & op(e0, % 186.24/29.46 | | | | | | | | | | | e1) = all_72_0 & $i(all_72_0)) % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, % 186.24/29.46 | | | | | | | | | | | all_72_1, e0, e4, simplifying with (176), (4114) % 186.24/29.46 | | | | | | | | | | | gives: % 186.24/29.46 | | | | | | | | | | | (4116) all_72_1 = all_30_2 % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | BETA: splitting (171) gives: % 186.24/29.46 | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | (4117) ~ (all_26_2 = e0) % 186.24/29.46 | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | BETA: splitting (174) gives: % 186.24/29.46 | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | (4118) ~ (all_28_2 = e1) % 186.24/29.46 | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | BETA: splitting (177) gives: % 186.24/29.46 | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | (4119) ~ (all_30_2 = e3) % 186.24/29.46 | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | BETA: splitting (183) gives: % 186.24/29.46 | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | (4120) ~ (all_34_2 = e4) % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (11), (12), (13), (137), % 186.24/29.46 | | | | | | | | | | | | | | | (140), (143), (146), (155), (161), (170), (173), % 186.24/29.46 | | | | | | | | | | | | | | | (176), (182), (185), (186), (188), (189), (191), % 186.24/29.46 | | | | | | | | | | | | | | | (201), (219), (224), (237), (246), (257), (278), % 186.24/29.46 | | | | | | | | | | | | | | | (280), (284), (382), (385), (404), (480), (486), % 186.24/29.46 | | | | | | | | | | | | | | | (492), (498), (505), (750), (751), (763), (773), % 186.24/29.46 | | | | | | | | | | | | | | | (783), (1255), (1306), (1317), (1328), (1343), % 186.24/29.46 | | | | | | | | | | | | | | | (1350), (1353), (1366), (1367), (1448), (1492), % 186.24/29.46 | | | | | | | | | | | | | | | (1500), (1529), (1560), (1578), (1597), (1601), % 186.24/29.46 | | | | | | | | | | | | | | | (1606), (1608), (1611), (1612), (1613), (1614), % 186.24/29.46 | | | | | | | | | | | | | | | (1621), (1622), (1623), (1624), (4074), (4084), % 186.24/29.46 | | | | | | | | | | | | | | | (4095), (4101), (4108), (4109), (4117), (4118), % 186.24/29.46 | | | | | | | | | | | | | | | (4119), (4120), (function-axioms) are inconsistent % 186.24/29.46 | | | | | | | | | | | | | | | by sub-proof #308. % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | Case 2: % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | (4121) all_34_2 = e4 % 186.24/29.46 | | | | | | | | | | | | | | | (4122) op(e4, e1) = all_34_1 & $i(all_34_1) & ( ~ % 186.24/29.46 | | | | | | | | | | | | | | | (all_34_1 = e2) | ( ~ (all_34_0 = e3) & op(e1, % 186.24/29.46 | | | | | | | | | | | | | | | e2) = all_34_0 & $i(all_34_0))) % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | ALPHA: (4122) implies: % 186.24/29.46 | | | | | | | | | | | | | | | (4123) op(e4, e1) = all_34_1 % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | COMBINE_EQS: (1379), (4121) imply: % 186.24/29.46 | | | | | | | | | | | | | | | (4124) all_232_2 = e4 % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | REDUCE: (1600), (4121) imply: % 186.24/29.46 | | | | | | | | | | | | | | | (4125) op(e4, all_20_2) = e0 % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | REDUCE: (1617), (4121) imply: % 186.24/29.46 | | | | | | | | | | | | | | | (4126) op(e1, e4) = e0 % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | BETA: splitting (463) gives: % 186.24/29.46 | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | Case 1: % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | (4127) ~ (all_232_2 = e4) % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | REDUCE: (4124), (4127) imply: % 186.24/29.46 | | | | | | | | | | | | | | | | (4128) $false % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | CLOSE: (4128) is inconsistent. % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | Case 2: % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | (4129) op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 186.24/29.46 | | | | | | | | | | | | | | | | (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, % 186.24/29.46 | | | | | | | | | | | | | | | | e3) = all_232_0 & $i(all_232_0))) % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | ALPHA: (4129) implies: % 186.24/29.46 | | | | | | | | | | | | | | | | (4130) op(e4, e1) = all_232_1 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, e0, % 186.24/29.46 | | | | | | | | | | | | | | | | e4, e1, simplifying with (155), (4126) gives: % 186.24/29.46 | | | | | | | | | | | | | | | | (4131) all_16_2 = e0 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 186.24/29.46 | | | | | | | | | | | | | | | | all_232_1, e1, e4, simplifying with (170), (4130) % 186.24/29.46 | | | | | | | | | | | | | | | | gives: % 186.24/29.46 | | | | | | | | | | | | | | | | (4132) all_232_1 = all_26_2 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_1, % 186.24/29.46 | | | | | | | | | | | | | | | | all_232_1, e1, e4, simplifying with (4123), (4130) % 186.24/29.46 | | | | | | | | | | | | | | | | gives: % 186.24/29.46 | | | | | | | | | | | | | | | | (4133) all_232_1 = all_34_1 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (4132), (4133) imply: % 186.24/29.46 | | | | | | | | | | | | | | | | (4134) all_34_1 = all_26_2 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (1302), (4131) imply: % 186.24/29.46 | | | | | | | | | | | | | | | | (4135) all_66_2 = e0 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | COMBINE_EQS: (1365), (4131) imply: % 186.24/29.46 | | | | | | | | | | | | | | | | (4136) all_170_2 = e0 % 186.24/29.46 | | | | | | | | | | | | | | | | % 186.24/29.46 | | | | | | | | | | | | | | | | REDUCE: (1462), (4131) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | (4137) ~ (all_244_15 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | REDUCE: (1460), (4131) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | (4138) ~ (all_4_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | REDUCE: (1614), (4131) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | (4139) op(e1, e0) = e4 % 186.24/29.47 | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | (4140) ~ (all_66_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | REDUCE: (4135), (4140) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | (4141) $false % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | CLOSE: (4141) is inconsistent. % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | (4142) op(e0, e1) = all_66_1 & $i(all_66_1) & ( ~ % 186.24/29.47 | | | | | | | | | | | | | | | | | (all_66_1 = e3) | ( ~ (all_66_0 = e2) & op(e1, % 186.24/29.47 | | | | | | | | | | | | | | | | | e3) = all_66_0 & $i(all_66_0))) % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | ALPHA: (4142) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | (4143) op(e0, e1) = all_66_1 % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4144) ~ (all_170_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | REDUCE: (4136), (4144) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4145) $false % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | CLOSE: (4145) is inconsistent. % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4146) op(e0, e1) = all_170_1 & $i(all_170_1) & ( ~ % 186.24/29.47 | | | | | | | | | | | | | | | | | | (all_170_1 = e2) | ( ~ (all_170_0 = e3) & op(e1, % 186.24/29.47 | | | | | | | | | | | | | | | | | | e2) = all_170_0 & $i(all_170_0))) % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | ALPHA: (4146) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4147) op(e0, e1) = all_170_1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4148) ~ (all_170_1 = e2) | ( ~ (all_170_0 = e3) & % 186.24/29.47 | | | | | | | | | | | | | | | | | | op(e1, e2) = all_170_0 & $i(all_170_0)) % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, % 186.24/29.47 | | | | | | | | | | | | | | | | | | all_170_1, e1, e0, simplifying with (161), (4147) % 186.24/29.47 | | | | | | | | | | | | | | | | | | gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4149) all_170_1 = all_20_2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_66_1, % 186.24/29.47 | | | | | | | | | | | | | | | | | | all_170_1, e1, e0, simplifying with (4143), (4147) % 186.24/29.47 | | | | | | | | | | | | | | | | | | gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4150) all_170_1 = all_66_1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4149), (4150) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | (4151) all_66_1 = all_20_2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | (4152) ~ (all_36_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4153) ~ (all_38_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (12), (161), (170), (173), (185), (188), % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (480), (486), (505), (750), (763), (1560), (4084), % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4095), (4117), (4118), (4137), (4152), (4153), % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | #310. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4154) all_38_2 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4155) op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | e4) = all_38_0 & $i(all_38_0))) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | ALPHA: (4155) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4156) op(e0, e2) = all_38_1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1255), (4154) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4157) all_188_2 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1529), (4154) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4158) ~ (all_244_8 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1494), (4154) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4159) ~ (all_10_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | SIMP: (4159) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4160) ~ (all_10_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1612), (4154) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4161) op(e2, e0) = e1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (4162) ~ (all_188_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4157), (4162) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (4163) $false % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4163) is inconsistent. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (4164) op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | e3) = all_188_0 & $i(all_188_0))) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4164) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (4165) op(e0, e2) = all_188_1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | (4166) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e2) = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (143), (1623), (1624), (4166), % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | #546. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | (4167) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4167) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | (4168) all_252_8 = e0 & op(e2, e2) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4168) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | (4169) op(e2, e2) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (4158), (4169), (function-axioms) are % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #448. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | (4170) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4170) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4171) all_252_14 = e0 & op(e1, e2) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4171) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4172) op(e1, e2) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (4172), (function-axioms) are % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4173) all_252_22 = e0 & op(e0, e2) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4173) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4174) op(e0, e2) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1, % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (4156), (4174) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4175) all_38_1 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_188_1, e2, e0, simplifying with (173), (4165) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4176) all_188_1 = all_28_2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_1, % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | all_188_1, e2, e0, simplifying with (4156), (4165) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4177) all_188_1 = all_38_1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, e1, % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (191), (4161) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4178) all_40_2 = e1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4176), (4177) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4179) all_38_1 = all_28_2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4179) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4180) all_38_1 = all_28_2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4175), (4180) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4181) all_28_2 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4181) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4182) all_28_2 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4103), (4182) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4183) ~ (e4 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1598), (4178), (4182) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4184) op(e1, e0) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (4139), (4184), (function-axioms) are % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4185) all_112_2 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1326), (4185) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4186) all_62_2 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4186) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4187) all_62_2 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1488), (4187) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4188) ~ (all_10_2 = e2) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4188) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4189) ~ (all_10_2 = e2) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (736), (1431), (1585), (1607), (1625), (4107), % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | (4160), (4189), (function-axioms) are inconsistent % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #567. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | (4190) all_36_2 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | REDUCE: (1540), (4190) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | (4191) ~ (all_26_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | REDUCE: (1552), (4190) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | (4192) ~ (all_20_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | SIMP: (4192) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | (4193) ~ (all_20_2 = e0) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (4148) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4194) ~ (all_170_1 = e2) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (4149), (4194) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4195) ~ (all_20_2 = e2) % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (4196) all_250_23 = e4 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (4105), (4196) are inconsistent by % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | (4197) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | e1 | all_250_23 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4197) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | (4198) all_250_23 = e3 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (4080), (4198) are inconsistent by % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | sub-proof #488. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | (4199) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4199) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | (4200) all_250_23 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (4195), (4200) are inconsistent by % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #487. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | (4201) all_250_23 = e1 | all_250_23 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4201) gives: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4202) all_250_23 = e1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (4202) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4203) all_20_2 = e1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4203) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4204) all_20_2 = e1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4125), (4204) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4205) op(e4, e1) = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4117), (4205), (function-axioms) are % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #452. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | (4206) all_250_23 = e0 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (4193), (4206) are inconsistent by % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #486. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4207) all_170_1 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4149), (4207) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4208) all_20_2 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | SIMP: (4208) implies: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4209) all_20_2 = e2 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REDUCE: (1621), (4209) imply: % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | (4210) op(e0, e2) = e1 % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4118), (4210), (function-axioms) are % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 186.24/29.47 | | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | (4211) all_30_2 = e3 % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | REDUCE: (4082), (4211) imply: % 186.24/29.47 | | | | | | | | | | | | | | (4212) op(e3, e3) = e0 % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | REDUCE: (4083), (4211) imply: % 186.24/29.47 | | | | | | | | | | | | | | (4213) op(e3, e3) = e4 % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_3, % 186.24/29.47 | | | | | | | | | | | | | | e0, e3, e3, simplifying with (498), (4212) gives: % 186.24/29.47 | | | | | | | | | | | | | | (4214) all_244_3 = e0 % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_3, % 186.24/29.47 | | | | | | | | | | | | | | e4, e3, e3, simplifying with (498), (4213) gives: % 186.24/29.47 | | | | | | | | | | | | | | (4215) all_244_3 = e4 % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | COMBINE_EQS: (4214), (4215) imply: % 186.24/29.47 | | | | | | | | | | | | | | (4216) e4 = e0 % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | REDUCE: (11), (4216) imply: % 186.24/29.47 | | | | | | | | | | | | | | (4217) $false % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | | CLOSE: (4217) is inconsistent. % 186.24/29.47 | | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | (4218) all_28_2 = e1 % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | COMBINE_EQS: (1186), (4218) imply: % 186.24/29.47 | | | | | | | | | | | | | (4219) all_162_2 = e1 % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | REDUCE: (1538), (4218) imply: % 186.24/29.47 | | | | | | | | | | | | | (4220) ~ (all_244_24 = e1) % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | REDUCE: (4103), (4218) imply: % 186.24/29.47 | | | | | | | | | | | | | (4221) ~ (e4 = e1) % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | REDUCE: (4079), (4218) imply: % 186.24/29.47 | | | | | | | | | | | | | (4222) ~ (e3 = e1) % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | REDUCE: (1620), (4218) imply: % 186.24/29.47 | | | | | | | | | | | | | (4223) op(e0, e1) = e2 % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (12), (137), (140), (143), (161), % 186.24/29.47 | | | | | | | | | | | | | (368), (480), (492), (521), (750), (773), (1563), % 186.24/29.47 | | | | | | | | | | | | | (1622), (1623), (1624), (4084), (4095), (4110), % 186.24/29.47 | | | | | | | | | | | | | (4219), (4220), (4223), (function-axioms) are % 186.24/29.47 | | | | | | | | | | | | | inconsistent by sub-proof #306. % 186.24/29.47 | | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | End of split % 186.24/29.47 | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | Case 2: % 186.24/29.47 | | | | | | | | | | | | % 186.24/29.47 | | | | | | | | | | | | (4224) all_26_2 = e0 % 186.24/29.48 | | | | | | | | | | | | (4225) op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 186.24/29.48 | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 186.24/29.48 | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | ALPHA: (4225) implies: % 186.24/29.48 | | | | | | | | | | | | (4226) op(e0, e4) = all_26_1 % 186.24/29.48 | | | | | | | | | | | | (4227) ~ (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 186.24/29.48 | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0)) % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | COMBINE_EQS: (1341), (4224) imply: % 186.24/29.48 | | | | | | | | | | | | (4228) all_44_2 = e0 % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | REDUCE: (1479), (4224) imply: % 186.24/29.48 | | | | | | | | | | | | (4229) ~ (all_84_2 = e0) % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | REDUCE: (1542), (4224) imply: % 186.24/29.48 | | | | | | | | | | | | (4230) ~ (all_38_2 = e0) % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | REDUCE: (1545), (4224) imply: % 186.24/29.48 | | | | | | | | | | | | (4231) ~ (all_20_2 = e0) % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | SIMP: (4231) implies: % 186.24/29.48 | | | | | | | | | | | | (4232) ~ (all_20_2 = e0) % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | REDUCE: (1603), (4224) imply: % 186.24/29.48 | | | | | | | | | | | | (4233) op(e4, e0) = e1 % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | BETA: splitting (198) gives: % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | (4234) ~ (all_44_2 = e0) % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | REDUCE: (4228), (4234) imply: % 186.24/29.48 | | | | | | | | | | | | | (4235) $false % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | CLOSE: (4235) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | (4236) op(e0, e4) = all_44_1 & $i(all_44_1) & ( ~ % 186.24/29.48 | | | | | | | | | | | | | (all_44_1 = e2) | ( ~ (all_44_0 = e3) & op(e4, % 186.24/29.48 | | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0))) % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | ALPHA: (4236) implies: % 186.24/29.48 | | | | | | | | | | | | | (4237) op(e0, e4) = all_44_1 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1, % 186.24/29.48 | | | | | | | | | | | | | e4, e0, simplifying with (4110), (4237) gives: % 186.24/29.48 | | | | | | | | | | | | | (4238) all_44_1 = e3 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1, % 186.24/29.48 | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (4226), (4237) % 186.24/29.48 | | | | | | | | | | | | | gives: % 186.24/29.48 | | | | | | | | | | | | | (4239) all_44_1 = all_26_1 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 186.24/29.48 | | | | | | | | | | | | | e0, e4, simplifying with (176), (4233) gives: % 186.24/29.48 | | | | | | | | | | | | | (4240) all_30_2 = e1 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | COMBINE_EQS: (4238), (4239) imply: % 186.24/29.48 | | | | | | | | | | | | | (4241) all_26_1 = e3 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | COMBINE_EQS: (4116), (4240) imply: % 186.24/29.48 | | | | | | | | | | | | | (4242) all_72_1 = e1 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | COMBINE_EQS: (1202), (4240) imply: % 186.24/29.48 | | | | | | | | | | | | | (4243) all_132_2 = e1 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | REDUCE: (1480), (4240) imply: % 186.24/29.48 | | | | | | | | | | | | | (4244) ~ (all_84_2 = e1) % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | REDUCE: (4082), (4240) imply: % 186.24/29.48 | | | | | | | | | | | | | (4245) op(e1, e3) = e0 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | REDUCE: (4083), (4240) imply: % 186.24/29.48 | | | | | | | | | | | | | (4246) op(e3, e1) = e4 % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | BETA: splitting (4115) gives: % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | (4247) ~ (all_72_1 = e1) % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | REDUCE: (4242), (4247) imply: % 186.24/29.48 | | | | | | | | | | | | | | (4248) $false % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | CLOSE: (4248) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | (4249) ~ (all_72_0 = e2) & op(e0, e1) = all_72_0 & % 186.24/29.48 | | | | | | | | | | | | | | $i(all_72_0) % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | ALPHA: (4249) implies: % 186.24/29.48 | | | | | | | | | | | | | | (4250) ~ (all_72_0 = e2) % 186.24/29.48 | | | | | | | | | | | | | | (4251) op(e0, e1) = all_72_0 % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | BETA: splitting (4227) gives: % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | (4252) ~ (all_26_1 = e3) % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | REDUCE: (4241), (4252) imply: % 186.24/29.48 | | | | | | | | | | | | | | | (4253) $false % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | CLOSE: (4253) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | (4254) ~ (all_26_0 = e2) & op(e4, e3) = all_26_0 & % 186.24/29.48 | | | | | | | | | | | | | | | $i(all_26_0) % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | ALPHA: (4254) implies: % 186.24/29.48 | | | | | | | | | | | | | | | (4255) ~ (all_26_0 = e2) % 186.24/29.48 | | | | | | | | | | | | | | | (4256) op(e4, e3) = all_26_0 % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | (4257) ~ (all_132_2 = e1) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (4243), (4257) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4258) $false % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | CLOSE: (4258) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, % 186.24/29.48 | | | | | | | | | | | | | | | | all_72_0, e1, e0, simplifying with (161), (4251) % 186.24/29.48 | | | | | | | | | | | | | | | | gives: % 186.24/29.48 | | | | | | | | | | | | | | | | (4259) all_72_0 = all_20_2 % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e0, % 186.24/29.48 | | | | | | | | | | | | | | | | e3, e1, simplifying with (224), (4245) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | (4260) all_62_2 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e4, % 186.24/29.48 | | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (4246) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | (4261) all_36_2 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, % 186.24/29.48 | | | | | | | | | | | | | | | | all_26_0, e3, e4, simplifying with (257), (4256) % 186.24/29.48 | | | | | | | | | | | | | | | | gives: % 186.24/29.48 | | | | | | | | | | | | | | | | (4262) all_84_2 = all_26_0 % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | COMBINE_EQS: (989), (4262) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4263) all_250_1 = all_26_0 % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (1475), (4262) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4264) ~ (all_26_0 = all_10_2) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (4102), (4262) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4265) ~ (all_26_0 = e4) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (4244), (4262) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4266) ~ (all_26_0 = e1) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (4229), (4262) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4267) ~ (all_26_0 = e0) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (4250), (4259) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4268) ~ (all_20_2 = e2) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (1488), (4260) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4269) ~ (all_10_2 = e0) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | SIMP: (4269) implies: % 186.24/29.48 | | | | | | | | | | | | | | | | (4270) ~ (all_10_2 = e0) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | REDUCE: (1549), (4261) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | (4271) ~ (all_38_2 = e4) % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | BETA: splitting (746) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | (4272) all_250_1 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | COMBINE_EQS: (4263), (4272) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | (4273) all_26_0 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | REDUCE: (4265), (4273) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | (4274) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | CLOSE: (4274) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | (4275) all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 | % 186.24/29.48 | | | | | | | | | | | | | | | | | all_250_1 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | BETA: splitting (4275) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | (4276) all_250_1 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4263), (4276) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | (4277) all_26_0 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | REDUCE: (4264), (4277) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | (4278) ~ (all_10_2 = e3) % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | SIMP: (4278) implies: % 186.24/29.48 | | | | | | | | | | | | | | | | | | (4279) ~ (all_10_2 = e3) % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | BETA: splitting (736) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4280) all_250_11 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1431), (4280) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4281) all_10_2 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | REDUCE: (4107), (4281) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4282) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | CLOSE: (4282) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4283) all_250_11 = e3 | all_250_11 = e2 | all_250_11 = % 186.24/29.48 | | | | | | | | | | | | | | | | | | | e1 | all_250_11 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (4283) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4284) all_250_11 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1431), (4284) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4285) all_10_2 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (4279), (4285) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4286) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | CLOSE: (4286) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4287) all_250_11 = e2 | all_250_11 = e1 | all_250_11 = % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4287) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | (4288) all_250_11 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1431), (4288) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | (4289) all_10_2 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1494), (4289) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | (4290) ~ (all_38_2 = e2) % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | (4291) all_250_23 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (4291) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | (4292) all_20_2 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4105), (4292) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | (4293) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4293) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | (4294) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_23 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4294) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | (4295) all_250_23 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (4295) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | (4296) all_20_2 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4080), (4296) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | (4297) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4297) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | (4298) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4298) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | (4299) all_250_23 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (4299) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | (4300) all_20_2 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4268), (4300) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | (4301) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4301) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | (4302) all_250_23 = e1 | all_250_23 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4302) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4303) all_250_23 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (4303) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4304) all_20_2 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1557), (4304) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4305) ~ (all_38_2 = e1) % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (735) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4306) all_250_13 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (4306) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4307) all_38_2 = e4 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4271), (4307) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4308) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4308) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | (4309) all_250_13 = e3 | all_250_13 = e2 | all_250_13 = % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_13 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4309) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4310) all_250_13 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (4310) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4311) all_38_2 = e3 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1612), (4311) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4312) op(e2, e3) = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (1625), (4312), (function-axioms) are % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4313) all_250_13 = e2 | all_250_13 = e1 | all_250_13 = % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4313) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4314) all_250_13 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (4314) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4315) all_38_2 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4290), (4315) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4316) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4316) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4317) all_250_13 = e1 | all_250_13 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4317) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4318) all_250_13 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (4318) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4319) all_38_2 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4319) implies: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4320) all_38_2 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4305), (4320) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4321) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4321) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4322) all_250_13 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1430), (4322) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4323) all_38_2 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4323) implies: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4324) all_38_2 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4230), (4324) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4325) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4325) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4326) all_250_23 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (4326) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4327) all_20_2 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4232), (4327) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | (4328) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4328) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | (4329) all_250_11 = e1 | all_250_11 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1431), (1625), (4270), (4329) are inconsistent by % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | sub-proof #568. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | (4330) all_250_1 = e2 | all_250_1 = e1 | all_250_1 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | BETA: splitting (4330) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4331) all_250_1 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4263), (4331) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4332) all_26_0 = e2 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | REDUCE: (4255), (4332) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4333) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | CLOSE: (4333) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | (4334) all_250_1 = e1 | all_250_1 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (4334) gives: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4335) all_250_1 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4263), (4335) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4336) all_26_0 = e1 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (4266), (4336) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4337) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | CLOSE: (4337) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4338) all_250_1 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4263), (4338) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4339) all_26_0 = e0 % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | REDUCE: (4267), (4339) imply: % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | (4340) $false % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | CLOSE: (4340) is inconsistent. % 186.24/29.48 | | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | | % 186.24/29.48 | | | | | | | | | | End of split % 186.24/29.48 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | End of split % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | End of split % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | End of split % 186.24/29.49 | | | | | | | % 186.24/29.49 | | | | | | End of split % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | End of split % 186.24/29.49 | | | | | % 186.24/29.49 | | | | Case 2: % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | (4341) all_10_2 = e1 % 186.24/29.49 | | | | | (4342) op(e1, e2) = all_10_1 & $i(all_10_1) & ( ~ (all_10_1 = e4) | % 186.24/29.49 | | | | | ( ~ (all_10_0 = e0) & op(e2, e4) = all_10_0 & % 186.24/29.49 | | | | | $i(all_10_0))) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | ALPHA: (4342) implies: % 186.24/29.49 | | | | | (4343) op(e1, e2) = all_10_1 % 186.24/29.49 | | | | | (4344) ~ (all_10_1 = e4) | ( ~ (all_10_0 = e0) & op(e2, e4) = % 186.24/29.49 | | | | | all_10_0 & $i(all_10_0)) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | COMBINE_EQS: (897), (4341) imply: % 186.24/29.49 | | | | | (4345) all_124_2 = e1 % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1481), (4341) imply: % 186.24/29.49 | | | | | (4346) ~ (all_244_3 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1492), (4341) imply: % 186.24/29.49 | | | | | (4347) ~ (all_244_8 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1475), (4341) imply: % 186.24/29.49 | | | | | (4348) ~ (all_84_2 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1454), (4341) imply: % 186.24/29.49 | | | | | (4349) ~ (all_64_2 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1488), (4341) imply: % 186.24/29.49 | | | | | (4350) ~ (all_62_2 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1496), (4341) imply: % 186.24/29.49 | | | | | (4351) ~ (all_40_2 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1494), (4341) imply: % 186.24/29.49 | | | | | (4352) ~ (all_38_2 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1490), (4341) imply: % 186.24/29.49 | | | | | (4353) ~ (all_22_2 = e1) % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | REDUCE: (1611), (4341) imply: % 186.24/29.49 | | | | | (4354) op(e2, e1) = e3 % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | BETA: splitting (315) gives: % 186.24/29.49 | | | | | % 186.24/29.49 | | | | | Case 1: % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | (4355) ~ (all_124_2 = e1) % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | REDUCE: (4345), (4355) imply: % 186.24/29.49 | | | | | | (4356) $false % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | CLOSE: (4356) is inconsistent. % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | Case 2: % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | (4357) op(e1, e2) = all_124_1 & $i(all_124_1) & ( ~ (all_124_1 = % 186.24/29.49 | | | | | | e0) | ( ~ (all_124_0 = e4) & op(e2, e0) = all_124_0 & % 186.24/29.49 | | | | | | $i(all_124_0))) % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | ALPHA: (4357) implies: % 186.24/29.49 | | | | | | (4358) op(e1, e2) = all_124_1 % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | BETA: splitting (769) gives: % 186.24/29.49 | | | | | | % 186.24/29.49 | | | | | | Case 1: % 186.24/29.49 | | | | | | | % 186.24/29.49 | | | | | | | (4359) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & % 186.24/29.49 | | | | | | | op(e2, e3) = e1) % 186.24/29.49 | | | | | | | % 186.24/29.49 | | | | | | | BETA: splitting (4359) gives: % 186.24/29.49 | | | | | | | % 186.24/29.49 | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | (4360) all_252_6 = e1 & op(e2, e4) = e1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | ALPHA: (4360) implies: % 186.24/29.49 | | | | | | | | (4361) op(e2, e4) = e1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e1, % 186.24/29.49 | | | | | | | | e4, e2, simplifying with (227), (4361) gives: % 186.24/29.49 | | | | | | | | (4362) all_64_2 = e1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (4349), (4362) imply: % 186.24/29.49 | | | | | | | | (4363) $false % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | CLOSE: (4363) is inconsistent. % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | (4364) all_252_7 = e1 & op(e2, e3) = e1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | ALPHA: (4364) implies: % 186.24/29.49 | | | | | | | | (4365) all_252_7 = e1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 186.24/29.49 | | | | | | | | all_124_1, e2, e1, simplifying with (137), (4358) % 186.24/29.49 | | | | | | | | gives: % 186.24/29.49 | | | | | | | | (4366) all_124_1 = all_4_2 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 186.24/29.49 | | | | | | | | all_124_1, e2, e1, simplifying with (4343), (4358) % 186.24/29.49 | | | | | | | | gives: % 186.24/29.49 | | | | | | | | (4367) all_124_1 = all_10_1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, e3, % 186.24/29.49 | | | | | | | | e1, e2, simplifying with (188), (4354) gives: % 186.24/29.49 | | | | | | | | (4368) all_38_2 = e3 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | COMBINE_EQS: (4366), (4367) imply: % 186.24/29.49 | | | | | | | | (4369) all_10_1 = all_4_2 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | COMBINE_EQS: (1195), (4368) imply: % 186.24/29.49 | | | | | | | | (4370) all_190_2 = e3 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | COMBINE_EQS: (887), (4368) imply: % 186.24/29.49 | | | | | | | | (4371) all_242_2 = e3 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1455), (4368) imply: % 186.24/29.49 | | | | | | | | (4372) ~ (all_64_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1559), (4368) imply: % 186.24/29.49 | | | | | | | | (4373) ~ (all_40_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1549), (4368) imply: % 186.24/29.49 | | | | | | | | (4374) ~ (all_36_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | SIMP: (4374) implies: % 186.24/29.49 | | | | | | | | (4375) ~ (all_36_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1542), (4368) imply: % 186.24/29.49 | | | | | | | | (4376) ~ (all_26_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | SIMP: (4376) implies: % 186.24/29.49 | | | | | | | | (4377) ~ (all_26_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1557), (4368) imply: % 186.24/29.49 | | | | | | | | (4378) ~ (all_20_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | SIMP: (4378) implies: % 186.24/29.49 | | | | | | | | (4379) ~ (all_20_2 = e3) % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1592), (4368) imply: % 186.24/29.49 | | | | | | | | (4380) op(e3, all_4_2) = e1 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | REDUCE: (1591), (4368) imply: % 186.24/29.49 | | | | | | | | (4381) op(all_4_2, e3) = e2 % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | BETA: splitting (478) gives: % 186.24/29.49 | | | | | | | | % 186.24/29.49 | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | (4382) ~ (all_242_2 = e3) % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | REDUCE: (4371), (4382) imply: % 186.24/29.49 | | | | | | | | | (4383) $false % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | CLOSE: (4383) is inconsistent. % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | (4384) op(e3, e2) = all_242_1 & $i(all_242_1) & ( ~ % 186.24/29.49 | | | | | | | | | (all_242_1 = e4) | ( ~ (all_242_0 = e0) & op(e2, % 186.24/29.49 | | | | | | | | | e4) = all_242_0 & $i(all_242_0))) % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | ALPHA: (4384) implies: % 186.24/29.49 | | | | | | | | | (4385) op(e3, e2) = all_242_1 % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | BETA: splitting (771) gives: % 186.24/29.49 | | | | | | | | | % 186.24/29.49 | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | (4386) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = % 186.24/29.49 | | | | | | | | | | e3 & op(e2, e3) = e3) % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | BETA: splitting (4386) gives: % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | (4387) all_252_6 = e3 & op(e2, e4) = e3 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | REF_CLOSE: (227), (4372), (4387), (function-axioms) are % 186.24/29.49 | | | | | | | | | | | inconsistent by sub-proof #432. % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | (4388) all_252_7 = e3 & op(e2, e3) = e3 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | ALPHA: (4388) implies: % 186.24/29.49 | | | | | | | | | | | (4389) all_252_7 = e3 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | COMBINE_EQS: (4365), (4389) imply: % 186.24/29.49 | | | | | | | | | | | (4390) e3 = e1 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | SIMP: (4390) implies: % 186.24/29.49 | | | | | | | | | | | (4391) e3 = e1 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | REDUCE: (9), (4391) imply: % 186.24/29.49 | | | | | | | | | | | (4392) $false % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | CLOSE: (4392) is inconsistent. % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | End of split % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | (4393) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = % 186.24/29.49 | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 & % 186.24/29.49 | | | | | | | | | | op(e2, e0) = e3) % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | BETA: splitting (4393) gives: % 186.24/29.49 | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | (4394) all_252_8 = e3 & op(e2, e2) = e3 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | ALPHA: (4394) implies: % 186.24/29.49 | | | | | | | | | | | (4395) op(e2, e2) = e3 % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | REF_CLOSE: (188), (492), (1529), (4354), (4395), % 186.24/29.49 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.49 | | | | | | | | | | | #495. % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | (4396) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 % 186.24/29.49 | | | | | | | | | | | = e3 & op(e2, e0) = e3) % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | BETA: splitting (4396) gives: % 186.24/29.49 | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | (4397) all_252_11 = e3 & op(e2, e1) = e3 % 186.24/29.49 | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | ALPHA: (4397) implies: % 186.24/29.49 | | | | | | | | | | | | (4398) all_252_11 = e3 % 186.24/29.49 | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | BETA: splitting (407) gives: % 186.24/29.49 | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | (4399) ~ (all_190_2 = e3) % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | REDUCE: (4370), (4399) imply: % 186.24/29.49 | | | | | | | | | | | | | (4400) $false % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | CLOSE: (4400) is inconsistent. % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | (4401) op(e3, e2) = all_190_1 & $i(all_190_1) & ( ~ % 186.24/29.49 | | | | | | | | | | | | | (all_190_1 = e0) | ( ~ (all_190_0 = e4) & op(e2, % 186.24/29.49 | | | | | | | | | | | | | e0) = all_190_0 & $i(all_190_0))) % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | ALPHA: (4401) implies: % 186.24/29.49 | | | | | | | | | | | | | (4402) op(e3, e2) = all_190_1 % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 186.24/29.49 | | | | | | | | | | | | | all_242_1, e2, e3, simplifying with (143), (4385) % 186.24/29.49 | | | | | | | | | | | | | gives: % 186.24/29.49 | | | | | | | | | | | | | (4403) all_242_1 = all_8_2 % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_190_1, % 186.24/29.49 | | | | | | | | | | | | | all_242_1, e2, e3, simplifying with (4385), (4402) % 186.24/29.49 | | | | | | | | | | | | | gives: % 186.24/29.49 | | | | | | | | | | | | | (4404) all_242_1 = all_190_1 % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | COMBINE_EQS: (4403), (4404) imply: % 186.24/29.49 | | | | | | | | | | | | | (4405) all_190_1 = all_8_2 % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | BETA: splitting (150) gives: % 186.24/29.49 | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | (4406) ~ (all_12_2 = e3) % 186.24/29.49 | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | BETA: splitting (153) gives: % 186.24/29.49 | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | (4407) ~ (all_14_2 = e1) % 186.24/29.49 | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | REDUCE: (1356), (4407) imply: % 186.24/29.49 | | | | | | | | | | | | | | | (4408) ~ (all_12_2 = e1) % 186.24/29.49 | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 186.24/29.49 | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | (4409) ~ (all_16_2 = e3) % 186.24/29.49 | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | (4410) ~ (all_18_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | REDUCE: (1231), (4410) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | (4411) ~ (all_12_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4412) ~ (all_24_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | REDUCE: (1349), (4412) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4413) ~ (all_16_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4414) ~ (all_34_2 = e4) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4415) ~ (all_62_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (155), (182), (224), (231), (350), (393), % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (732), (733), (857), (1253), (1265), (1302), % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (1428), (1460), (1587), (1591), (1603), (1612), % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (1614), (1616), (1622), (4409), (4413), (4414), % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4415), (function-axioms) are inconsistent by % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | sub-proof #569. % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4416) all_62_2 = e2 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1326), (4416) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4417) all_112_2 = e2 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (1615), (4416) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4418) op(e1, e2) = e3 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | (4419) ~ (all_112_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4417), (4419) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | (4420) $false % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4420) is inconsistent. % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (4418) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | (4421) all_4_2 = e3 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4380), (4421) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | (4422) op(e3, e3) = e1 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (4346), (4422), (function-axioms) are % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #305. % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4423) all_34_2 = e4 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (463), (730), (1379), (1427), (1457), % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (1593), (1604), (1617), (4406), (4408), (4411), % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4423), (function-axioms) are inconsistent by % 186.24/29.49 | | | | | | | | | | | | | | | | | | | sub-proof #437. % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4424) all_24_2 = e2 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1349), (4424) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4425) all_16_2 = e2 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | REDUCE: (1452), (4425) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4426) ~ (all_64_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | REDUCE: (1457), (4425) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4427) ~ (all_12_2 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | REDUCE: (1614), (4425) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4428) op(e1, e2) = e4 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, % 186.24/29.49 | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (4428) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4429) all_4_2 = e4 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4369), (4429) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4430) all_10_1 = e4 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1032), (4429) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4431) all_192_2 = e4 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | REDUCE: (4381), (4429) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4432) op(e4, e3) = e2 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | REDUCE: (4380), (4429) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | (4433) op(e3, e4) = e1 % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | BETA: splitting (4344) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4434) ~ (all_10_1 = e4) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | REDUCE: (4430), (4434) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4435) $false % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | CLOSE: (4435) is inconsistent. % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4436) ~ (all_10_0 = e0) & op(e2, e4) = all_10_0 & % 186.24/29.49 | | | | | | | | | | | | | | | | | | | $i(all_10_0) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | ALPHA: (4436) implies: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4437) ~ (all_10_0 = e0) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | (4438) op(e2, e4) = all_10_0 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4439) ~ (all_192_2 = e4) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (4431), (4439) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4440) $false % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | CLOSE: (4440) is inconsistent. % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | all_10_0, e4, e2, simplifying with (227), (4438) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4441) all_64_2 = all_10_0 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2, % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | e1, e4, e3, simplifying with (280), (4433) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4442) all_100_2 = e1 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e2, % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (4432) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4443) all_84_2 = e2 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1432), (4441) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4444) all_250_10 = all_10_0 % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (1446), (4442) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4445) ~ (all_12_2 = e1) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (4441) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4446) ~ (all_12_2 = all_10_0) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | SIMP: (4446) implies: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4447) ~ (all_12_2 = all_10_0) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (4372), (4441) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4448) ~ (all_10_0 = e3) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (4426), (4441) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4449) ~ (all_10_0 = e2) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (4349), (4441) imply: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | (4450) ~ (all_10_0 = e1) % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (737) gives: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.49 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4451) all_250_10 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4444), (4451) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4452) all_10_0 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4447), (4452) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4453) ~ (all_12_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4454) all_250_20 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1427), (4454) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4455) all_12_2 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4455) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4456) all_12_2 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4453), (4456) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4457) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4457) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4458) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_20 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4458) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4459) all_250_20 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1427), (4459) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4460) all_12_2 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4406), (4460) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4461) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4461) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4462) all_250_20 = e2 | all_250_20 = e1 | all_250_20 = % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4462) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4463) all_250_20 = e2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1427), (4463) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4464) all_12_2 = e2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4411), (4464) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4465) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4465) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4466) all_250_20 = e1 | all_250_20 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4466) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4467) all_250_20 = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1427), (4467) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4468) all_12_2 = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4408), (4468) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4469) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4469) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4470) all_250_20 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1427), (4470) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4471) all_12_2 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1470), (4471) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4472) ~ (all_20_2 = e0) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4408), (4471) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4473) ~ (e1 = e0) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4474) ~ (all_28_2 = e1) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4475) ~ (all_32_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1352), (4475) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4476) ~ (all_20_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (219), (727), (1350), (1424), (1599), % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617), (1621), (4379), (4472), (4474), (4476), % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | #484. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4477) all_32_2 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (1352), (1621), (4408), (4477), % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | #459. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4478) all_28_2 = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (137), (140), (143), (149), (161), % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (480), (492), (521), (750), (773), (1468), % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (1503), (1538), (1563), (1620), (1622), (1623), % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (1624), (4478), (function-axioms) are inconsistent % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #472. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4479) all_250_10 = e3 | all_250_10 = e2 | all_250_10 = % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | e1 | all_250_10 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4479) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4480) all_250_10 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4444), (4480) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4481) all_10_0 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4448), (4481) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4482) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4482) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4483) all_250_10 = e2 | all_250_10 = e1 | all_250_10 = % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4483) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4484) all_250_10 = e2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4444), (4484) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4485) all_10_0 = e2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4449), (4485) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4486) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4486) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4487) all_250_10 = e1 | all_250_10 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4487) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4488) all_250_10 = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4444), (4488) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4489) all_10_0 = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4450), (4489) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4490) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4490) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4491) all_250_10 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4444), (4491) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4492) all_10_0 = e0 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4437), (4492) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4493) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4493) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | (4494) all_18_2 = e2 % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (137), (140), (143), (173), (428), (434), % 186.24/29.50 | | | | | | | | | | | | | | | | | (480), (492), (521), (773), (828), (1231), (1372), % 186.24/29.50 | | | | | | | | | | | | | | | | | (1472), (1618), (1622), (1623), (1624), (4494), % 186.24/29.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.50 | | | | | | | | | | | | | | | | | #433. % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | End of split % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | (4495) all_16_2 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | (4496) op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ % 186.24/29.50 | | | | | | | | | | | | | | | | (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, % 186.24/29.50 | | | | | | | | | | | | | | | | e2) = all_16_0 & $i(all_16_0))) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | ALPHA: (4496) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | (4497) op(e3, e1) = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | (4498) ~ (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, % 186.24/29.50 | | | | | | | | | | | | | | | | e2) = all_16_0 & $i(all_16_0)) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | COMBINE_EQS: (1294), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4499) all_144_2 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1439), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4500) ~ (all_244_0 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1445), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4501) ~ (all_100_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1459), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4502) ~ (all_62_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1457), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4503) ~ (all_12_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1460), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4504) ~ (all_4_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | SIMP: (4504) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | (4505) ~ (all_4_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1588), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4506) op(all_26_2, e3) = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | REDUCE: (1614), (4495) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | (4507) op(e1, e3) = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | (4508) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 186.24/29.50 | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (504), (4500), (4501), (4508), % 186.24/29.50 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.50 | | | | | | | | | | | | | | | | | #559. % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | (4509) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 186.24/29.50 | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 186.24/29.50 | | | | | | | | | | | | | | | | | op(e0, e4) = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | BETA: splitting (4509) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | (4510) all_252_6 = e3 & op(e2, e4) = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (4372), (4510), (function-axioms) are % 186.24/29.50 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #432. % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | (4511) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 186.24/29.50 | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | BETA: splitting (4511) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | (4512) all_252_12 = e3 & op(e1, e4) = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | ALPHA: (4512) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | (4513) all_252_12 = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4514) ~ (all_144_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (4499), (4514) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4515) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | CLOSE: (4515) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4516) op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (all_144_1 = e0) | ( ~ (all_144_0 = e2) & op(e1, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | e0) = all_144_0 & $i(all_144_0))) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | ALPHA: (4516) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4517) op(e3, e1) = all_144_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e4, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (224), (4507) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4518) all_62_2 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | all_144_1, e1, e3, simplifying with (185), (4517) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4519) all_144_1 = all_36_2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_1, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | all_144_1, e1, e3, simplifying with (4497), (4517) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4520) all_144_1 = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4519), (4520) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4521) all_36_2 = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | SIMP: (4521) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4522) all_36_2 = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1345), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4523) all_52_2 = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1170), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4524) all_74_2 = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1314), (4518) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4525) all_114_2 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (860), (4518) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4526) all_130_2 = e4 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4527) all_250_8 = all_16_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1476), (4518) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4528) ~ (all_84_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1497), (4518) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4529) ~ (all_22_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | SIMP: (4529) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4530) ~ (all_22_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1498), (4518) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4531) ~ (all_4_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | SIMP: (4531) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4532) ~ (all_4_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1524), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4533) ~ (all_16_1 = all_8_2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (4375), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4534) ~ (all_16_1 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1589), (4518), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4535) op(e4, all_16_1) = e3 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | REDUCE: (1608), (4522) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | (4536) op(e3, all_16_1) = e1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4537) ~ (all_114_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4525), (4537) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4538) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | CLOSE: (4538) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4539) op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (all_114_1 = e0) | ( ~ (all_114_0 = e2) & op(e1, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | e0) = all_114_0 & $i(all_114_0))) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4539) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4540) op(e4, e1) = all_114_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | (4541) ~ (all_114_1 = e0) | ( ~ (all_114_0 = e2) & % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_114_0 & $i(all_114_0)) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4542) ~ (all_96_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1330), (4542) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | (4543) ~ (all_34_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (323) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4544) ~ (all_130_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4526), (4544) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4545) $false % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4545) is inconsistent. % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4546) op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (all_130_1 = e2) | ( ~ (all_130_0 = e0) & op(e1, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_130_0 & $i(all_130_0))) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4546) implies: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4547) op(e4, e1) = all_130_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | all_130_1, e1, e4, simplifying with (170), (4547) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4548) all_130_1 = all_26_2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_114_1, % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | all_130_1, e1, e4, simplifying with (4540), (4547) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4549) all_130_1 = all_114_1 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4548), (4549) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | (4550) all_114_1 = all_26_2 % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4551) ~ (all_18_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1231), (4551) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | (4552) ~ (all_12_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | (4553) ~ (all_22_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (4554) ~ (all_26_2 = e0) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4555) ~ (all_28_2 = e1) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4556) ~ (all_30_2 = e3) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4557) ~ (all_36_2 = e0) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4558) ~ (all_52_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4523), (4558) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4559) ~ (all_16_1 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4560) ~ (all_56_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1292), (4560) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4561) ~ (all_8_2 = e4) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4562) ~ (all_58_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1350), (4562) imply: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4563) ~ (all_20_2 = e2) % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives: % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4564) ~ (all_80_2 = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (4564) imply: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4565) ~ (all_6_2 = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4566) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4566) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4567) all_252_0 = e3 & op(e4, e4) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4567) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4568) op(e4, e4) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (4500), (4568), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #561. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4569) all_252_1 = e3 & op(e4, e3) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4569) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4570) all_252_1 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4571) op(e4, e3) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4572) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4572) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4573) all_252_1 = e2 & op(e4, e3) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (4570), (4573) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4574) all_252_3 = e2 & op(e3, e3) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4574) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4575) all_252_3 = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4576) op(e3, e3) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4577) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (257), (4571), (4575), (4577), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #303. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4578) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4578) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4579) all_252_7 = e0 & op(e2, e3) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4365), (4579) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #302. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4580) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4580) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4581) all_252_13 = e0 & op(e1, e3) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (4507), (4581), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_3, % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, e3, simplifying with (498), (4576) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4582) all_244_3 = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (526), (4582) imply: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4583) op(e2, e2) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (492), (1529), (4354), (4583), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #495. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4584) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (164), (4365), (4507), (4553), (4584), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #300. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4585) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4585) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4586) all_252_4 = e3 & op(e4, e2) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4586) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4587) op(e4, e2) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (4565), (4587), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #494. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4588) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (176), (4377), (4556), (4588), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #298. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4589) all_80_2 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1251), (4589) imply: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4590) all_6_2 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4590) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4591) all_6_2 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1478), (4591) imply: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4592) ~ (all_84_2 = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1513), (4591) imply: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4593) ~ (all_28_2 = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1602), (4591) imply: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4594) op(e4, e3) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4595) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4595) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4596) all_252_0 = e3 & op(e4, e4) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4596) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4597) op(e4, e4) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (4500), (4597), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #561. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4598) all_252_1 = e3 & op(e4, e3) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4598) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4599) all_252_1 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4600) op(e4, e3) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4601) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4601) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4602) all_252_1 = e2 & op(e4, e3) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (4599), (4602) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4603) all_252_3 = e2 & op(e3, e3) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4603) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4604) all_252_3 = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4605) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (257), (4600), (4604), (4605), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #303. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4606) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4606) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4607) all_252_7 = e0 & op(e2, e3) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4365), (4607) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #302. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4608) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4608) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4609) all_252_13 = e0 & op(e1, e3) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (4507), (4609), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4610) all_252_21 = e0 & op(e0, e3) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4610) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4611) all_252_21 = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4612) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4612) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4613) all_252_20 = e3 & op(e0, e4) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4613) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4614) op(e0, e4) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (4406), (4614), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4615) all_252_21 = e3 & op(e0, e3) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4615) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4616) all_252_21 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4611), (4616) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #334. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4617) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4617) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4618) all_252_22 = e3 & op(e0, e2) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4593), (4618), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4619) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4619) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4620) all_252_23 = e3 & op(e0, e1) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4620) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4621) op(e0, e1) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (4379), (4621), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4622) all_252_24 = e3 & op(e0, e0) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4622) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4623) all_252_24 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4624) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (4353), (4408), (4624), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #478. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4625) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4625) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4626) all_252_22 = e1 & op(e0, e2) = e1 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4626) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4627) op(e0, e2) = e1 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4555), (4627), (function-axioms) are % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4628) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4628) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4629) all_252_23 = e1 & op(e0, e1) = e1 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4629) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4630) all_252_23 = e1 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4631) op(e0, e1) = e1 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4632) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (4552), (4553), (4632), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4633) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4633) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4634) all_252_22 = e2 & op(e0, e2) = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4634) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4635) all_252_22 = e2 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4636) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4636) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4637) all_252_4 = e4 & op(e4, e2) = e4 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4637) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4638) all_252_4 = e4 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4639) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (4554), (4557), (4639), % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4640) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4640) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4641) all_252_11 = e0 & op(e2, e1) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4641) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4642) all_252_11 = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4398), (4642) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4643) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4643) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4644) all_252_15 = e0 & op(e1, e1) = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4644) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4645) all_252_15 = e0 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4646) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4646) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4647) all_252_4 = e3 & op(e4, e2) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4647) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4648) all_252_4 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4638), (4648) are inconsistent by sub-proof % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #296. % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4649) all_252_5 = e3 & op(e3, e2) = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4649) implies: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4650) all_252_5 = e3 % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (774) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4651) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4651) gives: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4652) all_252_4 = e1 & op(e4, e2) = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4652) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4653) all_252_4 = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4638), (4653) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4654) e4 = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4654) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4655) e4 = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (4655) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4656) $false % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4656) is inconsistent. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4657) all_252_5 = e1 & op(e3, e2) = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4657) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4658) all_252_5 = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4650), (4658) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4659) e3 = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4659) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4660) $false % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4660) is inconsistent. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4661) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4661) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4662) all_252_8 = e1 & op(e2, e2) = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4662) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4663) op(e2, e2) = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (4347), (4663), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #490. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4664) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (13), (173), (182), (760), (4507), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4513), (4543), (4555), (4645), (4664), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #408. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4665) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4665) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4666) all_252_8 = e3 & op(e2, e2) = e3 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4666) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4667) op(e2, e2) = e3 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (492), (1529), (4354), (4667), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #495. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4668) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4668) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4669) all_252_14 = e3 & op(e1, e2) = e3 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (4505), (4669), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4670) all_252_22 = e3 & op(e0, e2) = e3 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4593), (4670), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #509. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4671) all_252_23 = e0 & op(e0, e1) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4671) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4672) all_252_23 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4630), (4672) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4673) all_252_5 = e4 & op(e3, e2) = e4 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4673) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4674) op(e3, e2) = e4 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (4561), (4674), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4675) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4675) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4676) all_252_8 = e4 & op(e2, e2) = e4 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (137), (140), (143), (773), (1622), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623), (1624), (4635), (4676), (function-axioms) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4677) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4677) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4678) all_252_14 = e4 & op(e1, e2) = e4 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (758), (759), (760), (4507), (4513), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4543), (4678), (function-axioms) are inconsistent % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #412. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4679) all_252_22 = e4 & op(e0, e2) = e4 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (4635), (4679) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #294. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4680) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4680) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4681) all_252_23 = e2 & op(e0, e1) = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4681) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4682) op(e0, e1) = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (161), (4631), (4682), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #475. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4683) all_252_24 = e2 & op(e0, e0) = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4683) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4684) all_252_24 = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (4623), (4684) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #376. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4685) all_252_24 = e1 & op(e0, e0) = e1 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4623), (4685) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #399. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4686) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (13), (164), (4365), (4507), (4553), (4686), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #300. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4687) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4687) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4688) all_252_4 = e3 & op(e4, e2) = e3 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4688) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4689) all_252_4 = e3 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e2, % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (4594) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4690) all_84_2 = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1479), (4690) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4691) ~ (all_26_2 = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4691) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4692) ~ (all_26_2 = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1477), (4690) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4693) ~ (all_22_2 = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4528), (4690) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4694) ~ (e4 = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4592), (4690) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4695) ~ (e3 = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4696) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4497), (4559), (4692), (4696), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #393. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4697) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4697) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4698) all_252_11 = e2 & op(e2, e1) = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4698) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4699) all_252_11 = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4398), (4699) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4700) e3 = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (4700) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4701) $false % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4701) is inconsistent. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4702) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4702) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4703) all_252_15 = e2 & op(e1, e1) = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4703) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4704) all_252_15 = e2 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4705) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4705) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4706) all_252_12 = e0 & op(e1, e4) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4706) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4707) all_252_12 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4513), (4707) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #381. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4708) all_252_13 = e0 & op(e1, e3) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (4507), (4708), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #428. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4709) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4709) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4710) all_252_14 = e0 & op(e1, e2) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4710) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4711) op(e1, e2) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (4711), (function-axioms) are % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4712) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4712) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4713) all_252_15 = e0 & op(e1, e1) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4713) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4714) all_252_15 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4704), (4714) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #405. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4715) all_252_19 = e0 & op(e1, e0) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4715) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4716) all_252_19 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4717) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (4554), (4557), (4717), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #451. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4718) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4718) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4719) all_252_11 = e0 & op(e2, e1) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4719) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4720) all_252_11 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4398), (4720) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4721) e3 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4721) imply: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4722) $false % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4722) is inconsistent. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4723) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4723) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4724) all_252_15 = e0 & op(e1, e1) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4724) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4725) all_252_15 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (12), (13), (182), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759), (760), (4507), (4513), (4543), (4716), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4725), (function-axioms) are inconsistent by % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #409. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4726) all_252_23 = e0 & op(e0, e1) = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4726) implies: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4727) all_252_23 = e0 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4728) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (4353), (4408), (4728), % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #478. % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4729) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4729) gives: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4730) all_252_22 = e1 & op(e0, e2) = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4730) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4731) op(e0, e2) = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (4555), (4731), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4732) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4732) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4733) all_252_23 = e1 & op(e0, e1) = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4727), (4733) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #293. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4734) all_252_24 = e1 & op(e0, e0) = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4734) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4735) all_252_24 = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4736) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (164), (4552), (4553), (4736), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4737) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4737) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4738) all_252_22 = e2 & op(e0, e2) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4738) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4739) all_252_22 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4740) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e2) = e4) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4740) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4741) all_252_4 = e4 & op(e4, e2) = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4741) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4742) all_252_4 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4689), (4742) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #296. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4743) all_252_5 = e4 & op(e3, e2) = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4743) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4744) op(e3, e2) = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (4561), (4744), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4745) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 & % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e4) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4745) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4746) all_252_8 = e4 & op(e2, e2) = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (137), (140), (143), (773), (1622), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623), (1624), (4739), (4746), (function-axioms) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4747) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4747) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4748) all_252_14 = e4 & op(e1, e2) = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4748) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4749) all_252_14 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (12), (759), (4507), (4513), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4704), (4716), (4749), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #413. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4750) all_252_22 = e4 & op(e0, e2) = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (4739), (4750) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #294. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4751) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4751) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4752) all_252_23 = e2 & op(e0, e1) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (4563), (4752), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4753) all_252_24 = e2 & op(e0, e0) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4753) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4754) all_252_24 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4735), (4754) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4755) e2 = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (4755) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4756) $false % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4756) is inconsistent. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4757) all_252_23 = e2 & op(e0, e1) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (4563), (4757), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4758) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (176), (4377), (4556), (4758), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #298. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4759) all_58_2 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1350), (1621), (4555), (4759), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4760) all_56_2 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1292), (4760) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4761) all_8_2 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4533), (4761) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4762) ~ (all_16_1 = e4) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (739) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4763) all_250_8 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4527), (4763) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4764) all_16_1 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4764) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4765) all_16_1 = e4 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4762), (4765) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4766) $false % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4766) is inconsistent. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4767) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_8 = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4767) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4768) all_250_8 = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4527), (4768) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4769) all_16_1 = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4769) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4770) all_16_1 = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4534), (4770) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4771) $false % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4771) is inconsistent. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4772) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4772) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4773) all_250_8 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4527), (4773) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4774) all_16_1 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4774) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4775) all_16_1 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4559), (4775) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4776) $false % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4776) is inconsistent. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4777) all_250_8 = e1 | all_250_8 = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (932), (1590), (1615), (4375), (4557), (4777), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #292. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4778) all_52_2 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4523), (4778) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4779) all_16_1 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4779) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4780) all_16_1 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (140), (143), (243), (732), (857), (1511), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1520), (1591), (1612), (4498), (4524), (4532), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4535), (4536), (4780), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4781) all_36_2 = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4522), (4781) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4782) all_16_1 = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4535), (4782) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4783) op(e4, e0) = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (4556), (4783), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4784) all_30_2 = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1200), (4784) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4785) all_236_2 = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1571), (4784) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4786) ~ (all_244_24 = e3) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1604), (4784) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4787) op(e4, e3) = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (164), (173), (255), (257), (469), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (752), (1332), (1477), (1595), (1609), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620), (4379), (4406), (4553), (4785), (4786), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4787), (function-axioms) are inconsistent by % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #480. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4788) all_28_2 = e1 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1531), (4788) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4789) ~ (all_4_2 = e1) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4789) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4790) ~ (all_4_2 = e1) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (732), (857), (1591), (1612), (1622), (4505), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4532), (4790), (function-axioms) are inconsistent % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #575. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (4791) all_26_2 = e0 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (164), (1619), (4379), (4506), (4541), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (4550), (4791), (function-axioms) are inconsistent % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #332. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4792) all_22_2 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1483), (4792) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4793) ~ (all_244_3 = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1506), (4792) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4794) ~ (all_244_24 = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1477), (4792) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4795) ~ (all_84_2 = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1503), (4792) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4796) ~ (all_28_2 = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4530), (4792) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4797) ~ (e4 = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (4792) imply: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | (4798) op(e0, e2) = e3 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (4799) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4799) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4800) all_252_1 = e2 & op(e4, e3) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (4795), (4800), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #523. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4801) all_252_3 = e2 & op(e3, e3) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (4793), (4801), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #496. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | (4802) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4802) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4803) all_252_7 = e2 & op(e2, e3) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4803) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4804) all_252_7 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4365), (4804) are inconsistent by sub-proof % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | #301. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4805) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4805) gives: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4806) all_252_13 = e2 & op(e1, e3) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4806) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4807) op(e1, e3) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (4507), (4807), (function-axioms) are % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #529. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4808) all_252_21 = e2 & op(e0, e3) = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4808) implies: % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4809) all_252_21 = e2 % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (137), (140), (143), (149), (161), (173), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (362), (480), (492), (521), (752), (773), (1362), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468), (1536), (1538), (1622), (1623), (1624), % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4794), (4796), (4798), (4809), (function-axioms) % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #455. % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.53 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | (4810) all_18_2 = e2 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (137), (140), (143), (173), (428), (434), % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | (480), (492), (521), (773), (828), (1231), (1372), % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | (1472), (1618), (1622), (1623), (1624), (4810), % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | #433. % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | (4811) all_96_2 = e2 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1330), (4811) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | (4812) all_34_2 = e2 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4812) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | (4813) all_34_2 = e2 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (4813) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | (4814) op(e1, e2) = e0 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (4814), (function-axioms) are % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (4815) all_252_20 = e3 & op(e0, e4) = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | ALPHA: (4815) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (4816) op(e0, e4) = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (4406), (4816), (function-axioms) are % 186.24/29.54 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | (4817) all_14_2 = e1 % 186.24/29.54 | | | | | | | | | | | | | | | (4818) op(e1, e0) = all_14_1 & $i(all_14_1) & ( ~ % 186.24/29.54 | | | | | | | | | | | | | | | (all_14_1 = e2) | ( ~ (all_14_0 = e3) & op(e0, % 186.24/29.54 | | | | | | | | | | | | | | | e2) = all_14_0 & $i(all_14_0))) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | ALPHA: (4818) implies: % 186.24/29.54 | | | | | | | | | | | | | | | (4819) op(e1, e0) = all_14_1 % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | COMBINE_EQS: (1356), (4817) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4820) all_12_2 = e1 % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | COMBINE_EQS: (1357), (4820) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4821) all_42_2 = e1 % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REDUCE: (1440), (4820) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4822) ~ (all_244_0 = e1) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REDUCE: (1472), (4820) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4823) ~ (all_244_24 = e1) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REDUCE: (1468), (4820) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4824) ~ (all_28_2 = e1) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REDUCE: (1457), (4820) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4825) ~ (all_16_2 = e1) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REDUCE: (1618), (4820) imply: % 186.24/29.54 | | | | | | | | | | | | | | | (4826) op(e0, e1) = e4 % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (11), (13), (137), (140), (143), % 186.24/29.54 | | | | | | | | | | | | | | | (146), (149), (156), (161), (164), (165), (168), % 186.24/29.54 | | | | | | | | | | | | | | | (170), (171), (173), (176), (177), (180), (182), % 186.24/29.54 | | | | | | | | | | | | | | | (183), (185), (186), (188), (189), (191), (195), % 186.24/29.54 | | | | | | | | | | | | | | | (203), (224), (227), (231), (257), (269), (280), % 186.24/29.54 | | | | | | | | | | | | | | | (301), (323), (343), (362), (373), (393), (404), % 186.24/29.54 | | | | | | | | | | | | | | | (410), (480), (486), (492), (498), (504), (514), % 186.24/29.54 | | | | | | | | | | | | | | | (521), (729), (733), (749), (751), (752), (758), % 186.24/29.54 | | | | | | | | | | | | | | | (763), (773), (785), (792), (860), (1032), (1253), % 186.24/29.54 | | | | | | | | | | | | | | | (1255), (1294), (1302), (1314), (1349), (1352), % 186.24/29.54 | | | | | | | | | | | | | | | (1358), (1362), (1364), (1426), (1428), (1439), % 186.24/29.54 | | | | | | | | | | | | | | | (1445), (1452), (1477), (1483), (1490), (1497), % 186.24/29.54 | | | | | | | | | | | | | | | (1503), (1504), (1506), (1529), (1536), (1538), % 186.24/29.54 | | | | | | | | | | | | | | | (1551), (1554), (1563), (1587), (1588), (1589), % 186.24/29.54 | | | | | | | | | | | | | | | (1595), (1597), (1599), (1600), (1603), (1604), % 186.24/29.54 | | | | | | | | | | | | | | | (1608), (1609), (1612), (1614), (1619), (1621), % 186.24/29.54 | | | | | | | | | | | | | | | (1622), (1623), (1624), (4353), (4406), (4819), % 186.24/29.54 | | | | | | | | | | | | | | | (4821), (4822), (4823), (4824), (4825), (4826), % 186.24/29.54 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.54 | | | | | | | | | | | | | | | #314. % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | End of split % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | (4827) all_12_2 = e3 % 186.24/29.54 | | | | | | | | | | | | | | (4828) op(e3, e0) = all_12_1 & $i(all_12_1) & ( ~ % 186.24/29.54 | | | | | | | | | | | | | | (all_12_1 = e2) | ( ~ (all_12_0 = e1) & op(e0, % 186.24/29.54 | | | | | | | | | | | | | | e2) = all_12_0 & $i(all_12_0))) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | ALPHA: (4828) implies: % 186.24/29.54 | | | | | | | | | | | | | | (4829) op(e3, e0) = all_12_1 % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | COMBINE_EQS: (1374), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4830) all_212_2 = e3 % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1440), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4831) ~ (all_244_0 = e3) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1472), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4832) ~ (all_244_24 = e3) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1446), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4833) ~ (all_100_2 = e3) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1468), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4834) ~ (all_28_2 = e3) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1466), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4835) ~ (all_22_2 = e3) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1457), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4836) ~ (all_16_2 = e3) % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1593), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4837) op(e3, all_30_2) = e4 % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | REDUCE: (1618), (4827) imply: % 186.24/29.54 | | | | | | | | | | | | | | (4838) op(e0, e3) = e4 % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | BETA: splitting (794) gives: % 186.24/29.54 | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | Case 1: % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | (4839) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 186.24/29.54 | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | REF_CLOSE: (280), (504), (4831), (4833), (4839), % 186.24/29.54 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.24/29.54 | | | | | | | | | | | | | | | #559. % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | (4840) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 186.24/29.54 | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 186.24/29.54 | | | | | | | | | | | | | | | op(e0, e4) = e3) % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | BETA: splitting (4840) gives: % 186.24/29.54 | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | Case 1: % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | (4841) all_252_6 = e3 & op(e2, e4) = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | REF_CLOSE: (227), (4372), (4841), (function-axioms) are % 186.24/29.54 | | | | | | | | | | | | | | | | inconsistent by sub-proof #432. % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | (4842) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 186.24/29.54 | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | BETA: splitting (4842) gives: % 186.24/29.54 | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | Case 1: % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | (4843) all_252_12 = e3 & op(e1, e4) = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (4836), (4843), (function-axioms) are % 186.24/29.54 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #513. % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | (4844) all_252_20 = e3 & op(e0, e4) = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | ALPHA: (4844) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | (4845) all_252_20 = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | BETA: splitting (437) gives: % 186.24/29.54 | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4846) ~ (all_212_2 = e3) % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (4830), (4846) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4847) $false % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | CLOSE: (4847) is inconsistent. % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4848) op(e3, e0) = all_212_1 & $i(all_212_1) & ( ~ % 186.24/29.54 | | | | | | | | | | | | | | | | | | (all_212_1 = e1) | ( ~ (all_212_0 = e2) & op(e0, % 186.24/29.54 | | | | | | | | | | | | | | | | | | e1) = all_212_0 & $i(all_212_0))) % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | ALPHA: (4848) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4849) op(e3, e0) = all_212_1 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_2, e4, % 186.24/29.54 | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (164), (4838) gives: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4850) all_22_2 = e4 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_2, % 186.24/29.54 | | | | | | | | | | | | | | | | | | all_212_1, e0, e3, simplifying with (203), (4849) % 186.24/29.54 | | | | | | | | | | | | | | | | | | gives: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4851) all_212_1 = all_48_2 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1, % 186.24/29.54 | | | | | | | | | | | | | | | | | | all_212_1, e0, e3, simplifying with (4829), (4849) % 186.24/29.54 | | | | | | | | | | | | | | | | | | gives: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4852) all_212_1 = all_12_1 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4851), (4852) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4853) all_48_2 = all_12_1 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | SIMP: (4853) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4854) all_48_2 = all_12_1 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1340), (4850) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4855) all_72_2 = e4 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1335), (4850) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4856) all_90_2 = e4 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (1483), (4850) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4857) ~ (all_244_3 = e4) % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (1506), (4850) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4858) ~ (all_244_24 = e4) % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (1503), (4850) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4859) ~ (all_28_2 = e4) % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (1596), (4850), (4854) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4860) op(all_12_1, e4) = e0 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (1609), (4854) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4861) op(e3, all_12_1) = e0 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | REDUCE: (1619), (4850) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | (4862) op(e0, e4) = e3 % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | BETA: splitting (266) gives: % 186.24/29.54 | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (4863) ~ (all_90_2 = e4) % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | REDUCE: (4856), (4863) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (4864) $false % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | CLOSE: (4864) is inconsistent. % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (4865) op(e4, e0) = all_90_1 & $i(all_90_1) & ( ~ % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (all_90_1 = e2) | ( ~ (all_90_0 = e1) & op(e0, % 186.24/29.54 | | | | | | | | | | | | | | | | | | | e2) = all_90_0 & $i(all_90_0))) % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | ALPHA: (4865) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | (4866) op(e4, e0) = all_90_1 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | Case 1: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | (4867) ~ (all_72_2 = e4) % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | REDUCE: (4855), (4867) imply: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | (4868) $false % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | CLOSE: (4868) is inconsistent. % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | Case 2: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | (4869) op(e4, e0) = all_72_1 & $i(all_72_1) & ( ~ % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | (all_72_1 = e1) | ( ~ (all_72_0 = e2) & op(e0, % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | e1) = all_72_0 & $i(all_72_0))) % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (4869) implies: % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | (4870) op(e4, e0) = all_72_1 % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | (4871) ~ (all_72_1 = e1) | ( ~ (all_72_0 = e2) & op(e0, % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | e1) = all_72_0 & $i(all_72_0)) % 186.24/29.54 | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | all_90_1, e0, e4, simplifying with (176), (4866) % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | (4872) all_90_1 = all_30_2 % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_72_1, % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | all_90_1, e0, e4, simplifying with (4866), (4870) % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | (4873) all_90_1 = all_72_1 % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4872), (4873) imply: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | (4874) all_72_1 = all_30_2 % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | SIMP: (4874) implies: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | (4875) all_72_1 = all_30_2 % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | (4876) ~ (all_26_2 = e0) % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | (4877) ~ (all_28_2 = e1) % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | (4878) ~ (all_30_2 = e3) % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | | (4879) ~ (all_34_2 = e4) % 186.64/29.54 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (11), (12), (13), (137), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (140), (143), (146), (155), (161), (170), (173), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (176), (182), (185), (186), (188), (189), (191), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (201), (219), (224), (237), (246), (257), (278), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (280), (284), (382), (385), (404), (480), (486), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (492), (498), (505), (750), (751), (763), (773), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (783), (1255), (1306), (1317), (1328), (1343), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (1350), (1353), (1366), (1367), (1448), (1492), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (1500), (1529), (1560), (1578), (1597), (1601), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (1606), (1608), (1611), (1612), (1613), (1614), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (1621), (1622), (1623), (1624), (4829), (4838), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4845), (4858), (4860), (4861), (4876), (4877), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4878), (4879), (function-axioms) are inconsistent % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #308. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4880) all_34_2 = e4 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (4880) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4881) op(e1, e0) = e4 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | (4882) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4882) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4883) all_252_16 = e3 & op(e4, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4883) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4884) op(e4, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (176), (4878), (4884), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #539. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4885) all_252_17 = e3 & op(e3, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4885) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4886) op(e3, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (498), (1448), (4829), (4860), (4861), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4886), (function-axioms) are inconsistent by % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #313. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | (4887) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4887) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4888) all_252_18 = e3 & op(e2, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4888) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4889) op(e2, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (4373), (4889), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #566. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (4890) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4890) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4891) all_252_19 = e3 & op(e1, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (4881), (4891), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #291. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4892) all_252_24 = e3 & op(e0, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (4832), (4892), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #507. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4893) all_30_2 = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4837), (4893) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4894) op(e3, e3) = e4 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (498), (4857), (4894), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #563. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4895) all_28_2 = e1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1186), (4895) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4896) all_162_2 = e1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1538), (4895) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4897) ~ (all_244_24 = e1) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4859), (4895) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4898) ~ (e4 = e1) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4834), (4895) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4899) ~ (e3 = e1) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (4895) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4900) op(e0, e1) = e2 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (12), (137), (140), (143), (161), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (368), (480), (492), (521), (750), (773), (1563), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (1622), (1623), (1624), (4838), (4845), (4862), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4896), (4897), (4900), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #306. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4901) all_26_2 = e0 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4902) op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4902) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4903) op(e0, e4) = all_26_1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4904) ~ (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0)) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1341), (4901) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4905) all_44_2 = e0 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1545), (4901) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4906) ~ (all_20_2 = e0) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | SIMP: (4906) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4907) ~ (all_20_2 = e0) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1603), (4901) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | (4908) op(e4, e0) = e1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4909) ~ (all_44_2 = e0) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4905), (4909) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4910) $false % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4910) is inconsistent. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4911) op(e0, e4) = all_44_1 & $i(all_44_1) & ( ~ % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (all_44_1 = e2) | ( ~ (all_44_0 = e3) & op(e4, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0))) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4911) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4912) op(e0, e4) = all_44_1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_44_1, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | e4, e0, simplifying with (4862), (4912) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4913) all_44_1 = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (4903), (4912) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4914) all_44_1 = all_26_1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (4908) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4915) all_30_2 = e1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4913), (4914) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4916) all_26_1 = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4916) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4917) all_26_1 = e3 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4875), (4915) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4918) all_72_1 = e1 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4837), (4915) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | (4919) op(e3, e1) = e4 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4871) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4920) ~ (all_72_1 = e1) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4918), (4920) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4921) $false % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4921) is inconsistent. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4922) ~ (all_72_0 = e2) & op(e0, e1) = all_72_0 & % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | $i(all_72_0) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4922) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4923) ~ (all_72_0 = e2) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | (4924) op(e0, e1) = all_72_0 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4904) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4925) ~ (all_26_1 = e3) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4917), (4925) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4926) $false % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4926) is inconsistent. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | all_72_0, e1, e0, simplifying with (161), (4924) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4927) all_72_0 = all_20_2 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e4, % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (4919) gives: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4928) all_36_2 = e4 % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4923), (4927) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4929) ~ (all_20_2 = e2) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1552), (4928) imply: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4930) ~ (all_20_2 = e4) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4930) implies: % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4931) ~ (all_20_2 = e4) % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (727), (1424), (1599), (1617), (4379), (4907), % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | (4929), (4931), (function-axioms) are inconsistent % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #485. % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | (4932) all_252_18 = e3 & op(e2, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | ALPHA: (4932) implies: % 186.64/29.55 | | | | | | | | | | | | (4933) op(e2, e0) = e3 % 186.64/29.55 | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | | REF_CLOSE: (191), (4373), (4933), (function-axioms) are % 186.64/29.55 | | | | | | | | | | | | inconsistent by sub-proof #566. % 186.64/29.55 | | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | | % 186.64/29.55 | | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | | % 186.64/29.55 | | | | | | | | | End of split % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | End of split % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | End of split % 186.64/29.55 | | | | | | | % 186.64/29.55 | | | | | | Case 2: % 186.64/29.55 | | | | | | | % 186.64/29.55 | | | | | | | (4934) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & % 186.64/29.55 | | | | | | | op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 186.64/29.55 | | | | | | | % 186.64/29.55 | | | | | | | BETA: splitting (4934) gives: % 186.64/29.55 | | | | | | | % 186.64/29.55 | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | | (4935) all_252_8 = e1 & op(e2, e2) = e1 % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | | ALPHA: (4935) implies: % 186.64/29.55 | | | | | | | | (4936) op(e2, e2) = e1 % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | | REF_CLOSE: (492), (4347), (4936), (function-axioms) are % 186.64/29.55 | | | | | | | | inconsistent by sub-proof #490. % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | | (4937) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 = e1 % 186.64/29.55 | | | | | | | | & op(e2, e0) = e1) % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | | BETA: splitting (4937) gives: % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | | Case 1: % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | | (4938) all_252_11 = e1 & op(e2, e1) = e1 % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | | ALPHA: (4938) implies: % 186.64/29.55 | | | | | | | | | (4939) op(e2, e1) = e1 % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | | REF_CLOSE: (9), (188), (4354), (4939), (function-axioms) are % 186.64/29.55 | | | | | | | | | inconsistent by sub-proof #290. % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | Case 2: % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | | (4940) all_252_18 = e1 & op(e2, e0) = e1 % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | | ALPHA: (4940) implies: % 186.64/29.55 | | | | | | | | | (4941) op(e2, e0) = e1 % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | | REF_CLOSE: (191), (4351), (4941), (function-axioms) are % 186.64/29.55 | | | | | | | | | inconsistent by sub-proof #516. % 186.64/29.55 | | | | | | | | | % 186.64/29.55 | | | | | | | | End of split % 186.64/29.55 | | | | | | | | % 186.64/29.55 | | | | | | | End of split % 186.64/29.55 | | | | | | | % 186.64/29.55 | | | | | | End of split % 186.64/29.55 | | | | | | % 186.64/29.55 | | | | | End of split % 186.64/29.55 | | | | | % 186.64/29.55 | | | | End of split % 186.64/29.55 | | | | % 186.64/29.55 | | | Case 2: % 186.64/29.55 | | | | % 186.64/29.55 | | | | (4942) all_8_2 = e0 % 186.64/29.55 | | | | (4943) op(e0, e3) = all_8_1 & $i(all_8_1) & ( ~ (all_8_1 = e1) | ( ~ % 186.64/29.55 | | | | (all_8_0 = e4) & op(e3, e1) = all_8_0 & $i(all_8_0))) % 186.64/29.55 | | | | % 186.64/29.55 | | | | ALPHA: (4943) implies: % 186.64/29.55 | | | | (4944) op(e0, e3) = all_8_1 % 186.64/29.55 | | | | % 186.64/29.55 | | | | COMBINE_EQS: (1219), (4942) imply: % 186.64/29.55 | | | | (4945) all_156_2 = e0 % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1519), (4942) imply: % 186.64/29.55 | | | | (4946) ~ (all_244_8 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1449), (4942) imply: % 186.64/29.55 | | | | (4947) ~ (all_100_2 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1526), (4942) imply: % 186.64/29.55 | | | | (4948) ~ (all_48_2 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1524), (4942) imply: % 186.64/29.55 | | | | (4949) ~ (all_36_2 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1522), (4942) imply: % 186.64/29.55 | | | | (4950) ~ (all_28_2 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1508), (4942) imply: % 186.64/29.55 | | | | (4951) ~ (all_6_2 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1520), (4942) imply: % 186.64/29.55 | | | | (4952) ~ (all_4_2 = e0) % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1586), (4942) imply: % 186.64/29.55 | | | | (4953) op(e0, all_10_2) = e2 % 186.64/29.55 | | | | % 186.64/29.55 | | | | REDUCE: (1607), (4942) imply: % 186.64/29.55 | | | | (4954) op(e3, e0) = e2 % 186.64/29.55 | | | | % 186.64/29.55 | | | | BETA: splitting (359) gives: % 186.64/29.55 | | | | % 186.64/29.55 | | | | Case 1: % 186.64/29.55 | | | | | % 186.64/29.55 | | | | | (4955) ~ (all_156_2 = e0) % 186.64/29.55 | | | | | % 186.64/29.55 | | | | | REDUCE: (4945), (4955) imply: % 186.64/29.55 | | | | | (4956) $false % 186.64/29.55 | | | | | % 186.64/29.55 | | | | | CLOSE: (4956) is inconsistent. % 186.64/29.55 | | | | | % 186.64/29.55 | | | | Case 2: % 186.64/29.55 | | | | | % 186.64/29.55 | | | | | (4957) op(e0, e3) = all_156_1 & $i(all_156_1) & ( ~ (all_156_1 = % 186.64/29.55 | | | | | e4) | ( ~ (all_156_0 = e1) & op(e3, e4) = all_156_0 & % 186.64/29.55 | | | | | $i(all_156_0))) % 186.64/29.55 | | | | | % 186.64/29.56 | | | | | ALPHA: (4957) implies: % 186.64/29.56 | | | | | (4958) op(e0, e3) = all_156_1 % 186.64/29.56 | | | | | % 186.64/29.56 | | | | | BETA: splitting (773) gives: % 186.64/29.56 | | | | | % 186.64/29.56 | | | | | Case 1: % 186.64/29.56 | | | | | | % 186.64/29.56 | | | | | | (4959) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & % 186.64/29.56 | | | | | | op(e3, e2) = e0) % 186.64/29.56 | | | | | | % 186.64/29.56 | | | | | | BETA: splitting (4959) gives: % 186.64/29.56 | | | | | | % 186.64/29.56 | | | | | | Case 1: % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | (4960) all_252_4 = e0 & op(e4, e2) = e0 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | ALPHA: (4960) implies: % 186.64/29.56 | | | | | | | (4961) op(e4, e2) = e0 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REF_CLOSE: (140), (1623), (4961), (function-axioms) are % 186.64/29.56 | | | | | | | inconsistent by sub-proof #548. % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | Case 2: % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | (4962) all_252_5 = e0 & op(e3, e2) = e0 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | ALPHA: (4962) implies: % 186.64/29.56 | | | | | | | (4963) all_252_5 = e0 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_2, % 186.64/29.56 | | | | | | | all_156_1, e3, e0, simplifying with (164), (4958) % 186.64/29.56 | | | | | | | gives: % 186.64/29.56 | | | | | | | (4964) all_156_1 = all_22_2 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 186.64/29.56 | | | | | | | all_156_1, e3, e0, simplifying with (4944), (4958) % 186.64/29.56 | | | | | | | gives: % 186.64/29.56 | | | | | | | (4965) all_156_1 = all_8_1 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_2, e2, % 186.64/29.56 | | | | | | | e0, e3, simplifying with (203), (4954) gives: % 186.64/29.56 | | | | | | | (4966) all_48_2 = e2 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | COMBINE_EQS: (4964), (4965) imply: % 186.64/29.56 | | | | | | | (4967) all_22_2 = all_8_1 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | COMBINE_EQS: (1181), (4967) imply: % 186.64/29.56 | | | | | | | (4968) all_104_2 = all_8_1 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | COMBINE_EQS: (1099), (4966) imply: % 186.64/29.56 | | | | | | | (4969) all_228_2 = e2 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1486), (4966) imply: % 186.64/29.56 | | | | | | | (4970) ~ (all_244_3 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1483), (4967) imply: % 186.64/29.56 | | | | | | | (4971) ~ (all_244_3 = all_8_1) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1575), (4966) imply: % 186.64/29.56 | | | | | | | (4972) ~ (all_244_24 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1572), (4966) imply: % 186.64/29.56 | | | | | | | (4973) ~ (all_40_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | SIMP: (4973) implies: % 186.64/29.56 | | | | | | | (4974) ~ (all_40_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1554), (4966) imply: % 186.64/29.56 | | | | | | | (4975) ~ (all_36_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | SIMP: (4975) implies: % 186.64/29.56 | | | | | | | (4976) ~ (all_36_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1573), (4966) imply: % 186.64/29.56 | | | | | | | (4977) ~ (all_34_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | SIMP: (4977) implies: % 186.64/29.56 | | | | | | | (4978) ~ (all_34_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1565), (4966) imply: % 186.64/29.56 | | | | | | | (4979) ~ (all_30_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | SIMP: (4979) implies: % 186.64/29.56 | | | | | | | (4980) ~ (all_30_2 = e2) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1503), (4967) imply: % 186.64/29.56 | | | | | | | (4981) ~ (all_28_2 = all_8_1) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1504), (4967) imply: % 186.64/29.56 | | | | | | | (4982) ~ (all_20_2 = all_8_1) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | SIMP: (4982) implies: % 186.64/29.56 | | | | | | | (4983) ~ (all_20_2 = all_8_1) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1466), (4967) imply: % 186.64/29.56 | | | | | | | (4984) ~ (all_12_2 = all_8_1) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | SIMP: (4984) implies: % 186.64/29.56 | | | | | | | (4985) ~ (all_12_2 = all_8_1) % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1596), (4966), (4967) imply: % 186.64/29.56 | | | | | | | (4986) op(e2, all_8_1) = e0 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1595), (4966), (4967) imply: % 186.64/29.56 | | | | | | | (4987) op(all_8_1, e2) = e3 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | REDUCE: (1619), (4967) imply: % 186.64/29.56 | | | | | | | (4988) op(e0, all_8_1) = e3 % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | BETA: splitting (204) gives: % 186.64/29.56 | | | | | | | % 186.64/29.56 | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | (4989) ~ (all_48_2 = e2) % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | REDUCE: (4966), (4989) imply: % 186.64/29.56 | | | | | | | | (4990) $false % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | CLOSE: (4990) is inconsistent. % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | (4991) op(e2, e3) = all_48_1 & $i(all_48_1) & ( ~ (all_48_1 = % 186.64/29.56 | | | | | | | | e1) | ( ~ (all_48_0 = e4) & op(e3, e1) = all_48_0 % 186.64/29.56 | | | | | | | | & $i(all_48_0))) % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | ALPHA: (4991) implies: % 186.64/29.56 | | | | | | | | (4992) op(e2, e3) = all_48_1 % 186.64/29.56 | | | | | | | | (4993) ~ (all_48_1 = e1) | ( ~ (all_48_0 = e4) & op(e3, e1) % 186.64/29.56 | | | | | | | | = all_48_0 & $i(all_48_0)) % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | BETA: splitting (755) gives: % 186.64/29.56 | | | | | | | | % 186.64/29.56 | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | % 186.64/29.56 | | | | | | | | | (4994) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = % 186.64/29.56 | | | | | | | | | e2 & op(e3, e0) = e2) % 186.64/29.56 | | | | | | | | | % 186.64/29.56 | | | | | | | | | BETA: splitting (4994) gives: % 186.64/29.56 | | | | | | | | | % 186.64/29.56 | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | (4995) all_252_16 = e2 & op(e4, e0) = e2 % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | ALPHA: (4995) implies: % 186.64/29.56 | | | | | | | | | | (4996) op(e4, e0) = e2 % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e2, % 186.64/29.56 | | | | | | | | | | e0, e4, simplifying with (176), (4996) gives: % 186.64/29.56 | | | | | | | | | | (4997) all_30_2 = e2 % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | REDUCE: (4980), (4997) imply: % 186.64/29.56 | | | | | | | | | | (4998) $false % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | CLOSE: (4998) is inconsistent. % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | (4999) all_252_17 = e2 & op(e3, e0) = e2 % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | ALPHA: (4999) implies: % 186.64/29.56 | | | | | | | | | | (5000) all_252_17 = e2 % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | BETA: splitting (457) gives: % 186.64/29.56 | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | (5001) ~ (all_228_2 = e2) % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | REDUCE: (4969), (5001) imply: % 186.64/29.56 | | | | | | | | | | | (5002) $false % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | CLOSE: (5002) is inconsistent. % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | (5003) op(e2, e3) = all_228_1 & $i(all_228_1) & ( ~ % 186.64/29.56 | | | | | | | | | | | (all_228_1 = e4) | ( ~ (all_228_0 = e1) & op(e3, % 186.64/29.56 | | | | | | | | | | | e4) = all_228_0 & $i(all_228_0))) % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | ALPHA: (5003) implies: % 186.64/29.56 | | | | | | | | | | | (5004) op(e2, e3) = all_228_1 % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, % 186.64/29.56 | | | | | | | | | | | all_228_1, e3, e2, simplifying with (146), (5004) % 186.64/29.56 | | | | | | | | | | | gives: % 186.64/29.56 | | | | | | | | | | | (5005) all_228_1 = all_10_2 % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_1, % 186.64/29.56 | | | | | | | | | | | all_228_1, e3, e2, simplifying with (4992), (5004) % 186.64/29.56 | | | | | | | | | | | gives: % 186.64/29.56 | | | | | | | | | | | (5006) all_228_1 = all_48_1 % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | COMBINE_EQS: (5005), (5006) imply: % 186.64/29.56 | | | | | | | | | | | (5007) all_48_1 = all_10_2 % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | BETA: splitting (147) gives: % 186.64/29.56 | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | (5008) ~ (all_10_2 = e1) % 186.64/29.56 | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | BETA: splitting (150) gives: % 186.64/29.56 | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | (5009) ~ (all_12_2 = e3) % 186.64/29.56 | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | BETA: splitting (153) gives: % 186.64/29.56 | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | (5010) ~ (all_14_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | REDUCE: (1356), (5010) imply: % 186.64/29.56 | | | | | | | | | | | | | | (5011) ~ (all_12_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | BETA: splitting (156) gives: % 186.64/29.56 | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | (5012) ~ (all_16_2 = e3) % 186.64/29.56 | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 186.64/29.56 | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | (5013) ~ (all_18_2 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | REDUCE: (1231), (5013) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | (5014) ~ (all_12_2 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | BETA: splitting (162) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | (5015) ~ (all_20_2 = e3) % 186.64/29.56 | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | (5016) ~ (all_22_2 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | REDUCE: (4967), (5016) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | (5017) ~ (all_8_1 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | (5018) ~ (all_24_2 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | REDUCE: (1349), (5018) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | (5019) ~ (all_16_2 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5020) ~ (all_26_2 = e0) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (149), (161), (170), (173), (174), (185), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (188), (189), (191), (219), (404), (480), (486), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (514), (751), (763), (1255), (1350), (1538), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (1556), (1597), (1598), (1612), (1613), (1621), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (4944), (4949), (4950), (4972), (5014), (5017), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5020), (function-axioms) are inconsistent by % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | sub-proof #283. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5021) all_26_2 = e0 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5022) op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | ALPHA: (5022) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5023) op(e0, e4) = all_26_1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1341), (5021) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5024) all_44_2 = e0 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | REDUCE: (1603), (5021) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | (5025) op(e4, e0) = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5026) ~ (all_44_2 = e0) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5024), (5026) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5027) $false % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | CLOSE: (5027) is inconsistent. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5028) op(e0, e4) = all_44_1 & $i(all_44_1) & ( ~ % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (all_44_1 = e2) | ( ~ (all_44_0 = e3) & op(e4, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0))) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5028) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5029) op(e0, e4) = all_44_1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (149), (5029) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5030) all_44_1 = all_12_2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (5023), (5029) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5031) all_44_1 = all_26_1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (5025) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5032) all_30_2 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5030), (5031) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5033) all_26_1 = all_12_2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1316), (5032) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5034) all_54_2 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1202), (5032) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5035) all_132_2 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1480), (5032) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | (5036) ~ (all_84_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | (5037) ~ (all_54_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5034), (5037) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | (5038) $false % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5038) is inconsistent. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | (5039) op(e1, e4) = all_54_1 & $i(all_54_1) & ( ~ % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | (all_54_1 = e2) | ( ~ (all_54_0 = e3) & op(e4, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | e2) = all_54_0 & $i(all_54_0))) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5039) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | (5040) op(e1, e4) = all_54_1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (326) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5041) ~ (all_132_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5035), (5041) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5042) $false % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5042) is inconsistent. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5043) op(e1, e4) = all_132_1 & $i(all_132_1) & ( ~ % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (all_132_1 = e3) | ( ~ (all_132_0 = e2) & op(e4, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_132_0 & $i(all_132_0))) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5043) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5044) op(e1, e4) = all_132_1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | all_132_1, e4, e1, simplifying with (155), (5044) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5045) all_132_1 = all_16_2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_54_1, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | all_132_1, e4, e1, simplifying with (5040), (5044) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5046) all_132_1 = all_54_1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5045), (5046) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | (5047) all_54_1 = all_16_2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5048) ~ (all_28_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (173), (219), (480), (751), (1350), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (1597), (1613), (1621), (4944), (4950), (4972), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5014), (5017), (5048), (function-axioms) are % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #286. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5049) all_28_2 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1186), (5049) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5050) all_162_2 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1536), (5049) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5051) ~ (all_20_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5051) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5052) ~ (all_20_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4981), (5049) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5053) ~ (all_8_1 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5053) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5054) ~ (all_8_1 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1531), (5049) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5055) ~ (all_4_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5055) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5056) ~ (all_4_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (5049) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | (5057) op(e0, e1) = e2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (368) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | (5058) ~ (all_162_2 = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5050), (5058) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | (5059) $false % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5059) is inconsistent. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, e2, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (161), (5057) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | (5060) all_20_2 = e2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1560), (5060) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | (5061) ~ (all_244_15 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (5062) ~ (all_62_2 = e2) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (155), (182), (224), (486), (760), (1591), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (1612), (4978), (5019), (5056), (5061), (5062), % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | #282. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (5063) all_62_2 = e2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1615), (5063) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (5064) op(e1, e2) = e3 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (224), (5063) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (5065) op(e1, e3) = e2 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5066) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5066) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5067) all_252_1 = e1 & op(e4, e3) = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5067) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5068) op(e4, e3) = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e1, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (5068) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5069) all_84_2 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5036), (5069) imply: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5070) $false % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5070) is inconsistent. % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5071) all_252_3 = e1 & op(e3, e3) = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5071) implies: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5072) op(e3, e3) = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e3, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (5064) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5073) all_4_2 = e3 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_3, % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, e3, simplifying with (498), (5072) gives: % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5074) all_244_3 = e1 % 186.64/29.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1533), (5073) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5075) ~ (all_244_15 = e3) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (526), (5074) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5076) op(e1, e1) = e3 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5075), (5076), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5077) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5077) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5078) all_252_7 = e1 & op(e2, e3) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5078) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5079) op(e2, e3) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (5008), (5079), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #554. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5080) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5080) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5081) all_252_13 = e1 & op(e1, e3) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5081) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5082) op(e1, e3) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e2, e3, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (5065), (5082) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5083) e2 = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5083) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5084) $false % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5084) is inconsistent. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5085) all_252_21 = e1 & op(e0, e3) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4944), (5054), (5085), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #281. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5086) all_24_2 = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1349), (5086) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5087) all_16_2 = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | SIMP: (5087) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5088) all_16_2 = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | REDUCE: (1462), (5088) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5089) ~ (all_244_15 = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | REDUCE: (1457), (5088) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5090) ~ (all_12_2 = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | REDUCE: (1460), (5088) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5091) ~ (all_4_2 = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | SIMP: (5091) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5092) ~ (all_4_2 = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | REDUCE: (5012), (5088) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5093) ~ (e3 = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | REDUCE: (1587), (5088) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5094) op(e2, all_26_2) = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | REDUCE: (1614), (5088) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5095) op(e1, e2) = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e4, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (137), (5095) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5096) all_4_2 = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1253), (5096) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5097) all_180_2 = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1032), (5096) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | (5098) all_192_2 = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | (5099) ~ (all_180_2 = e4) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (5097), (5099) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | (5100) $false % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | CLOSE: (5100) is inconsistent. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | (5101) op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | e0) = all_180_0 & $i(all_180_0))) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | ALPHA: (5101) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | (5102) op(e4, e1) = all_180_1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | (5103) ~ (all_180_1 = e0) | ( ~ (all_180_0 = e3) & % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_180_0 & $i(all_180_0)) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5104) ~ (all_192_2 = e4) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5098), (5104) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5105) $false % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (5105) is inconsistent. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5106) op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | e3) = all_192_0 & $i(all_192_0))) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5106) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5107) op(e4, e1) = all_192_1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | all_192_1, e1, e4, simplifying with (170), (5107) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5108) all_192_1 = all_26_2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_180_1, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | all_192_1, e1, e4, simplifying with (5102), (5107) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5109) all_192_1 = all_180_1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5108), (5109) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5110) all_180_1 = all_26_2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | SIMP: (5110) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | (5111) all_180_1 = all_26_2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5112) ~ (all_26_2 = e0) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (149), (161), (170), (173), (174), (185), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (188), (189), (191), (219), (404), (480), (486), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (514), (751), (763), (1255), (1350), (1538), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (1556), (1597), (1598), (1612), (1613), (1621), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (4944), (4949), (4950), (4972), (5014), (5017), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5112), (function-axioms) are inconsistent by % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | sub-proof #283. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5113) all_26_2 = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5111), (5113) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5114) all_180_1 = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1544), (5113) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5115) ~ (all_244_15 = e0) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1603), (5113) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5116) op(e4, e0) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (5113) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5117) op(e4, e1) = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5094), (5113) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | (5118) op(e2, e0) = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5103) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | (5119) ~ (all_180_1 = e0) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5114), (5119) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | (5120) $false % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5120) is inconsistent. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | (5121) ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | $i(all_180_0) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5121) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | (5122) ~ (all_180_0 = e3) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | (5123) op(e1, e0) = all_180_0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | (5124) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5124) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | all_180_0, e0, e1, simplifying with (182), (5123) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5125) all_180_0 = all_34_2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, e4, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (191), (5118) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5126) all_40_2 = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (5116) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5127) all_30_2 = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5122), (5125) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5128) ~ (all_34_2 = e3) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1576), (5126) imply: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5129) ~ (all_34_2 = e4) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5129) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5130) ~ (all_34_2 = e4) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (731), (845), (1569), (1600), (1621), (4978), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5127), (5128), (5130), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #280. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5131) all_252_10 = e0 & op(e3, e1) = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5131) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5132) op(e3, e1) = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (185), (4949), (5132), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | (5133) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5133) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5134) all_252_11 = e0 & op(e2, e1) = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5134) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | (5135) all_252_11 = e0 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (5136) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (185), (4976), (5117), (5136), % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | #441. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (5137) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5137) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5138) all_252_11 = e2 & op(e2, e1) = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5135), (5138) are inconsistent by sub-proof % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | #279. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5139) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5139) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5140) all_252_15 = e2 & op(e1, e1) = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5140) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5141) op(e1, e1) = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5089), (5141), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5142) all_252_23 = e2 & op(e0, e1) = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5142) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5143) op(e0, e1) = e2 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5144) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5144) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5145) all_252_9 = e4 & op(e4, e1) = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5145) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5146) op(e4, e1) = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5117), (5146), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #427. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5147) all_252_10 = e4 & op(e3, e1) = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5147) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5148) all_252_10 = e4 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (764) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5149) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5149) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5150) all_252_9 = e1 & op(e4, e1) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5117), (5150), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #278. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5151) all_252_10 = e1 & op(e3, e1) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5148), (5151) are inconsistent by sub-proof % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #277. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5152) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5152) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5153) all_252_11 = e1 & op(e2, e1) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5135), (5153) are inconsistent by sub-proof % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5154) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5154) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5155) all_252_15 = e1 & op(e1, e1) = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5155) implies: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5156) all_252_15 = e1 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5157) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5157) gives: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5158) all_252_9 = e3 & op(e4, e1) = e3 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5117), (5158), (function-axioms) are % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5159) all_252_10 = e3 & op(e3, e1) = e3 % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5148), (5159) are inconsistent by sub-proof % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #274. % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5160) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (161), (5015), (5135), (5156), (5160), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #271. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5161) all_252_23 = e1 & op(e0, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (149), (173), (480), (751), (1597), (1613), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4972), (5014), (5017), (5161), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #269. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5162) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5162) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5163) all_252_11 = e4 & op(e2, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5135), (5163) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #268. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5164) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5164) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5165) all_252_15 = e4 & op(e1, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5165) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5166) all_252_15 = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (764) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5167) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5167) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5168) all_252_9 = e1 & op(e4, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5117), (5168), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #278. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5169) all_252_10 = e1 & op(e3, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5169) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5170) all_252_10 = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (14), (161), (766), (5015), (5117), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5135), (5166), (5170), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #263. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5171) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5171) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5172) all_252_11 = e1 & op(e2, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5135), (5172) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #262. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5173) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5173) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5174) all_252_15 = e1 & op(e1, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5166), (5174) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #394. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5175) all_252_23 = e1 & op(e0, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (149), (173), (480), (751), (1597), (1613), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4972), (5014), (5017), (5175), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #269. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5176) all_252_23 = e4 & op(e0, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5176) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5177) op(e0, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (5143), (5177), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #322. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | (5178) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5178) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (5179) all_252_15 = e0 & op(e1, e1) = e0 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5179) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (5180) op(e1, e1) = e0 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5115), (5180), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (5181) all_252_23 = e0 & op(e0, e1) = e0 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5181) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (5182) all_252_23 = e0 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (5183) op(e0, e1) = e0 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5184) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (185), (4976), (5117), (5184), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | #441. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5185) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5185) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5186) all_252_11 = e2 & op(e2, e1) = e2 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5186) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5187) all_252_11 = e2 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5188) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5188) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5189) all_252_9 = e4 & op(e4, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5189) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5190) op(e4, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5117), (5190), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #427. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5191) all_252_10 = e4 & op(e3, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5191) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5192) all_252_10 = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (764) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5193) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5193) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5194) all_252_9 = e1 & op(e4, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5117), (5194), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #278. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5195) all_252_10 = e1 & op(e3, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5192), (5195) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #277. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5196) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5196) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5197) all_252_11 = e1 & op(e2, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5187), (5197) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #357. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5198) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5198) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5199) all_252_15 = e1 & op(e1, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5199) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5200) all_252_15 = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5201) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5201) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5202) all_252_9 = e3 & op(e4, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5117), (5202), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5203) all_252_10 = e3 & op(e3, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5192), (5203) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #274. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5204) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5204) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5205) all_252_11 = e3 & op(e2, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5187), (5205) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #356. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5206) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5206) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5207) all_252_15 = e3 & op(e1, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5200), (5207) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #272. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5208) all_252_23 = e3 & op(e0, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5208) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5209) op(e0, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5183), (5209), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #449. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5210) all_252_23 = e1 & op(e0, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (149), (173), (480), (751), (1597), (1613), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4972), (5014), (5017), (5210), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #269. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5211) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5211) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5212) all_252_11 = e4 & op(e2, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (5187), (5212) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #261. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5213) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5213) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5214) all_252_15 = e4 & op(e1, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5214) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5215) all_252_15 = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (764) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5216) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5216) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5217) all_252_9 = e1 & op(e4, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5117), (5217), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #278. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5218) all_252_10 = e1 & op(e3, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5218) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5219) all_252_10 = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5220) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (5117), (5219), (5220), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #266. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5221) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5221) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5222) all_252_11 = e3 & op(e2, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5187), (5222) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #356. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5223) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5223) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5224) all_252_15 = e3 & op(e1, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5215), (5224) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #265. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5225) all_252_23 = e3 & op(e0, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5226) op(e0, e1) = e3 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5183), (5226), (function-axioms) are % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #449. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5227) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5227) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5228) all_252_11 = e1 & op(e2, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5187), (5228) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #517. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5229) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5229) gives: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5230) all_252_15 = e1 & op(e1, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5215), (5230) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #394. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5231) all_252_23 = e1 & op(e0, e1) = e1 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (149), (173), (480), (751), (1597), (1613), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4972), (5014), (5017), (5231), % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #269. % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5232) all_252_23 = e4 & op(e0, e1) = e4 % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5232) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5233) op(e0, e1) = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5183), (5233), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5234) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5234) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5235) all_252_15 = e2 & op(e1, e1) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5235) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5236) op(e1, e1) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5089), (5236), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #515. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5237) all_252_23 = e2 & op(e0, e1) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5237) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5238) all_252_23 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5182), (5238) are inconsistent by sub-proof % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #260. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5239) all_22_2 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4967), (5239) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5240) all_8_1 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | REDUCE: (4986), (5240) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5241) op(e2, e2) = e0 % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (4946), (5241), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #448. % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | (5242) all_20_2 = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | REDUCE: (1621), (5242) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | (5243) op(e0, e3) = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | REDUCE: (161), (5242) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | (5244) op(e0, e1) = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5245) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 186.64/29.59 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | BETA: splitting (5245) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5246) all_252_20 = e2 & op(e0, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | ALPHA: (5246) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5247) op(e0, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (5014), (5247), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #544. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5248) all_252_21 = e2 & op(e0, e3) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | ALPHA: (5248) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5249) op(e0, e3) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, e1, % 186.64/29.59 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (4944), (5243) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5250) all_8_1 = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, e2, % 186.64/29.59 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (4944), (5249) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5251) all_8_1 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5250), (5251) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5252) e2 = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | SIMP: (5252) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5253) e2 = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5253) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5254) $false % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | CLOSE: (5254) is inconsistent. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5255) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 186.64/29.59 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 186.64/29.59 | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (173), (480), (1597), (1613), (4950), % 186.64/29.59 | | | | | | | | | | | | | | | | | | (4972), (5244), (5255), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #259. % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | End of split % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | (5256) all_18_2 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | (5257) op(e2, e0) = all_18_1 & $i(all_18_1) & ( ~ % 186.64/29.59 | | | | | | | | | | | | | | | | (all_18_1 = e3) | ( ~ (all_18_0 = e1) & op(e0, % 186.64/29.59 | | | | | | | | | | | | | | | | e3) = all_18_0 & $i(all_18_0))) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | ALPHA: (5257) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | (5258) op(e2, e0) = all_18_1 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (1231), (5256) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5259) all_12_2 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | SIMP: (5259) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | (5260) all_12_2 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | COMBINE_EQS: (828), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5261) all_210_2 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1440), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5262) ~ (all_244_0 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1446), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5263) ~ (all_100_2 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1453), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5264) ~ (all_64_2 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1468), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5265) ~ (all_28_2 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1470), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5266) ~ (all_20_2 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1457), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5267) ~ (all_16_2 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (4985), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5268) ~ (all_8_1 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | SIMP: (5268) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | (5269) ~ (all_8_1 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (5009), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5270) ~ (e3 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1594), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5271) op(all_30_2, e2) = e0 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1593), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5272) op(e2, all_30_2) = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | REDUCE: (1618), (5260) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | (5273) op(e0, e2) = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | BETA: splitting (434) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | (5274) ~ (all_210_2 = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | REDUCE: (5261), (5274) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | (5275) $false % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | CLOSE: (5275) is inconsistent. % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | (5276) op(e2, e0) = all_210_1 & $i(all_210_1) & ( ~ % 186.64/29.59 | | | | | | | | | | | | | | | | | (all_210_1 = e1) | ( ~ (all_210_0 = e3) & op(e0, % 186.64/29.59 | | | | | | | | | | | | | | | | | e1) = all_210_0 & $i(all_210_0))) % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | ALPHA: (5276) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | (5277) op(e2, e0) = all_210_1 % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | BETA: splitting (792) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5278) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = % 186.64/29.59 | | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (504), (5262), (5263), (5278), % 186.64/29.59 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.59 | | | | | | | | | | | | | | | | | | #325. % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | (5279) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = % 186.64/29.59 | | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 & % 186.64/29.59 | | | | | | | | | | | | | | | | | | op(e0, e4) = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | BETA: splitting (5279) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5280) all_252_6 = e2 & op(e2, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (5264), (5280), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #467. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | (5281) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (5281) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5282) all_252_12 = e2 & op(e1, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (5282) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5283) op(e1, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (5267), (5283), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #573. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5284) all_252_20 = e2 & op(e0, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (5284) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5285) all_252_20 = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, e4, % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (173), (5273) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5286) all_28_2 = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | all_210_1, e0, e2, simplifying with (191), (5277) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5287) all_210_1 = all_40_2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1, % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | all_210_1, e0, e2, simplifying with (5258), (5277) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5288) all_210_1 = all_18_1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5287), (5288) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5289) all_40_2 = all_18_1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | SIMP: (5289) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5290) all_40_2 = all_18_1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1284), (5286) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5291) all_108_2 = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1372), (5286) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5292) all_206_2 = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1536), (5286) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5293) ~ (all_20_2 = e4) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | SIMP: (5293) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5294) ~ (all_20_2 = e4) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1513), (5286) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5295) ~ (all_6_2 = e4) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | SIMP: (5295) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5296) ~ (all_6_2 = e4) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1597), (5286), (5290) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5297) op(e4, all_18_1) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (1620), (5286) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | (5298) op(e0, e4) = e2 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | (5299) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5299) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | (5300) all_252_20 = e4 & op(e0, e4) = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5300) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | (5301) op(e0, e4) = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (5298), (5301), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #426. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | (5302) all_252_21 = e4 & op(e0, e3) = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5302) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | (5303) all_252_21 = e4 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | (5304) ~ (all_230_2 = e3) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1378), (5304) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | (5305) ~ (all_20_2 = e3) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | (5306) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (149), (5009), (5303), (5306), % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | #258. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | (5307) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5307) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5308) all_252_22 = e3 & op(e0, e2) = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5308) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5309) op(e0, e2) = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5273), (5309), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | (5310) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5310) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5311) all_252_23 = e3 & op(e0, e1) = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5311) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5312) op(e0, e1) = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5305), (5312), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5313) all_252_24 = e3 & op(e0, e0) = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5313) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (5314) all_252_24 = e3 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5315) all_252_24 = e0 & op(e0, e0) = e0 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5315) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5316) all_252_24 = e0 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14), (149), (161), (752), (5009), (5273), % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5303), (5305), (5316), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #257. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5317) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5317) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5318) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5319) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5319) gives: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5320) all_252_20 = e1 & op(e0, e4) = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5320) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5321) op(e0, e4) = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5298), (5321), (function-axioms) are % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #323. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5322) all_252_21 = e1 & op(e0, e3) = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5322) implies: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5323) all_252_21 = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5303), (5323) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5324) e4 = e1 % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12), (5324) imply: % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5325) $false % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5325) is inconsistent. % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5326) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5326) gives: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5327) all_252_22 = e1 & op(e0, e2) = e1 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5327) implies: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5328) op(e0, e2) = e1 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5328), (function-axioms) are % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5329) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5329) gives: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5330) all_252_23 = e1 & op(e0, e1) = e1 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5330) implies: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5331) all_252_23 = e1 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5318) gives: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5332) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5332) gives: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5333) all_252_20 = e0 & op(e0, e4) = e0 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5298), (5333), (function-axioms) are % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #255. % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5334) all_252_21 = e0 & op(e0, e3) = e0 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5334) implies: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5335) all_252_21 = e0 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5303), (5335) imply: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5336) e4 = e0 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (5336) imply: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5337) $false % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5337) is inconsistent. % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5338) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (5273), (5331), (5338), % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #254. % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5339) all_252_24 = e1 & op(e0, e0) = e1 % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5314), (5339) are inconsistent by sub-proof % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #399. % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | (5340) op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_230_0 & $i(all_230_0))) % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4954), (5273), (5340), (function-axioms) are % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253. % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | End of split % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | | % 186.64/29.60 | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | (5341) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5341) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | (5342) all_252_22 = e4 & op(e0, e2) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5342) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | (5343) all_252_22 = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | (5344) ~ (all_108_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5291), (5344) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | (5345) $false % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5345) is inconsistent. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | (5346) op(e4, e0) = all_108_1 & $i(all_108_1) & ( ~ % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | (all_108_1 = e1) | ( ~ (all_108_0 = e3) & op(e0, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_108_0 & $i(all_108_0))) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5346) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | (5347) op(e4, e0) = all_108_1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | (5348) ~ (all_230_2 = e3) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1378), (5348) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | (5349) ~ (all_20_2 = e3) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (428) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5350) ~ (all_206_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5292), (5350) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5351) $false % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5351) is inconsistent. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5352) op(e4, e0) = all_206_1 & $i(all_206_1) & ( ~ % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (all_206_1 = e3) | ( ~ (all_206_0 = e1) & op(e0, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_206_0 & $i(all_206_0))) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5352) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5353) op(e4, e0) = all_206_1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5354) ~ (all_206_1 = e3) | ( ~ (all_206_0 = e1) & % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_206_0 & $i(all_206_0)) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_206_1, e0, e4, simplifying with (176), (5353) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5355) all_206_1 = all_30_2 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_108_1, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | all_206_1, e0, e4, simplifying with (5347), (5353) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5356) all_206_1 = all_108_1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5355), (5356) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | (5357) all_108_1 = all_30_2 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (5358) ~ (all_26_2 = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5359) ~ (all_30_2 = e3) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5360) ~ (all_34_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5361) ~ (all_54_2 = e1) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1316), (5361) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5362) ~ (all_30_2 = e1) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5363) ~ (all_64_2 = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5364) ~ (all_66_2 = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1302), (5364) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5365) ~ (all_16_2 = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5366) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5366) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5367) all_252_0 = e0 & op(e4, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5367) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5368) op(e4, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (504), (743), (962), (1442), (1443), % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980), (5271), (5359), (5362), (5368), % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #252. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5369) all_252_2 = e0 & op(e3, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (280), (4947), (5369), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #251. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5370) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5370) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5371) all_252_6 = e0 & op(e2, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5371) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5372) op(e2, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (5363), (5372), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5373) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5373) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5374) all_252_12 = e0 & op(e1, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (155), (5365), (5374), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #532. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5375) all_252_20 = e0 & op(e0, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5298), (5375), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #255. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5376) all_66_2 = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1302), (5376) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5377) all_16_2 = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1614), (5377) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5378) op(e1, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (5360), (5378), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5379) all_64_2 = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1377), (5379) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5380) all_224_2 = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1610), (5379) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5381) op(e2, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5382) ~ (all_224_2 = e0) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5380), (5382) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5383) $false % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5383) is inconsistent. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1, e4, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (5258), (5381) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5384) all_18_1 = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5297), (5384) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5385) op(e4, e4) = e2 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (5262), (5385), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #500. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5386) all_54_2 = e1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1316), (5386) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5387) all_30_2 = e1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5387) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5388) all_30_2 = e1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1604), (5388) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5389) op(e4, e1) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5358), (5389), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #452. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5390) all_34_2 = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5391) op(e4, e1) = all_34_1 & $i(all_34_1) & ( ~ % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_34_1 = e2) | ( ~ (all_34_0 = e3) & op(e1, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_34_0 & $i(all_34_0))) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5391) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5392) op(e4, e1) = all_34_1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1379), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5393) all_232_2 = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1569), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5394) ~ (all_30_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5394) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5395) ~ (all_30_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1464), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5396) ~ (all_16_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5396) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5397) ~ (all_16_2 = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1600), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5398) op(e4, all_20_2) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1599), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399) op(all_20_2, e4) = e1 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1617), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400) op(e1, e4) = e0 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (182), (5390) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5401) op(e1, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5402) ~ (all_104_2 = e1) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4968), (5402) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5403) ~ (all_8_1 = e1) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (757) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5404) (all_252_16 = e4 & op(e4, e0) = e4) | (all_252_17 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5404) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5405) all_252_16 = e4 & op(e4, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5405) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5406) op(e4, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e4, % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (5406) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5407) all_30_2 = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5395), (5407) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5408) $false % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5408) is inconsistent. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5409) all_252_17 = e4 & op(e3, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5409) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5410) op(e3, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (4954), (5410), (function-axioms) are % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #250. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5411) (all_252_18 = e4 & op(e2, e0) = e4) | (all_252_19 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e0) = e4) | (all_252_24 = e4 & % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5411) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5412) all_252_18 = e4 & op(e2, e0) = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5412) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5413) all_252_18 = e4 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5414) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (176), (5000), (5359), (5414), % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #248. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5415) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5415) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5416) all_252_18 = e3 & op(e2, e0) = e3 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5416) implies: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5417) all_252_18 = e3 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5413), (5417) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5418) e4 = e3 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (5418) imply: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5419) $false % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5419) is inconsistent. % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5420) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5420) gives: % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5421) all_252_19 = e3 & op(e1, e0) = e3 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5401), (5421), (function-axioms) are % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #291. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5422) all_252_24 = e3 & op(e0, e0) = e3 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5422) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5423) all_252_24 = e3 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (754) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5424) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5424) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5425) all_252_16 = e1 & op(e4, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5425) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5426) op(e4, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5427) all_252_24 = e0 & op(e0, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5427) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5428) all_252_24 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5423), (5428) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5429) e3 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5429) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5430) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5430) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5431) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5431) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5432) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5432) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5433) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5433) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5434) all_252_16 = e0 & op(e4, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5434) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5435) op(e4, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e0, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (5435) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5436) all_30_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e4, simplifying with (176), (5426) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5437) all_30_2 = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5436), (5437) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5438) e1 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5438) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5439) e1 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (5439) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5440) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5441) all_252_17 = e0 & op(e3, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5441) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5442) all_252_17 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5000), (5442) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5443) e2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5443) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5444) e2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (5444) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5445) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5445) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5446) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5446) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5447) all_252_18 = e0 & op(e2, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5413), (5447) are inconsistent by sub-proof % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #359. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5448) all_252_19 = e0 & op(e1, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5448) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5449) op(e1, e0) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5401), (5449), (function-axioms) are % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5450) all_252_17 = e1 & op(e3, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5000), (5450) are inconsistent by sub-proof % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5451) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5451) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5452) all_252_18 = e1 & op(e2, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5413), (5452) are inconsistent by sub-proof % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #246. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5453) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5453) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5454) all_252_19 = e1 & op(e1, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5454) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5455) op(e1, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5401), (5455), (function-axioms) are % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #527. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5456) all_252_24 = e1 & op(e0, e0) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5456) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5457) all_252_24 = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5423), (5457) are inconsistent by sub-proof % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #245. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5458) (all_252_19 = e4 & op(e1, e0) = e4) | (all_252_24 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5458) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5459) all_252_19 = e4 & op(e1, e0) = e4 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5459) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5460) all_252_19 = e4 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (463) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5461) ~ (all_232_2 = e4) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5393), (5461) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5462) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5462) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5463) op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_232_0 & $i(all_232_0))) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5463) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5464) op(e4, e1) = all_232_1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, e0, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e1, simplifying with (155), (5400) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5465) all_16_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_232_1, e1, e4, simplifying with (170), (5464) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5466) all_232_1 = all_26_2 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_232_1, e1, e4, simplifying with (5392), (5464) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5467) all_232_1 = all_34_1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5466), (5467) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5468) all_34_1 = all_26_2 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1302), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5469) all_66_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1365), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5470) all_170_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1462), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5471) ~ (all_244_15 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1452), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472) ~ (all_64_2 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1459), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5473) ~ (all_62_2 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5397), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5474) ~ (e4 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5012), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5475) ~ (e3 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5267), (5465) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5476) ~ (e2 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (758) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5477) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5477) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5478) all_252_12 = e0 & op(e1, e4) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5478) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5479) all_252_12 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5480) ~ (all_66_2 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5469), (5480) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5481) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5481) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5482) op(e0, e1) = all_66_1 & $i(all_66_1) & ( ~ % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_66_1 = e3) | ( ~ (all_66_0 = e2) & op(e1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_66_0 & $i(all_66_0))) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5482) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5483) op(e0, e1) = all_66_1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5484) ~ (all_170_2 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5470), (5484) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5485) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5485) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5486) op(e0, e1) = all_170_1 & $i(all_170_1) & ( ~ % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_170_1 = e2) | ( ~ (all_170_0 = e3) & op(e1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_170_0 & $i(all_170_0))) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5486) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5487) op(e0, e1) = all_170_1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_170_1, e1, e0, simplifying with (161), (5487) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5488) all_170_1 = all_20_2 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_66_1, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_170_1, e1, e0, simplifying with (5483), (5487) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5489) all_170_1 = all_66_1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5488), (5489) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5490) all_66_1 = all_20_2 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5491) ~ (all_38_2 = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5492) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5492) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5493) all_252_9 = e0 & op(e4, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5493) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5494) op(e4, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, e0, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e4, simplifying with (170), (5494) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5495) all_26_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5358), (5495) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5496) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5496) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5497) all_252_10 = e0 & op(e3, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5497) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5498) op(e3, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e0, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (5498) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5499) all_36_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4949), (5499) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5500) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5500) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5501) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5501) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5502) all_252_11 = e0 & op(e2, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5502) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5503) op(e2, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, e0, % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (188), (5503) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5504) all_38_2 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5491), (5504) imply: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5505) $false % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5505) is inconsistent. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5506) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5506) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5507) all_252_15 = e0 & op(e1, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5507) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5508) op(e1, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5471), (5508), (function-axioms) are % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5509) all_252_23 = e0 & op(e0, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5509) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5510) all_252_23 = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5511) op(e0, e1) = e0 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5512) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4944), (5298), (5403), (5512), % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #244. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5513) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5513) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5514) all_252_22 = e1 & op(e0, e2) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5514) implies: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5515) op(e0, e2) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5515), (function-axioms) are % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5516) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5516) gives: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5517) all_252_23 = e1 & op(e0, e1) = e1 % 186.87/29.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5510), (5517) are inconsistent by sub-proof % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #293. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5518) all_252_24 = e1 & op(e0, e0) = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5518) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5519) all_252_24 = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5520) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5520) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5521) all_252_20 = e3 & op(e0, e4) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5521) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5522) op(e0, e4) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (5009), (5522), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5523) all_252_21 = e3 & op(e0, e3) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5523) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5524) all_252_21 = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5525) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (176), (5000), (5359), (5525), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #248. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5526) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5526) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5527) all_252_18 = e3 & op(e2, e0) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5527) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5528) all_252_18 = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5529) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5529) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5530) all_252_6 = e0 & op(e2, e4) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5530) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5531) op(e2, e4) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (5472), (5531), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5532) all_252_7 = e0 & op(e2, e3) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5532) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5533) op(e2, e3) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0, % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (5533) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5534) all_10_2 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4953), (5534) imply: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5535) op(e0, e0) = e2 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (4972), (5535), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #477. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5536) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5536) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5537) all_252_8 = e0 & op(e2, e2) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5537) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5538) op(e2, e2) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (4946), (5538), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #448. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5539) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5539) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5540) all_252_11 = e0 & op(e2, e1) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5540) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5541) op(e2, e1) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (5491), (5541), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5542) all_252_18 = e0 & op(e2, e0) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5542) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5543) all_252_18 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5528), (5543) imply: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5544) e3 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (5544) imply: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5545) $false % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5545) is inconsistent. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5546) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5546) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5547) all_252_19 = e3 & op(e1, e0) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5460), (5547) are inconsistent by sub-proof % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5548) all_252_24 = e3 & op(e0, e0) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5548) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5549) all_252_24 = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5550) all_252_24 = e0 & op(e0, e0) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5550) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5551) all_252_24 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5549), (5551) are inconsistent by sub-proof % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #331. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5552) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5552) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5553) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5554) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (5285), (5524), (5554) are inconsistent % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #241. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5513) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5555) all_252_22 = e1 & op(e0, e2) = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5555) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5556) op(e0, e2) = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5556), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5516) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5557) all_252_23 = e1 & op(e0, e1) = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5557) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5558) all_252_23 = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (11), (5285), (5343), (5524), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5553), (5558) are inconsistent by sub-proof #238. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5519), (5549) are inconsistent by sub-proof % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #245. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5559) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5559) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5560) all_252_22 = e3 & op(e0, e2) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5560) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5561) op(e0, e2) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5273), (5561), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5562) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5562) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5563) all_252_23 = e3 & op(e0, e1) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5563) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5564) op(e0, e1) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5511), (5564), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #449. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5565) all_252_24 = e3 & op(e0, e0) = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5565) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5566) all_252_24 = e3 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5519), (5566) are inconsistent by sub-proof % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #245. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5567) all_38_2 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1557), (5567) imply: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5568) ~ (all_20_2 = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5568) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5569) ~ (all_20_2 = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1612), (5567) imply: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5570) op(e2, e0) = e1 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (188), (5567) imply: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5571) op(e2, e1) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5572) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5572) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5573) all_252_9 = e0 & op(e4, e1) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5573) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5574) all_252_9 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5575) op(e4, e1) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (227), (480), (504), (727), (749), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750), (752), (754), (756), (758), (759), (760), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761), (764), (765), (766), (767), (768), (769), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770), (771), (772), (774), (775), (776), (779), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781), (782), (783), (784), (785), (786), (787), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788), (790), (791), (793), (794), (795), (796), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797), (1424), (1563), (1576), (1597), (1613), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4963), (4974), (4976), (4978), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5000), (5009), (5262), (5266), (5269), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273), (5285), (5294), (5296), (5298), (5343), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5398), (5399), (5400), (5460), (5472), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5473), (5479), (5569), (5570), (5571), (5574), % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5575), (function-axioms) are inconsistent by % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #60. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5576) all_252_10 = e0 & op(e3, e1) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5576) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577) all_252_10 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5578) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5578) gives: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5579) all_252_6 = e0 & op(e2, e4) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5579) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5580) op(e2, e4) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (5472), (5580), (function-axioms) are % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5581) all_252_7 = e0 & op(e2, e3) = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5581) implies: % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5582) all_252_7 = e0 % 186.87/29.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (227), (480), (504), (727), (749), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750), (752), (754), (756), (758), (759), (760), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761), (764), (765), (766), (767), (768), (769), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770), (771), (772), (774), (775), (776), (779), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781), (782), (783), (784), (785), (786), (787), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788), (790), (791), (793), (794), (795), (796), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797), (1424), (1563), (1576), (1597), (1613), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4954), (4963), (4974), (4976), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978), (4983), (5000), (5009), (5262), (5266), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5269), (5273), (5285), (5294), (5296), (5298), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5343), (5349), (5398), (5399), (5400), (5460), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472), (5473), (5479), (5569), (5570), (5571), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577), (5582), (function-axioms) are inconsistent % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #36. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5583) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5583) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5584) all_252_8 = e0 & op(e2, e2) = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5584) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5585) all_252_8 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5586) op(e2, e2) = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (770) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5587) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e3) = e2) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5587) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5588) all_252_6 = e2 & op(e2, e4) = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5588) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5589) all_252_6 = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (149), (788), (790), (794), (796), (5009), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5285), (5298), (5479), (5589), (function-axioms) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #223. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5590) all_252_7 = e2 & op(e2, e3) = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5590) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5591) all_252_7 = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5592) all_250_23 = e4 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5294), (5592) are inconsistent by % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5593) ~ (all_250_23 = e4) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5594) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_23 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5594) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5595) all_250_23 = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5349), (5595) are inconsistent by % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #488. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5596) ~ (all_250_23 = e3) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5597) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5597) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5598) all_250_23 = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5266), (5598) are inconsistent by % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #487. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5599) ~ (all_250_23 = e2) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5600) all_250_23 = e1 | all_250_23 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5600) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5601) all_250_23 = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (5601) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5602) all_20_2 = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5602) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5603) all_20_2 = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1563), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5604) ~ (all_244_24 = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4983), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5605) ~ (all_8_1 = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5294), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5606) ~ (e4 = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5349), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5607) ~ (e3 = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5266), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5608) ~ (e2 = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5399), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5609) op(e1, e4) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5398), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5610) op(e4, e1) = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (5603) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5611) op(e0, e1) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5612) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5612) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5613) all_252_9 = e4 & op(e4, e1) = e4 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5613) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5614) all_252_9 = e4 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5615) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4944), (5298), (5403), (5615), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #244. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5616) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5616) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5617) all_252_22 = e1 & op(e0, e2) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5617) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5618) op(e0, e2) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5618), (function-axioms) are % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5619) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5619) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5620) all_252_23 = e1 & op(e0, e1) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5620) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5621) all_252_23 = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5622) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5622) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5623) all_252_9 = e3 & op(e4, e1) = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5610), (5623), (function-axioms) are % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5624) all_252_10 = e3 & op(e3, e1) = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5577), (5624) are inconsistent by sub-proof % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #59. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5625) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5625) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5626) all_252_11 = e3 & op(e2, e1) = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5626) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5627) all_252_11 = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5628) op(e2, e1) = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (772) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5629) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5629) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5630) all_252_6 = e4 & op(e2, e4) = e4 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5630) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5631) all_252_6 = e4 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (769) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5632) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12), (5591), (5631), (5632) are inconsistent % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #74. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5633) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5633) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5634) all_252_8 = e1 & op(e2, e2) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (750), (1424), (1563), (4944), (4983), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5266), (5273), (5285), (5294), (5569), (5585), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5600), (5621), (5634), (function-axioms) are % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5635) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5635) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5636) all_252_11 = e1 & op(e2, e1) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5627), (5636) are inconsistent by sub-proof % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #72. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5637) all_252_18 = e1 & op(e2, e0) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5637) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5638) all_252_18 = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5639) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5639) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640) all_252_16 = e3 & op(e4, e0) = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5640) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5641) all_252_16 = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5642) op(e4, e0) = e3 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (789) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5643) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e3) = e0) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5643) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5644) all_252_0 = e0 & op(e4, e4) = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5644) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5645) all_252_0 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (790) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5646) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5647) all_252_0 = e1 & op(e4, e4) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5645), (5647) are inconsistent by sub-proof % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #233. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5648) all_252_2 = e1 & op(e3, e4) = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5648) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5649) all_252_2 = e1 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (14), (149), (794), (5009), (5479), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5631), (5645), (5649), (function-axioms) are % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5650) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 & % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (12), (5298), (5479), (5631), (5650), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #214. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5651) all_252_1 = e0 & op(e4, e3) = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5651) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5652) all_252_1 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (793) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5653) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5653) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5654) all_252_0 = e2 & op(e4, e4) = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5654) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5655) op(e4, e4) = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (504), (5262), (5655), (function-axioms) are % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #500. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5656) all_252_1 = e2 & op(e4, e3) = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5656) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5657) all_252_1 = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5652), (5657) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5658) e2 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5658) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5659) e2 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5591), (5659) imply: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5660) all_252_7 = e0 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (227), (480), (504), (727), (749), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750), (752), (754), (756), (758), (759), (760), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761), (764), (765), (766), (767), (768), (769), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770), (771), (772), (774), (775), (776), (779), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781), (782), (783), (784), (785), (786), (787), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788), (790), (791), (793), (794), (795), (796), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797), (1424), (1563), (1576), (1597), (1613), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4954), (4963), (4974), (4976), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978), (4983), (5000), (5009), (5262), (5266), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5269), (5273), (5285), (5294), (5296), (5298), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5343), (5349), (5398), (5399), (5400), (5460), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472), (5473), (5479), (5569), (5570), (5571), % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577), (5660), (function-axioms) are inconsistent % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #36. % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5661) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 & % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2) % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5661) gives: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5662) all_252_4 = e2 & op(e4, e2) = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5662) implies: % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5663) all_252_4 = e2 % 186.87/29.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5664) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5664) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5665) all_252_4 = e3 & op(e4, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5663), (5665) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5666) all_252_5 = e3 & op(e3, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5666) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5667) all_252_5 = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4963), (5667) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5668) e3 = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (750), (764), (765), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (4944), (4976), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5349), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400), (5569), (5600), (5609), (5610), (5611), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5627), (5668), (function-axioms) are inconsistent % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #110. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5669) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5669) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5670) all_252_8 = e3 & op(e2, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5670) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5671) op(e2, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (5586), (5671), (function-axioms) are % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #468. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5672) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5672) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5673) all_252_14 = e3 & op(e1, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5673) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5674) all_252_14 = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (774) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5675) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5675) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5676) all_252_4 = e1 & op(e4, e2) = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5676) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5677) all_252_4 = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5663), (5677) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5678) e2 = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (5678) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5679) $false % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5679) is inconsistent. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5680) all_252_5 = e1 & op(e3, e2) = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4963), (5680) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5681) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5681) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5682) all_252_8 = e1 & op(e2, e2) = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5682) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5683) all_252_8 = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5585), (5683) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5684) e1 = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5684) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5685) e1 = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (5685) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5686) $false % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5686) is inconsistent. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5687) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5687) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5688) all_252_14 = e1 & op(e1, e2) = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5688) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5689) all_252_14 = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5674), (5689) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5690) e3 = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5690) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5691) $false % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5691) is inconsistent. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5692) all_252_22 = e1 & op(e0, e2) = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5692) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5693) op(e0, e2) = e1 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5693), (function-axioms) are % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5694) all_252_22 = e3 & op(e0, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5694) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5695) op(e0, e2) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5273), (5695), (function-axioms) are % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5696) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5696) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5697) all_252_9 = e2 & op(e4, e1) = e2 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (149), (788), (790), (794), (796), (5009), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5285), (5298), (5479), (5614), (5631), (5697), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #52. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5698) all_252_16 = e2 & op(e4, e0) = e2 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5698) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5699) all_252_16 = e2 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5641), (5699) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5700) e3 = e2 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5700) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5701) e3 = e2 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10), (5701) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5702) $false % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5702) is inconsistent. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5703) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e1) = e0) | (all_252_16 = e0 & % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e0) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5703) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5704) all_252_4 = e0 & op(e4, e2) = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5704) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5705) op(e4, e2) = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (1623), (5705), (function-axioms) are % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #548. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5706) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e4, e0) = e0) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5706) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5707) all_252_9 = e0 & op(e4, e1) = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5707) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5708) all_252_9 = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (480), (504), (727), (749), (750), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752), (754), (756), (758), (759), (760), (761), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764), (765), (766), (767), (769), (770), (771), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772), (774), (775), (776), (779), (781), (782), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783), (784), (785), (786), (787), (788), (790), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791), (793), (794), (795), (796), (797), (1424), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563), (1576), (1597), (1613), (4944), (4950), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4963), (4974), (4976), (4978), (4983), (5000), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5009), (5262), (5266), (5269), (5273), (5285), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5294), (5296), (5298), (5343), (5349), (5398), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399), (5400), (5460), (5473), (5479), (5569), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5570), (5571), (5585), (5610), (5708), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5709) all_252_16 = e0 & op(e4, e0) = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5642), (5709), (function-axioms) are % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #342. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5710) all_252_17 = e3 & op(e3, e0) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5000), (5710) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5711) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5711) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5712) all_252_18 = e3 & op(e2, e0) = e3 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5638), (5712) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #209. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5713) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (749), (750), (764), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765), (766), (767), (1424), (1563), (4944), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4976), (4983), (5266), (5273), (5285), (5294), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5298), (5349), (5400), (5460), (5569), (5571), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5600), (5604), (5609), (5610), (5611), (5627), % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5628), (5713), (function-axioms) are inconsistent % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #44. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5714) all_252_7 = e4 & op(e2, e3) = e4 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (5591), (5714) are inconsistent by sub-proof % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #68. % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5715) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e4) % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5715) gives: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5716) all_252_8 = e4 & op(e2, e2) = e4 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5716) implies: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5717) all_252_8 = e4 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5585), (5717) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5718) e4 = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5614), (5718) imply: % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5719) all_252_9 = e0 % 186.87/29.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (480), (504), (727), (749), (750), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752), (754), (756), (758), (759), (760), (761), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764), (765), (766), (767), (769), (770), (771), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772), (774), (775), (776), (779), (781), (782), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783), (784), (785), (786), (787), (788), (790), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791), (793), (794), (795), (796), (797), (1424), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563), (1576), (1597), (1613), (4944), (4950), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4963), (4974), (4976), (4978), (4983), (5000), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5009), (5262), (5266), (5269), (5273), (5285), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5294), (5296), (5298), (5343), (5349), (5398), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399), (5400), (5460), (5473), (5479), (5569), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5570), (5571), (5585), (5610), (5719), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (749), (750), (754), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756), (764), (765), (766), (767), (1424), (1563), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4976), (4983), (5000), (5266), (5273), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5285), (5294), (5298), (5349), (5400), (5403), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5460), (5569), (5571), (5600), (5604), (5609), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5610), (5611), (5627), (5628), (5720), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #43. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5721) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5721) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5722) all_252_15 = e3 & op(e1, e1) = e3 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5722) implies: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5723) all_252_15 = e3 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5724) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5724) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5725) all_252_12 = e2 & op(e1, e4) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (227), (480), (504), (727), (749), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750), (752), (754), (756), (758), (759), (760), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761), (764), (765), (766), (767), (768), (769), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770), (771), (772), (774), (775), (776), (779), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781), (782), (783), (784), (785), (786), (787), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788), (790), (791), (793), (794), (795), (796), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797), (1424), (1563), (1576), (1597), (1613), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4954), (4963), (4974), (4976), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978), (4983), (5000), (5009), (5262), (5266), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5269), (5273), (5285), (5294), (5296), (5298), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5343), (5349), (5398), (5399), (5400), (5460), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472), (5473), (5479), (5569), (5570), (5571), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577), (5591), (5725), (function-axioms) are % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5726) all_252_13 = e2 & op(e1, e3) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5726) implies: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5727) all_252_13 = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5728) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (185), (4976), (5614), (5728), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #198. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5729) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5729) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5730) all_252_11 = e2 & op(e2, e1) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5730) implies: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5731) all_252_11 = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5732) op(e2, e1) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (161), (182), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (191), (480), (750), (759), (764), (765), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (1576), (4944), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4976), (4983), (5266), (5273), (5285), (5294), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5298), (5349), (5398), (5399), (5400), (5479), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5569), (5570), (5571), (5600), (5723), (5727), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5731), (5732), (function-axioms) are inconsistent % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #119. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5733) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5733) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5734) all_252_15 = e2 & op(e1, e1) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5723), (5734) are inconsistent by sub-proof % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #114. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5735) all_252_23 = e2 & op(e0, e1) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5266), (5735), (function-axioms) are % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5736) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5736) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5737) all_252_14 = e2 & op(e1, e2) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5737) implies: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5738) all_252_14 = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5739) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (185), (4976), (5614), (5739), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #198. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5740) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5740) gives: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5741) all_252_11 = e2 & op(e2, e1) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5741) implies: % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5742) all_252_11 = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5743) op(e2, e1) = e2 % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (161), (182), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (191), (480), (750), (759), (764), (765), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (1576), (4944), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4976), (4983), (5266), (5273), (5285), (5294), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5398), (5399), (5400), (5479), (5569), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5570), (5571), (5600), (5621), (5723), (5738), % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5742), (5743), (function-axioms) are inconsistent % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #65. % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 186.87/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5744) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5744) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5745) all_252_15 = e2 & op(e1, e1) = e2 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5723), (5745) are inconsistent by sub-proof % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #114. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5746) all_252_23 = e2 & op(e0, e1) = e2 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5266), (5746), (function-axioms) are % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #540. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5747) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5747) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5748) all_252_15 = e2 & op(e1, e1) = e2 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5723), (5748) are inconsistent by sub-proof % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #202. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5749) all_252_19 = e2 & op(e1, e0) = e2 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (4978), (5749), (function-axioms) are % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5750) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5750) implies: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5751) op(e0, e1) = e3 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5349), (5751), (function-axioms) are % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5752) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5752) implies: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5753) op(e0, e0) = e1 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (5604), (5753), (function-axioms) are % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #474. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5754) all_252_10 = e4 & op(e3, e1) = e4 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5577), (5754) are inconsistent by sub-proof % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #37. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5755) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5755) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5756) all_252_11 = e4 & op(e2, e1) = e4 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (750), (764), (765), % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (4944), (4976), % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5298), % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5400), (5403), (5569), (5571), (5600), % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5604), (5609), (5610), (5756), (function-axioms) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #67. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5757) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5757) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5758) all_252_15 = e4 & op(e1, e1) = e4 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5758) implies: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759) all_252_15 = e4 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5760) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4944), (5298), (5403), (5760), % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #244. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5761) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5761) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5762) all_252_22 = e1 & op(e0, e2) = e1 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5762) implies: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5763) op(e0, e2) = e1 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5763), (function-axioms) are % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5764) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5764) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5765) all_252_23 = e1 & op(e0, e1) = e1 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5765) implies: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766) all_252_23 = e1 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5767) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5767) gives: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5768) all_252_12 = e2 & op(e1, e4) = e2 % 187.10/29.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (140), (149), (161), (173), (182), (185), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (224), (227), (480), (504), (727), (749), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750), (752), (754), (756), (758), (759), (760), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761), (764), (765), (766), (767), (768), (769), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770), (771), (772), (774), (775), (776), (779), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781), (782), (783), (784), (785), (786), (787), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788), (790), (791), (793), (794), (795), (796), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797), (1424), (1563), (1576), (1597), (1613), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944), (4950), (4954), (4963), (4974), (4976), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4978), (4983), (5000), (5009), (5262), (5266), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5269), (5273), (5285), (5294), (5296), (5298), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5343), (5349), (5398), (5399), (5400), (5460), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472), (5473), (5479), (5569), (5570), (5571), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577), (5591), (5768), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #35. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5769) all_252_13 = e2 & op(e1, e3) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5769) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5770) all_252_13 = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (12), (14), (182), (191), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (750), (759), (761), (1424), (1563), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (4944), (4983), (5266), (5273), (5285), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5294), (5460), (5479), (5569), (5570), (5600), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759), (5766), (5770), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #176. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5771) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5771) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5772) all_252_14 = e2 & op(e1, e2) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5772) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5773) all_252_14 = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (10), (12), (14), (182), (191), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (750), (759), (761), (1424), (1563), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (4944), (4983), (5266), (5273), (5285), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5294), (5460), (5479), (5569), (5570), (5600), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759), (5766), (5773), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #174. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5774) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5774) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5775) all_252_15 = e2 & op(e1, e1) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (5759), (5775) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #199. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5776) all_252_19 = e2 & op(e1, e0) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (182), (4978), (5776), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #438. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5777) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5777) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5778) op(e0, e0) = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (5604), (5778), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #474. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5779) all_252_23 = e4 & op(e0, e1) = e4 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5779) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5780) op(e0, e1) = e4 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (161), (5611), (5780), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5781) all_250_23 = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5569), (5781) are inconsistent by % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #486. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5782) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e1) = e2) | (all_252_18 = e2 & % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5782) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5783) all_252_8 = e2 & op(e2, e2) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5585), (5783) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #66. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5784) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e0) = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5784) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5785) all_252_11 = e2 & op(e2, e1) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5785) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5786) all_252_11 = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5787) op(e2, e1) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (161), (182), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185), (191), (480), (727), (750), (759), (760), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761), (764), (765), (766), (767), (1424), (1563), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576), (4944), (4976), (4978), (4983), (5266), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273), (5285), (5294), (5298), (5349), (5398), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399), (5400), (5460), (5479), (5569), (5570), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5571), (5577), (5786), (5787), (function-axioms) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #56. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5788) all_252_18 = e2 & op(e2, e0) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (4974), (5788), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #76. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5789) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5789) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5790) all_252_11 = e0 & op(e2, e1) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (161), (185), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (727), (750), (764), (765), (766), (767), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424), (1563), (4944), (4976), (4983), (5266), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273), (5285), (5294), (5349), (5398), (5399), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400), (5569), (5790), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5791) all_252_18 = e0 & op(e2, e0) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5791) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5792) all_252_18 = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5793) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5793) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5794) all_252_16 = e3 & op(e4, e0) = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5794) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5795) op(e4, e0) = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (182), (191), (480), (727), (754), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424), (1563), (1576), (5000), (5266), (5294), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5569), (5570), (5792), (5795), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #141. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5796) all_252_17 = e3 & op(e3, e0) = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5000), (5796) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5797) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5797) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5798) all_252_18 = e3 & op(e2, e0) = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5792), (5798) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #61. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5799) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5799) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5800) all_252_19 = e3 & op(e1, e0) = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5460), (5800) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #177. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5801) all_252_24 = e3 & op(e0, e0) = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5801) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5802) all_252_24 = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5803) all_252_24 = e0 & op(e0, e0) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5803) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5804) all_252_24 = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5802), (5804) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #331. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5805) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5805) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5806) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5806) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5807) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5807) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5808) all_252_20 = e0 & op(e0, e4) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5298), (5808), (function-axioms) are % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #255. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5809) all_252_21 = e0 & op(e0, e3) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5809) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5810) op(e0, e3) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5811) all_250_23 = e4 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5294), (5811) are inconsistent by % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5812) ~ (all_250_23 = e4) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5813) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_23 = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5813) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5814) all_250_23 = e3 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5349), (5814) are inconsistent by % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #488. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5815) ~ (all_250_23 = e3) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5816) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5816) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5817) all_250_23 = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5266), (5817) are inconsistent by % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #487. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5818) ~ (all_250_23 = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5819) all_250_23 = e1 | all_250_23 = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5819) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5820) all_250_23 = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (5820) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5821) all_20_2 = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5821) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5822) all_20_2 = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1563), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823) ~ (all_244_24 = e1) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4983), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5824) ~ (all_8_1 = e1) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5294), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5825) ~ (e4 = e1) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5349), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5826) ~ (e3 = e1) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5266), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5827) ~ (e2 = e1) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5399), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5828) op(e1, e4) = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5398), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5829) op(e4, e1) = e0 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (5822) imply: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5830) op(e0, e1) = e1 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (767) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5831) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5831) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5832) all_252_9 = e4 & op(e4, e1) = e4 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5832) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5833) all_252_9 = e4 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (765) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5834) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (185), (4976), (5833), (5834), % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #41. % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5835) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5835) gives: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5836) all_252_11 = e2 & op(e2, e1) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5836) implies: % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5837) all_252_11 = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5838) op(e2, e1) = e2 % 187.10/29.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (750), (764), (765), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (4944), (4976), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5298), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5400), (5569), (5571), (5806), (5819), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823), (5828), (5829), (5837), (5838), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #135. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5839) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5839) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5840) all_252_15 = e2 & op(e1, e1) = e2 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5840) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5841) all_252_15 = e2 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5842) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5842) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5843) all_252_9 = e3 & op(e4, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5829), (5843), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5844) all_252_10 = e3 & op(e3, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5577), (5844) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5845) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5845) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5846) all_252_11 = e3 & op(e2, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5846) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5847) all_252_11 = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5848) op(e2, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (750), (764), (765), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (4944), (4976), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5298), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5400), (5569), (5571), (5806), (5819), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823), (5828), (5829), (5847), (5848), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #45. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5849) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5849) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5850) all_252_15 = e3 & op(e1, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (5841), (5850) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #188. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5851) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5851) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5852) all_252_23 = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (480), (750), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273), (5285), (5343), (5806), (5823), (5852), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #186. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5853) all_252_23 = e2 & op(e0, e1) = e2 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (12), (750), (4944), (5273), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5285), (5802), (5810), (5853), (function-axioms) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #185. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5854) all_252_10 = e4 & op(e3, e1) = e4 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5577), (5854) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #91. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5855) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5855) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5856) all_252_11 = e4 & op(e2, e1) = e4 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (750), (764), (765), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (4944), (4976), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5298), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5400), (5403), (5569), (5571), (5819), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823), (5828), (5829), (5856), (function-axioms) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #67. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5857) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5857) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5858) all_252_15 = e4 & op(e1, e1) = e4 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5858) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5859) all_252_15 = e4 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5860) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5860) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5861) all_252_9 = e3 & op(e4, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5829), (5861), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #275. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5862) all_252_10 = e3 & op(e3, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5577), (5862) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #59. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5863) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5863) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5864) all_252_11 = e3 & op(e2, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5864) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5865) all_252_11 = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5866) op(e2, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (13), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (161), (185), (480), (750), (764), (765), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (767), (1424), (1563), (4944), (4976), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5298), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5349), (5400), (5569), (5571), (5806), (5819), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5823), (5828), (5829), (5865), (5866), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #45. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5867) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5867) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5868) all_252_15 = e3 & op(e1, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5868) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5869) all_252_15 = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5859), (5869) imply: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5870) e4 = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (5870) imply: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5871) $false % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5871) is inconsistent. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5872) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5872) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5873) all_252_23 = e3 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (11), (12), (480), (750), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273), (5285), (5343), (5806), (5823), (5873), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #186. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5874) all_252_23 = e4 & op(e0, e1) = e4 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5874) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5875) op(e0, e1) = e4 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (161), (5830), (5875), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5876) all_250_23 = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5569), (5876) are inconsistent by % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #486. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5877) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (480), (727), (750), (1424), (1563), (4944), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5349), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5569), (5877), (function-axioms) are inconsistent % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #170. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5878) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5878) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5879) all_252_11 = e0 & op(e2, e1) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (10), (11), (13), (14), (161), (185), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480), (727), (750), (764), (765), (766), (767), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424), (1563), (4944), (4976), (4983), (5266), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273), (5285), (5294), (5349), (5398), (5399), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400), (5569), (5879), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5880) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5880) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5881) all_252_15 = e0 & op(e1, e1) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5881) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5882) op(e1, e1) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5471), (5882), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5883) all_252_23 = e0 & op(e0, e1) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (727), (750), (1424), (1563), (4944), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4983), (5266), (5273), (5285), (5294), (5349), % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5569), (5883), (function-axioms) are inconsistent % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #171. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5884) all_252_13 = e0 & op(e1, e3) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (224), (5473), (5884), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5885) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5885) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5886) all_252_14 = e0 & op(e1, e2) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5886) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5887) op(e1, e2) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (137), (1622), (5887), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5888) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5888) gives: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5889) all_252_15 = e0 & op(e1, e1) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5889) implies: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5890) op(e1, e1) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5471), (5890), (function-axioms) are % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5891) all_252_19 = e0 & op(e1, e0) = e0 % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5460), (5891) are inconsistent by sub-proof % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #161. % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5892) all_252_24 = e4 & op(e0, e0) = e4 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5892) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5893) all_252_24 = e4 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5894) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5894) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5895) all_252_20 = e3 & op(e0, e4) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5895) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5896) op(e0, e4) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (5009), (5896), (function-axioms) are % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5897) all_252_21 = e3 & op(e0, e3) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5897) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5898) all_252_21 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5899) all_252_24 = e0 & op(e0, e0) = e0 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5893), (5899) are inconsistent by sub-proof % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #34. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5900) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5900) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5901) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5902) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (5285), (5898), (5902) are inconsistent % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #241. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5903) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5903) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5904) all_252_22 = e1 & op(e0, e2) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5904) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5905) op(e0, e2) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5905), (function-axioms) are % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5906) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5906) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5907) all_252_23 = e1 & op(e0, e1) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5907) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5908) all_252_23 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (11), (5285), (5343), (5898), % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5901), (5908) are inconsistent by sub-proof #238. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5909) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5893), (5909) are inconsistent by sub-proof % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5910) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5910) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5911) all_252_22 = e3 & op(e0, e2) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5911) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5912) op(e0, e2) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5273), (5912), (function-axioms) are % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5913) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5913) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5914) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5914) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5915) all_252_23 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5916) all_252_24 = e0 & op(e0, e0) = e0 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (5893), (5916) are inconsistent by sub-proof % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #34. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5917) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5917) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5918) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5919) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5919) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5920) all_252_20 = e1 & op(e0, e4) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5285), (5920) are inconsistent by sub-proof % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #242. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5921) all_252_21 = e1 & op(e0, e3) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5921) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5922) all_252_21 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (11), (5285), (5343), (5915), % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5918), (5922) are inconsistent by sub-proof #187. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5923) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5923) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5924) all_252_22 = e1 & op(e0, e2) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5924) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5925) op(e0, e2) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (5925), (function-axioms) are % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5926) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5926) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5927) all_252_23 = e1 & op(e0, e1) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5927) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5928) all_252_23 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5915), (5928) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5929) e3 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5929) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5930) e3 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5930) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5931) $false % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5931) is inconsistent. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5932) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5893), (5932) are inconsistent by sub-proof % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5933) all_252_24 = e3 & op(e0, e0) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5893), (5933) are inconsistent by sub-proof % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #32. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5934) all_104_2 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4968), (5934) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5935) all_8_1 = e1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4988), (5935) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5936) op(e0, e1) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5349), (5936), (function-axioms) are % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5937) all_30_2 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5938) op(e3, e4) = all_30_1 & $i(all_30_1) & ( ~ % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_30_1 = e2) | ( ~ (all_30_0 = e1) & op(e4, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_30_0 & $i(all_30_0))) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5938) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5939) op(e3, e4) = all_30_1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5355), (5937) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5940) all_206_1 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1200), (5937) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5941) all_236_2 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1571), (5937) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5942) ~ (all_244_24 = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1604), (5937) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5943) op(e4, e3) = e0 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5272), (5937) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5944) op(e2, e3) = e4 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5945) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5945) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5946) all_252_20 = e3 & op(e0, e4) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5946) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5947) op(e0, e4) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (5009), (5947), (function-axioms) are % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5948) all_252_21 = e3 & op(e0, e3) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5948) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5949) op(e0, e3) = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5354) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5950) ~ (all_206_1 = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5940), (5950) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5951) $false % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5951) is inconsistent. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5952) ~ (all_206_0 = e1) & op(e0, e3) = all_206_0 & % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_206_0) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5952) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5953) op(e0, e3) = all_206_0 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (469) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5954) ~ (all_236_2 = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5941), (5954) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5955) $false % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5955) is inconsistent. % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5956) op(e3, e4) = all_236_1 & $i(all_236_1) & ( ~ % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_236_1 = e1) | ( ~ (all_236_0 = e2) & op(e4, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_236_0 & $i(all_236_0))) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5956) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5957) op(e3, e4) = all_236_1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_206_0, e3, e0, simplifying with (4944), (5953) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5958) all_206_0 = all_8_1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_206_0, e3, e0, simplifying with (5949), (5953) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5959) all_206_0 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e4, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (5944) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5960) all_10_2 = e4 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_100_2, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_236_1, e4, e3, simplifying with (280), (5957) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5961) all_236_1 = all_100_2 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_1, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_236_1, e4, e3, simplifying with (5939), (5957) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5962) all_236_1 = all_30_1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_84_2, e0, % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e4, simplifying with (257), (5943) gives: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5963) all_84_2 = e0 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5961), (5962) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5964) all_100_2 = all_30_1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5958), (5959) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5965) all_8_1 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5965) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5966) all_8_1 = e3 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (953), (5964) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5967) all_250_5 = all_30_1 % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1448), (5964) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5968) ~ (all_244_3 = all_30_1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1474), (5963) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5969) ~ (all_244_3 = e0) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1481), (5960) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5970) ~ (all_244_3 = e4) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4971), (5966) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5971) ~ (all_244_3 = e3) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1450), (5964) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5972) ~ (all_36_2 = all_30_1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5972) implies: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5973) ~ (all_36_2 = all_30_1) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5263), (5964) imply: % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5974) ~ (all_30_1 = e2) % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4947), (5964) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5975) ~ (all_30_1 = e0) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1581), (5963), (5964) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5976) op(all_30_1, e0) = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5977) ~ (all_122_2 = e4) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1360), (5977) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5978) ~ (all_36_2 = e4) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5979) all_250_6 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (5979) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5980) all_244_3 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5970), (5980) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5981) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5981) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5982) all_250_6 = e3 | all_250_6 = e2 | all_250_6 = e1 | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5982) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5983) all_250_6 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (5983) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5984) all_244_3 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5971), (5984) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5985) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5985) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5986) all_250_6 = e2 | all_250_6 = e1 | all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5986) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5987) all_250_6 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (5987) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5988) all_244_3 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4970), (5988) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5989) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5989) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5990) all_250_6 = e1 | all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5990) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5991) all_250_6 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (5991) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5992) all_244_3 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1485), (5992) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5993) ~ (all_36_2 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5993) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5994) ~ (all_36_2 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (526), (5992) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5995) op(e1, e1) = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (739) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5996) all_250_8 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (5996) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5997) all_36_2 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5997) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5998) all_36_2 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5978), (5998) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5999) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5999) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6000) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_8 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6000) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6001) all_250_8 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (6001) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6002) all_36_2 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6002) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6003) all_36_2 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1551), (6003) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6004) ~ (all_244_15 = e3) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (5995), (6004), (function-axioms) are % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6005) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6005) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6006) all_250_8 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (6006) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6007) all_36_2 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6007) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6008) all_36_2 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4976), (6008) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6009) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6009) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6010) all_250_8 = e1 | all_250_8 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6010) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6011) all_250_8 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (6011) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6012) all_36_2 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6012) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6013) all_36_2 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5994), (6013) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6014) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6014) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6015) all_250_8 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (6015) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6016) all_36_2 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6016) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6017) all_36_2 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4949), (6017) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6018) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6018) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6019) all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (6019) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6020) all_244_3 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5969), (6020) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6021) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6021) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6022) all_122_2 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1360), (6022) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6023) all_36_2 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5973), (6023) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6024) ~ (all_30_1 = e4) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6024) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6025) ~ (all_30_1 = e4) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (741) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6026) all_250_6 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (6026) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6027) all_244_3 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5970), (6027) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6028) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6028) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6029) all_250_6 = e3 | all_250_6 = e2 | all_250_6 = e1 | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6029) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6030) all_250_6 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (6030) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6031) all_244_3 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5971), (6031) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6032) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6032) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6033) all_250_6 = e2 | all_250_6 = e1 | all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6033) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6034) all_250_6 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (6034) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6035) all_244_3 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4970), (6035) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6036) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6036) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6037) all_250_6 = e1 | all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6037) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6038) all_250_6 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (6038) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6039) all_244_3 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6039) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6040) all_244_3 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5968), (6040) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6041) ~ (all_30_1 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6041) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6042) ~ (all_30_1 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (742) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6043) all_250_5 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5967), (6043) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6044) all_30_1 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6025), (6044) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6045) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6045) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6046) all_250_5 = e3 | all_250_5 = e2 | all_250_5 = e1 | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_5 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6046) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6047) all_250_5 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5967), (6047) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6048) all_30_1 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6048) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6049) all_30_1 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5976), (6049) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6050) op(e3, e0) = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (4954), (6050), (function-axioms) are % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #250. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6051) all_250_5 = e2 | all_250_5 = e1 | all_250_5 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6051) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6052) all_250_5 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5967), (6052) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6053) all_30_1 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6053) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6054) all_30_1 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5974), (6054) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6055) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6055) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6056) all_250_5 = e1 | all_250_5 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6056) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6057) all_250_5 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5967), (6057) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6058) all_30_1 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6058) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6059) all_30_1 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6042), (6059) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6060) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6060) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6061) all_250_5 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5967), (6061) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6062) all_30_1 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6062) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6063) all_30_1 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5975), (6063) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6064) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6064) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6065) all_250_6 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (6065) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6066) all_244_3 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6066) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6067) all_244_3 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5969), (6067) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6068) $false % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6068) is inconsistent. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6069) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6069) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6070) all_252_22 = e3 & op(e0, e2) = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6070) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6071) op(e0, e2) = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5273), (6071), (function-axioms) are % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6072) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (480), (5349), (5942), (6072), % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (6073) all_26_2 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1545), (6073) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (6074) ~ (all_20_2 = e0) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6074) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (6075) ~ (all_20_2 = e0) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6076) all_250_23 = e4 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5294), (6076) are inconsistent by % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #489. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6077) ~ (all_250_23 = e4) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6078) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 | all_250_23 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6078) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6079) all_250_23 = e3 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5349), (6079) are inconsistent by % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #488. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6080) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6080) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6081) all_250_23 = e2 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (5266), (6081) are inconsistent by % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #487. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6082) ~ (all_250_23 = e2) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6083) all_250_23 = e1 | all_250_23 = e0 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6083) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6084) all_250_23 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1424), (6084) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6085) all_20_2 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6085) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6086) all_20_2 = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1563), (6086) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6087) ~ (all_244_24 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4983), (6086) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6088) ~ (all_8_1 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6088) implies: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6089) ~ (all_8_1 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5294), (6086) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6090) ~ (e4 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5266), (6086) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6091) ~ (e2 = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1599), (6086) imply: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6092) op(e1, all_34_2) = e1 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6093) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4944), (5298), (6089), (6093), % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #244. % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6094) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6094) gives: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6095) all_252_22 = e1 & op(e0, e2) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6095) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6096) op(e0, e2) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (6096), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6097) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6097) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6098) all_252_23 = e1 & op(e0, e1) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6098) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6099) all_252_23 = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e1, % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_2, e1, simplifying with (1617), (6092) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6100) e1 = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6099), (6100) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6101) all_252_23 = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (12), (480), (750), (4944), (5273), % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5285), (6087), (6089), (6101), (function-axioms) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #193. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6102) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6102) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6103) op(e0, e0) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (6087), (6103), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #474. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6104) all_250_23 = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1424), (6075), (6104) are inconsistent by % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #486. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | (6105) op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_230_0 & $i(all_230_0))) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4954), (5273), (6105), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | (6106) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6106) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | (6107) all_252_23 = e4 & op(e0, e1) = e4 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5294), (6107), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #518. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | (6108) all_252_24 = e4 & op(e0, e0) = e4 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6108) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | (6109) all_252_24 = e4 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (460) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | (6110) ~ (all_230_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1378), (6110) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | (6111) ~ (all_20_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | (6112) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6112) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6113) all_252_20 = e3 & op(e0, e4) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6113) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6114) op(e0, e4) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (5009), (6114), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6115) all_252_21 = e3 & op(e0, e3) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6115) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6116) all_252_21 = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6117) op(e0, e3) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6118) all_252_24 = e0 & op(e0, e0) = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (6109), (6118) are inconsistent by sub-proof % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | #34. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6119) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6119) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6120) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6121) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6121) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6122) all_252_20 = e1 & op(e0, e4) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6122) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6123) op(e0, e4) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5298), (6123), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #323. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6124) all_252_21 = e1 & op(e0, e3) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6124) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6125) op(e0, e3) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, e1, % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (4944), (6125) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6126) all_8_1 = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, e3, % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (4944), (6117) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6127) all_8_1 = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6126), (6127) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6128) e3 = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6128) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6129) e3 = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (6129) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6130) $false % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6130) is inconsistent. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6131) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6131) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6132) all_252_22 = e1 & op(e0, e2) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6132) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6133) op(e0, e2) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (5273), (6133), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6134) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6134) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6135) all_252_23 = e1 & op(e0, e1) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6135) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6136) all_252_23 = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6120) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6137) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6137) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6138) all_252_20 = e0 & op(e0, e4) = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5298), (6138), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #255. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6139) all_252_21 = e0 & op(e0, e3) = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6139) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6140) all_252_21 = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6116), (6140) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6141) e3 = e0 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (6141) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6142) $false % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6142) is inconsistent. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6143) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (5273), (6136), (6143), % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #254. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6144) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (6109), (6144) are inconsistent by sub-proof % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #33. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | (6145) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6145) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6146) all_252_22 = e3 & op(e0, e2) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6146) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6147) op(e0, e2) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (5273), (6147), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (6148) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6148) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6149) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6149) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6150) op(e0, e1) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (6111), (6150), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6151) all_252_24 = e3 & op(e0, e0) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (6109), (6151) are inconsistent by sub-proof % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | #32. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | (6152) op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_230_0 & $i(all_230_0))) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4954), (5273), (6152), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253. % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | End of split % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | (6153) all_16_2 = e3 % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1439), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6154) ~ (all_244_0 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1445), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6155) ~ (all_100_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1452), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6156) ~ (all_64_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1459), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6157) ~ (all_62_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1464), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6158) ~ (all_34_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1457), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6159) ~ (all_12_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1460), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6160) ~ (all_4_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | SIMP: (6160) implies: % 187.10/29.70 | | | | | | | | | | | | | | | (6161) ~ (all_4_2 = e3) % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | REDUCE: (1614), (6153) imply: % 187.10/29.70 | | | | | | | | | | | | | | | (6162) op(e1, e3) = e4 % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | BETA: splitting (794) gives: % 187.10/29.70 | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | (6163) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 187.10/29.70 | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | REF_CLOSE: (280), (504), (6154), (6155), (6163), % 187.10/29.70 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.70 | | | | | | | | | | | | | | | | #559. % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | (6164) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 187.10/29.70 | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 187.10/29.70 | | | | | | | | | | | | | | | | op(e0, e4) = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | BETA: splitting (6164) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | (6165) all_252_6 = e3 & op(e2, e4) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (6156), (6165), (function-axioms) are % 187.10/29.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #432. % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | Case 2: % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | (6166) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 187.10/29.70 | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | BETA: splitting (6166) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6167) all_252_12 = e3 & op(e1, e4) = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | ALPHA: (6167) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6168) all_252_12 = e3 % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e4, % 187.10/29.70 | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (224), (6162) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6169) all_62_2 = e4 % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | REDUCE: (1501), (6169) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6170) ~ (all_34_2 = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | SIMP: (6170) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6171) ~ (all_34_2 = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | REDUCE: (1488), (6169) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6172) ~ (all_10_2 = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | SIMP: (6172) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6173) ~ (all_10_2 = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | REDUCE: (1498), (6169) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6174) ~ (all_4_2 = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | SIMP: (6174) implies: % 187.10/29.70 | | | | | | | | | | | | | | | | | | (6175) ~ (all_4_2 = e4) % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | (6176) ~ (all_18_2 = e2) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | REDUCE: (1231), (6176) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | (6177) ~ (all_12_2 = e2) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | (6178) ~ (all_22_2 = e2) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (4967), (6178) imply: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | (6179) ~ (all_8_1 = e2) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | (6180) ~ (all_28_2 = e1) % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (161), (173), (219), (480), (751), (1350), % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | (1597), (1613), (1621), (4944), (4950), (4972), % 187.10/29.70 | | | | | | | | | | | | | | | | | | | | | (6177), (6179), (6180), (function-axioms) are % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #286. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (6181) all_28_2 = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1531), (6181) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (6182) ~ (all_4_2 = e1) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | SIMP: (6182) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (6183) ~ (all_4_2 = e1) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (732), (857), (1591), (1612), (1622), (6161), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (6175), (6183), (function-axioms) are inconsistent % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | by sub-proof #575. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6184) all_22_2 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (4967), (4986), (4987), (6184), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | #31. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6185) all_18_2 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6186) op(e2, e0) = all_18_1 & $i(all_18_1) & ( ~ % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (all_18_1 = e3) | ( ~ (all_18_0 = e1) & op(e0, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | e3) = all_18_0 & $i(all_18_0))) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | ALPHA: (6186) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6187) op(e2, e0) = all_18_1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1231), (6185) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6188) all_12_2 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (828), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6189) all_210_2 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (1453), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6190) ~ (all_64_2 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (1468), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6191) ~ (all_28_2 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (1470), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6192) ~ (all_20_2 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (4985), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6193) ~ (all_8_1 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | SIMP: (6193) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6194) ~ (all_8_1 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (5009), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6195) ~ (e3 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (1594), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6196) op(all_30_2, e2) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (1593), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6197) op(e2, all_30_2) = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | REDUCE: (1618), (6188) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6198) op(e0, e2) = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (434) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6199) ~ (all_210_2 = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (6189), (6199) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6200) $false % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | CLOSE: (6200) is inconsistent. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6201) op(e2, e0) = all_210_1 & $i(all_210_1) & ( ~ % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (all_210_1 = e1) | ( ~ (all_210_0 = e3) & op(e0, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | e1) = all_210_0 & $i(all_210_0))) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (6201) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6202) op(e2, e0) = all_210_1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (6203) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6203) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6204) all_252_20 = e2 & op(e0, e4) = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6204) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6205) all_252_20 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, e4, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (173), (6198) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6206) all_28_2 = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | all_210_1, e0, e2, simplifying with (191), (6202) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6207) all_210_1 = all_40_2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | all_210_1, e0, e2, simplifying with (6187), (6202) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6208) all_210_1 = all_18_1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6207), (6208) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6209) all_40_2 = all_18_1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6209) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6210) all_40_2 = all_18_1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1598), (6206), (6210) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6211) op(all_18_1, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | (6212) ~ (all_30_2 = e3) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | (6213) ~ (all_54_2 = e1) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1316), (6213) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | (6214) ~ (all_30_2 = e1) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | (6215) ~ (all_64_2 = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (6216) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6216) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6217) all_252_0 = e0 & op(e4, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6217) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6218) op(e4, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (504), (743), (962), (1442), (1443), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980), (6196), (6212), (6214), (6218), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | #252. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6219) all_252_2 = e0 & op(e3, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (12), (13), (14), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (280), (779), (781), (782), (4963), (5000), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6155), (6219), (function-axioms) are inconsistent % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #30. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (6220) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6220) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6221) all_252_6 = e0 & op(e2, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6221) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6222) op(e2, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, e0, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | e4, e2, simplifying with (227), (6222) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6223) all_64_2 = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6215), (6223) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6224) $false % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6224) is inconsistent. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6225) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6225) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6226) all_252_12 = e0 & op(e1, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6168), (6226) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6227) all_252_20 = e0 & op(e0, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6205), (6227) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #240. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | (6228) all_64_2 = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6156), (6228) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | (6229) ~ (e3 = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6190), (6228) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | (6230) ~ (e2 = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1610), (6228) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | (6231) op(e2, e0) = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (788) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (6232) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6232) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6233) all_252_0 = e0 & op(e4, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6233) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6234) op(e4, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (504), (743), (962), (1442), (1443), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980), (6196), (6212), (6214), (6234), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | #252. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6235) all_252_2 = e0 & op(e3, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (10), (11), (12), (13), (14), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (280), (779), (781), (782), (4963), (5000), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6155), (6235), (function-axioms) are inconsistent % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #30. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (6236) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6236) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_18_1, e4, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e2, simplifying with (6187), (6231) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6237) all_18_1 = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6211), (6237) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6238) op(e4, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (140), (504), (743), (962), (1442), (1443), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4980), (6196), (6212), (6214), (6238), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | #252. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6239) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6239) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6240) all_252_12 = e0 & op(e1, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6168), (6240) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6241) all_252_20 = e0 & op(e0, e4) = e0 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6205), (6241) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #240. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | (6242) all_54_2 = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1316), (6242) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | (6243) all_30_2 = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (731), (845), (1569), (1600), (1621), (4978), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | (6158), (6171), (6243), (function-axioms) are % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #280. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | (6244) all_30_2 = e3 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6197), (6244) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | (6245) op(e2, e3) = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e4, % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (146), (6245) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | (6246) all_10_2 = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6173), (6246) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | (6247) $false % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6247) is inconsistent. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | (6248) all_252_21 = e2 & op(e0, e3) = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4944), (6194), (6248), (function-axioms) are % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #289. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (6249) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (173), (480), (1597), (1613), (4950), % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | (4972), (6192), (6249), (function-axioms) are % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #287. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6250) all_252_20 = e3 & op(e0, e4) = e3 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | ALPHA: (6250) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6251) op(e0, e4) = e3 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (149), (5009), (6251), (function-axioms) are % 187.10/29.71 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512. % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | (6252) all_14_2 = e1 % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | COMBINE_EQS: (1356), (6252) imply: % 187.10/29.71 | | | | | | | | | | | | | | (6253) all_12_2 = e1 % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | SIMP: (6253) implies: % 187.10/29.71 | | | | | | | | | | | | | | (6254) all_12_2 = e1 % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | REDUCE: (1472), (6254) imply: % 187.10/29.71 | | | | | | | | | | | | | | (6255) ~ (all_244_24 = e1) % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | REDUCE: (1468), (6254) imply: % 187.10/29.71 | | | | | | | | | | | | | | (6256) ~ (all_28_2 = e1) % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | REDUCE: (4985), (6254) imply: % 187.10/29.71 | | | | | | | | | | | | | | (6257) ~ (all_8_1 = e1) % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | SIMP: (6257) implies: % 187.10/29.71 | | | | | | | | | | | | | | (6258) ~ (all_8_1 = e1) % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | REDUCE: (5009), (6254) imply: % 187.10/29.71 | | | | | | | | | | | | | | (6259) ~ (e3 = e1) % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | REDUCE: (1618), (6254) imply: % 187.10/29.71 | | | | | | | | | | | | | | (6260) op(e0, e1) = e4 % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.10/29.71 | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | (6261) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.10/29.71 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.10/29.71 | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | BETA: splitting (6261) gives: % 187.10/29.71 | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | (6262) all_252_20 = e1 & op(e0, e4) = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | ALPHA: (6262) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | (6263) all_252_20 = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | BETA: splitting (753) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | (6264) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 187.10/29.71 | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 187.10/29.71 | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | BETA: splitting (6264) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6265) all_252_20 = e4 & op(e0, e4) = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | ALPHA: (6265) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6266) all_252_20 = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6263), (6266) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6267) e4 = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | SIMP: (6267) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6268) e4 = e1 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | REDUCE: (12), (6268) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6269) $false % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | CLOSE: (6269) is inconsistent. % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6270) all_252_21 = e4 & op(e0, e3) = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | ALPHA: (6270) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | (6271) all_252_21 = e4 % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | (6272) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (6272) gives: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6273) all_252_20 = e2 & op(e0, e4) = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (6273) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6274) all_252_20 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6263), (6274) are inconsistent by sub-proof % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | #228. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6275) all_252_21 = e2 & op(e0, e3) = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (6275) implies: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6276) all_252_21 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6271), (6276) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6277) e4 = e2 % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (6277) imply: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | (6278) $false % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | CLOSE: (6278) is inconsistent. % 187.10/29.71 | | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.71 | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.71 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6279) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (173), (480), (1597), (1613), (4950), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (4972), (6260), (6279), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #29. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | (6280) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 187.10/29.72 | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 187.10/29.72 | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | BETA: splitting (6280) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | (6281) all_252_22 = e4 & op(e0, e2) = e4 % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | ALPHA: (6281) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | (6282) all_252_22 = e4 % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6283) all_252_24 = e0 & op(e0, e0) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | ALPHA: (6283) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6284) all_252_24 = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6285) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6285) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6286) all_252_20 = e3 & op(e0, e4) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6286) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6287) all_252_20 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6263), (6287) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | #312. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6288) all_252_21 = e3 & op(e0, e3) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6288) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6289) all_252_21 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (13), (173), (480), (751), (1597), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (1613), (4950), (4972), (6260), (6263), (6289), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | #28. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6290) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6290) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6291) all_252_22 = e3 & op(e0, e2) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6291) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6292) all_252_22 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6282), (6292) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6293) e4 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (14), (6293) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6294) $false % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6294) is inconsistent. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6295) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6295) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6296) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (6260), (6296), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6297) all_252_24 = e3 & op(e0, e0) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6297) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6298) all_252_24 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6284), (6298) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | #331. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6299) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.10/29.72 | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | ALPHA: (6299) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6300) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | = e0) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (6300) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6301) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (13), (173), (480), (751), (1597), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (1613), (4950), (4972), (6260), (6263), (6301), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | #26. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6302) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6302) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6303) all_252_22 = e0 & op(e0, e2) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6303) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6304) all_252_22 = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6282), (6304) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6305) e4 = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (6305) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6306) $false % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | CLOSE: (6306) is inconsistent. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6307) all_252_23 = e0 & op(e0, e1) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6307) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6308) op(e0, e1) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (6260), (6308), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | (6309) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 187.10/29.72 | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | BETA: splitting (6309) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6310) all_252_23 = e4 & op(e0, e1) = e4 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | ALPHA: (6310) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6311) all_252_23 = e4 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6312) ~ (all_22_2 = e2) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (4967), (6312) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6313) ~ (all_8_1 = e2) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6314) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6314) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6315) all_252_20 = e2 & op(e0, e4) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6315) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6316) all_252_20 = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6263), (6316) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6317) e2 = e1 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (6317) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6318) $false % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6318) is inconsistent. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6319) all_252_21 = e2 & op(e0, e3) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4944), (6313), (6319), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #289. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6320) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6320) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6321) all_252_22 = e2 & op(e0, e2) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6321) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6322) op(e0, e2) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1597), (1613), (4950), (6322), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | #288. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6323) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6323) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6324) all_252_23 = e2 & op(e0, e1) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6324) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6325) all_252_23 = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6311), (6325) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6326) e4 = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (6326) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6327) $false % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6327) is inconsistent. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6328) all_252_24 = e2 & op(e0, e0) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6328) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6329) op(e0, e0) = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (4972), (6329), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #477. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6330) all_22_2 = e2 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (492), (4967), (4986), (4987), (6330), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | #31. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6331) all_252_24 = e4 & op(e0, e0) = e4 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | ALPHA: (6331) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | (6332) all_252_24 = e4 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6333) all_252_24 = e0 & op(e0, e0) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (6332), (6333) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | #34. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6334) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (6334) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | (6335) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | = e0) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6335) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6336) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (13), (173), (480), (751), (1597), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (1613), (4950), (4972), (6260), (6263), (6336), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | #26. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | (6337) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6337) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6338) all_252_22 = e0 & op(e0, e2) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6338) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6339) all_252_22 = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (752) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6340) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6340) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6341) all_252_20 = e3 & op(e0, e4) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6341) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6342) all_252_20 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6263), (6342) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | #312. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6343) all_252_21 = e3 & op(e0, e3) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6343) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6344) all_252_21 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (13), (173), (480), (751), (1597), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (1613), (4950), (4972), (6260), (6263), (6344), % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | #28. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | (6345) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6345) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6346) all_252_22 = e3 & op(e0, e2) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6346) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6347) all_252_22 = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6339), (6347) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | #389. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | (6348) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6348) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | (6349) all_252_23 = e3 & op(e0, e1) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (6260), (6349), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | (6350) all_252_24 = e3 & op(e0, e0) = e3 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (6332), (6350) are inconsistent by sub-proof % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | #32. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6351) all_252_23 = e0 & op(e0, e1) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6351) implies: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6352) op(e0, e1) = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, e0, e1, % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (6260), (6352) gives: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6353) e4 = e0 % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (6353) imply: % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | (6354) $false % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6354) is inconsistent. % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | (6355) all_252_21 = e1 & op(e0, e3) = e1 % 187.10/29.72 | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | | REF_CLOSE: (4944), (6258), (6355), (function-axioms) are % 187.10/29.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #281. % 187.10/29.72 | | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | | End of split % 187.10/29.72 | | | | | | | | | | | | | | | % 187.10/29.72 | | | | | | | | | | | | | | Case 2: % 187.10/29.72 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | (6356) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.10/29.73 | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.10/29.73 | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | BETA: splitting (6356) gives: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | (6357) all_252_22 = e1 & op(e0, e2) = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | ALPHA: (6357) implies: % 187.10/29.73 | | | | | | | | | | | | | | | | (6358) op(e0, e2) = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, e1, % 187.10/29.73 | | | | | | | | | | | | | | | | e2, e0, simplifying with (173), (6358) gives: % 187.10/29.73 | | | | | | | | | | | | | | | | (6359) all_28_2 = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | REDUCE: (6256), (6359) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | (6360) $false % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | CLOSE: (6360) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | (6361) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.10/29.73 | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | BETA: splitting (6361) gives: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | (6362) all_252_23 = e1 & op(e0, e1) = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | ALPHA: (6362) implies: % 187.10/29.73 | | | | | | | | | | | | | | | | | (6363) op(e0, e1) = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (161), (6260), (6363), (function-axioms) are % 187.10/29.73 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #401. % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | (6364) all_252_24 = e1 & op(e0, e0) = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | ALPHA: (6364) implies: % 187.10/29.73 | | | | | | | | | | | | | | | | | (6365) op(e0, e0) = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (6255), (6365), (function-axioms) are % 187.10/29.73 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #474. % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | (6366) all_12_2 = e3 % 187.10/29.73 | | | | | | | | | | | | | (6367) op(e3, e0) = all_12_1 & $i(all_12_1) & ( ~ % 187.10/29.73 | | | | | | | | | | | | | (all_12_1 = e2) | ( ~ (all_12_0 = e1) & op(e0, % 187.10/29.73 | | | | | | | | | | | | | e2) = all_12_0 & $i(all_12_0))) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | ALPHA: (6367) implies: % 187.10/29.73 | | | | | | | | | | | | | (6368) op(e3, e0) = all_12_1 % 187.10/29.73 | | | | | | | | | | | | | (6369) ~ (all_12_1 = e2) | ( ~ (all_12_0 = e1) & op(e0, % 187.10/29.73 | | | | | | | | | | | | | e2) = all_12_0 & $i(all_12_0)) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | COMBINE_EQS: (1374), (6366) imply: % 187.10/29.73 | | | | | | | | | | | | | (6370) all_212_2 = e3 % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | REDUCE: (1468), (6366) imply: % 187.10/29.73 | | | | | | | | | | | | | (6371) ~ (all_28_2 = e3) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | REDUCE: (1618), (6366) imply: % 187.10/29.73 | | | | | | | | | | | | | (6372) op(e0, e3) = e4 % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | BETA: splitting (437) gives: % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | (6373) ~ (all_212_2 = e3) % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | REDUCE: (6370), (6373) imply: % 187.10/29.73 | | | | | | | | | | | | | | (6374) $false % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | CLOSE: (6374) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | (6375) op(e3, e0) = all_212_1 & $i(all_212_1) & ( ~ % 187.10/29.73 | | | | | | | | | | | | | | (all_212_1 = e1) | ( ~ (all_212_0 = e2) & op(e0, % 187.10/29.73 | | | | | | | | | | | | | | e1) = all_212_0 & $i(all_212_0))) % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | ALPHA: (6375) implies: % 187.10/29.73 | | | | | | | | | | | | | | (6376) op(e3, e0) = all_212_1 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_1, e4, % 187.10/29.73 | | | | | | | | | | | | | | e3, e0, simplifying with (4944), (6372) gives: % 187.10/29.73 | | | | | | | | | | | | | | (6377) all_8_1 = e4 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 187.10/29.73 | | | | | | | | | | | | | | all_212_1, e0, e3, simplifying with (4954), (6376) % 187.10/29.73 | | | | | | | | | | | | | | gives: % 187.10/29.73 | | | | | | | | | | | | | | (6378) all_212_1 = e2 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_1, % 187.10/29.73 | | | | | | | | | | | | | | all_212_1, e0, e3, simplifying with (6368), (6376) % 187.10/29.73 | | | | | | | | | | | | | | gives: % 187.10/29.73 | | | | | | | | | | | | | | (6379) all_212_1 = all_12_1 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | COMBINE_EQS: (6378), (6379) imply: % 187.10/29.73 | | | | | | | | | | | | | | (6380) all_12_1 = e2 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | REDUCE: (4981), (6377) imply: % 187.10/29.73 | | | | | | | | | | | | | | (6381) ~ (all_28_2 = e4) % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | BETA: splitting (6369) gives: % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | (6382) ~ (all_12_1 = e2) % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | REDUCE: (6380), (6382) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6383) $false % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | CLOSE: (6383) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | (6384) ~ (all_12_0 = e1) & op(e0, e2) = all_12_0 & % 187.10/29.73 | | | | | | | | | | | | | | | $i(all_12_0) % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | ALPHA: (6384) implies: % 187.10/29.73 | | | | | | | | | | | | | | | (6385) ~ (all_12_0 = e1) % 187.10/29.73 | | | | | | | | | | | | | | | (6386) op(e0, e2) = all_12_0 % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, % 187.10/29.73 | | | | | | | | | | | | | | | all_12_0, e2, e0, simplifying with (173), (6386) % 187.10/29.73 | | | | | | | | | | | | | | | gives: % 187.10/29.73 | | | | | | | | | | | | | | | (6387) all_28_2 = all_12_0 % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | COMBINE_EQS: (1425), (6387) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6388) all_250_22 = all_12_0 % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | REDUCE: (6381), (6387) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6389) ~ (all_12_0 = e4) % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | REDUCE: (6371), (6387) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6390) ~ (all_12_0 = e3) % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | REDUCE: (4950), (6387) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6391) ~ (all_12_0 = e0) % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | BETA: splitting (728) gives: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | (6392) all_250_22 = e4 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (6388), (6392) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | (6393) all_12_0 = e4 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | REDUCE: (6389), (6393) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | (6394) $false % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | CLOSE: (6394) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | (6395) all_250_22 = e3 | all_250_22 = e2 | all_250_22 = % 187.10/29.73 | | | | | | | | | | | | | | | | e1 | all_250_22 = e0 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | BETA: splitting (6395) gives: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | (6396) all_250_22 = e3 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (6388), (6396) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | (6397) all_12_0 = e3 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | REDUCE: (6390), (6397) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | (6398) $false % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | CLOSE: (6398) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | (6399) all_250_22 = e2 | all_250_22 = e1 | all_250_22 = % 187.10/29.73 | | | | | | | | | | | | | | | | | e0 % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | BETA: splitting (6399) gives: % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | (6400) all_250_22 = e2 % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6388), (6400) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | | (6401) all_12_0 = e2 % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | REDUCE: (6386), (6401) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | | (6402) op(e0, e2) = e2 % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | REF_CLOSE: (173), (1597), (1613), (4950), (6402), % 187.10/29.73 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.73 | | | | | | | | | | | | | | | | | | #288. % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | (6403) all_250_22 = e1 | all_250_22 = e0 % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | BETA: splitting (6403) gives: % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | (6404) all_250_22 = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6388), (6404) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | | | (6405) all_12_0 = e1 % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | REDUCE: (6385), (6405) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | | | (6406) $false % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | CLOSE: (6406) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | (6407) all_250_22 = e0 % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6388), (6407) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | | | (6408) all_12_0 = e0 % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | REDUCE: (6391), (6408) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | | | | (6409) $false % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | | CLOSE: (6409) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | (6410) all_10_2 = e1 % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | COMBINE_EQS: (5007), (6410) imply: % 187.10/29.73 | | | | | | | | | | | | (6411) all_48_1 = e1 % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | REDUCE: (1611), (6410) imply: % 187.10/29.73 | | | | | | | | | | | | (6412) op(e2, e1) = e3 % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | REDUCE: (4953), (6410) imply: % 187.10/29.73 | | | | | | | | | | | | (6413) op(e0, e1) = e2 % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | BETA: splitting (4993) gives: % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | (6414) ~ (all_48_1 = e1) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | REDUCE: (6411), (6414) imply: % 187.10/29.73 | | | | | | | | | | | | | (6415) $false % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | CLOSE: (6415) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | (6416) ~ (all_48_0 = e4) & op(e3, e1) = all_48_0 & % 187.10/29.73 | | | | | | | | | | | | | $i(all_48_0) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | ALPHA: (6416) implies: % 187.10/29.73 | | | | | | | | | | | | | (6417) ~ (all_48_0 = e4) % 187.10/29.73 | | | | | | | | | | | | | (6418) op(e3, e1) = all_48_0 % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, e2, % 187.10/29.73 | | | | | | | | | | | | | e1, e0, simplifying with (161), (6413) gives: % 187.10/29.73 | | | | | | | | | | | | | (6419) all_20_2 = e2 % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, e3, % 187.10/29.73 | | | | | | | | | | | | | e1, e2, simplifying with (188), (6412) gives: % 187.10/29.73 | | | | | | | | | | | | | (6420) all_38_2 = e3 % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, % 187.10/29.73 | | | | | | | | | | | | | all_48_0, e1, e3, simplifying with (185), (6418) % 187.10/29.73 | | | | | | | | | | | | | gives: % 187.10/29.73 | | | | | | | | | | | | | (6421) all_48_0 = all_36_2 % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | REDUCE: (6417), (6421) imply: % 187.10/29.73 | | | | | | | | | | | | | (6422) ~ (all_36_2 = e4) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | REDUCE: (1549), (6420) imply: % 187.10/29.73 | | | | | | | | | | | | | (6423) ~ (all_36_2 = e3) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | SIMP: (6423) implies: % 187.10/29.73 | | | | | | | | | | | | | (6424) ~ (all_36_2 = e3) % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | BETA: splitting (739) gives: % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | (6425) all_250_8 = e4 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | COMBINE_EQS: (932), (6425) imply: % 187.10/29.73 | | | | | | | | | | | | | | (6426) all_36_2 = e4 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | REDUCE: (6422), (6426) imply: % 187.10/29.73 | | | | | | | | | | | | | | (6427) $false % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | CLOSE: (6427) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | (6428) all_250_8 = e3 | all_250_8 = e2 | all_250_8 = e1 | % 187.10/29.73 | | | | | | | | | | | | | | all_250_8 = e0 % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | BETA: splitting (6428) gives: % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | (6429) all_250_8 = e3 % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | COMBINE_EQS: (932), (6429) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6430) all_36_2 = e3 % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | REDUCE: (6424), (6430) imply: % 187.10/29.73 | | | | | | | | | | | | | | | (6431) $false % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | CLOSE: (6431) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | (6432) ~ (all_250_8 = e3) % 187.10/29.73 | | | | | | | | | | | | | | | (6433) all_250_8 = e2 | all_250_8 = e1 | all_250_8 = e0 % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | BETA: splitting (6433) gives: % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | Case 1: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | (6434) all_250_8 = e2 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (6434) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | (6435) all_36_2 = e2 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | REDUCE: (4976), (6435) imply: % 187.10/29.73 | | | | | | | | | | | | | | | | (6436) $false % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | CLOSE: (6436) is inconsistent. % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | (6437) all_250_8 = e1 | all_250_8 = e0 % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | | REF_CLOSE: (932), (1590), (1615), (4949), (6424), (6437), % 187.10/29.73 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.10/29.73 | | | | | | | | | | | | | | | | #292. % 187.10/29.73 | | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | | % 187.10/29.73 | | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | | % 187.10/29.73 | | | | | | | | | End of split % 187.10/29.73 | | | | | | | | | % 187.10/29.73 | | | | | | | | Case 2: % 187.10/29.73 | | | | | | | | | % 187.10/29.73 | | | | | | | | | (6438) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = % 187.10/29.73 | | | | | | | | | e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, % 187.10/29.73 | | | | | | | | | e0) = e2) % 187.10/29.73 | | | | | | | | | % 187.10/29.73 | | | | | | | | | REF_CLOSE: (182), (191), (480), (4972), (4974), (4978), % 187.10/29.73 | | | | | | | | | (6438), (function-axioms) are inconsistent by % 187.10/29.73 | | | | | | | | | sub-proof #25. % 187.10/29.73 | | | | | | | | | % 187.10/29.73 | | | | | | | | End of split % 187.10/29.73 | | | | | | | | % 187.10/29.73 | | | | | | | End of split % 187.10/29.73 | | | | | | | % 187.10/29.73 | | | | | | End of split % 187.10/29.73 | | | | | | % 187.10/29.73 | | | | | Case 2: % 187.10/29.73 | | | | | | % 187.10/29.73 | | | | | | (6439) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & % 187.10/29.73 | | | | | | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 187.10/29.73 | | | | | | % 187.10/29.73 | | | | | | REF_CLOSE: (137), (173), (492), (1622), (4946), (4950), (6439), % 187.10/29.73 | | | | | | (function-axioms) are inconsistent by sub-proof #23. % 187.10/29.73 | | | | | | % 187.10/29.73 | | | | | End of split % 187.10/29.73 | | | | | % 187.10/29.73 | | | | End of split % 187.10/29.73 | | | | % 187.10/29.73 | | | End of split % 187.10/29.73 | | | % 187.10/29.73 | | Case 2: % 187.10/29.73 | | | % 187.10/29.73 | | | (6440) all_6_2 = e0 % 187.10/29.73 | | | (6441) op(e0, e4) = all_6_1 & $i(all_6_1) & ( ~ (all_6_1 = e1) | ( ~ % 187.10/29.73 | | | (all_6_0 = e3) & op(e4, e1) = all_6_0 & $i(all_6_0))) % 187.10/29.73 | | | % 187.10/29.73 | | | ALPHA: (6441) implies: % 187.10/29.73 | | | (6442) op(e0, e4) = all_6_1 % 187.10/29.73 | | | (6443) ~ (all_6_1 = e1) | ( ~ (all_6_0 = e3) & op(e4, e1) = all_6_0 & % 187.10/29.73 | | | $i(all_6_0)) % 187.10/29.73 | | | % 187.10/29.73 | | | COMBINE_EQS: (1370), (6440) imply: % 187.10/29.73 | | | (6444) all_196_2 = e0 % 187.10/29.73 | | | % 187.10/29.73 | | | REDUCE: (1442), (6440) imply: % 187.10/29.73 | | | (6445) ~ (all_244_0 = e0) % 187.10/29.73 | | | % 187.10/29.73 | | | REDUCE: (1510), (6440) imply: % 187.10/29.73 | | | (6446) ~ (all_244_8 = e0) % 187.10/29.73 | | | % 187.10/29.73 | | | REDUCE: (1517), (6440) imply: % 187.10/29.73 | | | (6447) ~ (all_30_2 = e0) % 187.10/29.73 | | | % 187.10/29.73 | | | REDUCE: (1513), (6440) imply: % 187.10/29.73 | | | (6448) ~ (all_28_2 = e0) % 187.10/29.73 | | | % 187.10/29.73 | | | REDUCE: (1515), (6440) imply: % 187.10/29.73 | | | (6449) ~ (all_26_2 = e0) % 187.10/29.73 | | | % 187.10/29.73 | | | REDUCE: (1508), (6440) imply: % 187.10/29.74 | | | (6450) ~ (all_8_2 = e0) % 187.10/29.74 | | | % 187.10/29.74 | | | REDUCE: (1511), (6440) imply: % 187.10/29.74 | | | (6451) ~ (all_4_2 = e0) % 187.10/29.74 | | | % 187.10/29.74 | | | REDUCE: (1584), (6440) imply: % 187.10/29.74 | | | (6452) op(e0, all_64_2) = e2 % 187.10/29.74 | | | % 187.10/29.74 | | | REDUCE: (1602), (6440) imply: % 187.10/29.74 | | | (6453) op(e4, e0) = e2 % 187.10/29.74 | | | % 187.10/29.74 | | | BETA: splitting (415) gives: % 187.10/29.74 | | | % 187.10/29.74 | | | Case 1: % 187.10/29.74 | | | | % 187.10/29.74 | | | | (6454) ~ (all_196_2 = e0) % 187.10/29.74 | | | | % 187.10/29.74 | | | | REDUCE: (6444), (6454) imply: % 187.10/29.74 | | | | (6455) $false % 187.10/29.74 | | | | % 187.10/29.74 | | | | CLOSE: (6455) is inconsistent. % 187.10/29.74 | | | | % 187.10/29.74 | | | Case 2: % 187.10/29.74 | | | | % 187.10/29.74 | | | | (6456) op(e0, e4) = all_196_1 & $i(all_196_1) & ( ~ (all_196_1 = e3) % 187.10/29.74 | | | | | ( ~ (all_196_0 = e1) & op(e4, e3) = all_196_0 & % 187.10/29.74 | | | | $i(all_196_0))) % 187.10/29.74 | | | | % 187.10/29.74 | | | | ALPHA: (6456) implies: % 187.10/29.74 | | | | (6457) op(e0, e4) = all_196_1 % 187.10/29.74 | | | | (6458) ~ (all_196_1 = e3) | ( ~ (all_196_0 = e1) & op(e4, e3) = % 187.10/29.74 | | | | all_196_0 & $i(all_196_0)) % 187.10/29.74 | | | | % 187.10/29.74 | | | | BETA: splitting (773) gives: % 187.10/29.74 | | | | % 187.10/29.74 | | | | Case 1: % 187.10/29.74 | | | | | % 187.10/29.74 | | | | | (6459) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & % 187.10/29.74 | | | | | op(e3, e2) = e0) % 187.10/29.74 | | | | | % 187.10/29.74 | | | | | BETA: splitting (6459) gives: % 187.10/29.74 | | | | | % 187.10/29.74 | | | | | Case 1: % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | (6460) all_252_4 = e0 & op(e4, e2) = e0 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | ALPHA: (6460) implies: % 187.10/29.74 | | | | | | (6461) all_252_4 = e0 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, % 187.10/29.74 | | | | | | all_196_1, e4, e0, simplifying with (149), (6457) % 187.10/29.74 | | | | | | gives: % 187.10/29.74 | | | | | | (6462) all_196_1 = all_12_2 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_1, % 187.10/29.74 | | | | | | all_196_1, e4, e0, simplifying with (6442), (6457) % 187.10/29.74 | | | | | | gives: % 187.10/29.74 | | | | | | (6463) all_196_1 = all_6_1 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e2, e0, % 187.10/29.74 | | | | | | e4, simplifying with (176), (6453) gives: % 187.10/29.74 | | | | | | (6464) all_30_2 = e2 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | COMBINE_EQS: (6462), (6463) imply: % 187.10/29.74 | | | | | | (6465) all_12_2 = all_6_1 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | SIMP: (6465) implies: % 187.10/29.74 | | | | | | (6466) all_12_2 = all_6_1 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | COMBINE_EQS: (1356), (6466) imply: % 187.10/29.74 | | | | | | (6467) all_14_2 = all_6_1 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | COMBINE_EQS: (1231), (6466) imply: % 187.10/29.74 | | | | | | (6468) all_18_2 = all_6_1 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | COMBINE_EQS: (1311), (6464) imply: % 187.10/29.74 | | | | | | (6469) all_128_2 = e2 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | COMBINE_EQS: (1097), (6464) imply: % 187.10/29.74 | | | | | | (6470) all_238_2 = e2 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | COMBINE_EQS: (1427), (6466) imply: % 187.10/29.74 | | | | | | (6471) all_250_20 = all_6_1 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1443), (6464) imply: % 187.10/29.74 | | | | | | (6472) ~ (all_244_0 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1571), (6464) imply: % 187.10/29.74 | | | | | | (6473) ~ (all_244_24 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1446), (6466) imply: % 187.10/29.74 | | | | | | (6474) ~ (all_100_2 = all_6_1) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1480), (6464) imply: % 187.10/29.74 | | | | | | (6475) ~ (all_84_2 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1565), (6464) imply: % 187.10/29.74 | | | | | | (6476) ~ (all_48_2 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1567), (6464) imply: % 187.10/29.74 | | | | | | (6477) ~ (all_40_2 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1569), (6464) imply: % 187.10/29.74 | | | | | | (6478) ~ (all_34_2 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1547), (6464) imply: % 187.10/29.74 | | | | | | (6479) ~ (all_26_2 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | SIMP: (6479) implies: % 187.10/29.74 | | | | | | (6480) ~ (all_26_2 = e2) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1468), (6466) imply: % 187.10/29.74 | | | | | | (6481) ~ (all_28_2 = all_6_1) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1466), (6466) imply: % 187.10/29.74 | | | | | | (6482) ~ (all_22_2 = all_6_1) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1470), (6466) imply: % 187.10/29.74 | | | | | | (6483) ~ (all_20_2 = all_6_1) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1457), (6466) imply: % 187.10/29.74 | | | | | | (6484) ~ (all_16_2 = all_6_1) % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1594), (6464), (6466) imply: % 187.10/29.74 | | | | | | (6485) op(e2, all_6_1) = e0 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1604), (6464) imply: % 187.10/29.74 | | | | | | (6486) op(e4, e2) = e0 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | REDUCE: (1618), (6466) imply: % 187.10/29.74 | | | | | | (6487) op(e0, all_6_1) = e4 % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | BETA: splitting (320) gives: % 187.10/29.74 | | | | | | % 187.10/29.74 | | | | | | Case 1: % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | (6488) ~ (all_128_2 = e2) % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | REDUCE: (6469), (6488) imply: % 187.10/29.74 | | | | | | | (6489) $false % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | CLOSE: (6489) is inconsistent. % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | Case 2: % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | (6490) op(e2, e4) = all_128_1 & $i(all_128_1) & ( ~ (all_128_1 % 187.10/29.74 | | | | | | | = e3) | ( ~ (all_128_0 = e1) & op(e4, e3) = % 187.10/29.74 | | | | | | | all_128_0 & $i(all_128_0))) % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | ALPHA: (6490) implies: % 187.10/29.74 | | | | | | | (6491) op(e2, e4) = all_128_1 % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | BETA: splitting (472) gives: % 187.10/29.74 | | | | | | | % 187.10/29.74 | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | (6492) ~ (all_238_2 = e2) % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | REDUCE: (6470), (6492) imply: % 187.10/29.74 | | | | | | | | (6493) $false % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | CLOSE: (6493) is inconsistent. % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | Case 2: % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | (6494) op(e2, e4) = all_238_1 & $i(all_238_1) & ( ~ % 187.10/29.74 | | | | | | | | (all_238_1 = e1) | ( ~ (all_238_0 = e3) & op(e4, e1) % 187.10/29.74 | | | | | | | | = all_238_0 & $i(all_238_0))) % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | ALPHA: (6494) implies: % 187.10/29.74 | | | | | | | | (6495) op(e2, e4) = all_238_1 % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | BETA: splitting (755) gives: % 187.10/29.74 | | | | | | | | % 187.10/29.74 | | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | | % 187.10/29.74 | | | | | | | | | (6496) (all_252_16 = e2 & op(e4, e0) = e2) | (all_252_17 = % 187.10/29.74 | | | | | | | | | e2 & op(e3, e0) = e2) % 187.10/29.74 | | | | | | | | | % 187.10/29.74 | | | | | | | | | BETA: splitting (6496) gives: % 187.10/29.74 | | | | | | | | | % 187.10/29.74 | | | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | (6497) all_252_16 = e2 & op(e4, e0) = e2 % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | ALPHA: (6497) implies: % 187.10/29.74 | | | | | | | | | | (6498) all_252_16 = e2 % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_64_2, % 187.10/29.74 | | | | | | | | | | all_238_1, e4, e2, simplifying with (227), (6495) % 187.10/29.74 | | | | | | | | | | gives: % 187.10/29.74 | | | | | | | | | | (6499) all_238_1 = all_64_2 % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_128_1, % 187.10/29.74 | | | | | | | | | | all_238_1, e4, e2, simplifying with (6491), (6495) % 187.10/29.74 | | | | | | | | | | gives: % 187.10/29.74 | | | | | | | | | | (6500) all_238_1 = all_128_1 % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | COMBINE_EQS: (6499), (6500) imply: % 187.10/29.74 | | | | | | | | | | (6501) all_128_1 = all_64_2 % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | BETA: splitting (147) gives: % 187.10/29.74 | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | (6502) ~ (all_10_2 = e1) % 187.10/29.74 | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | BETA: splitting (150) gives: % 187.10/29.74 | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | (6503) ~ (all_12_2 = e3) % 187.10/29.74 | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | REDUCE: (6466), (6503) imply: % 187.10/29.74 | | | | | | | | | | | | (6504) ~ (all_6_1 = e3) % 187.10/29.74 | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | BETA: splitting (153) gives: % 187.10/29.74 | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | (6505) ~ (all_14_2 = e1) % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | REDUCE: (6467), (6505) imply: % 187.10/29.74 | | | | | | | | | | | | | (6506) ~ (all_6_1 = e1) % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (14), % 187.10/29.74 | | | | | | | | | | | | | (137), (143), (146), (149), (155), (156), (159), % 187.10/29.74 | | | | | | | | | | | | | (161), (162), (164), (165), (168), (170), (173), % 187.10/29.74 | | | | | | | | | | | | | (174), (180), (182), (183), (185), (186), (188), % 187.10/29.74 | | | | | | | | | | | | | (189), (191), (192), (201), (203), (210), (216), % 187.10/29.74 | | | | | | | | | | | | | (219), (222), (224), (225), (227), (231), (234), % 187.10/29.74 | | | | | | | | | | | | | (237), (246), (249), (255), (257), (266), (280), % 187.10/29.74 | | | | | | | | | | | | | (284), (301), (323), (340), (343), (350), (353), % 187.10/29.74 | | | | | | | | | | | | | (362), (368), (376), (393), (396), (404), (410), % 187.10/29.74 | | | | | | | | | | | | | (418), (421), (463), (480), (486), (492), (498), % 187.10/29.74 | | | | | | | | | | | | | (504), (514), (521), (727), (729), (730), (731), % 187.10/29.74 | | | | | | | | | | | | | (732), (733), (736), (738), (740), (749), (750), % 187.10/29.74 | | | | | | | | | | | | | (751), (753), (754), (758), (759), (760), (761), % 187.10/29.74 | | | | | | | | | | | | | (763), (764), (765), (766), (767), (769), (774), % 187.10/29.74 | | | | | | | | | | | | | (775), (776), (777), (778), (780), (784), (785), % 187.10/29.74 | | | | | | | | | | | | | (788), (792), (802), (845), (857), (860), (867), % 187.10/29.74 | | | | | | | | | | | | | (1032), (1148), (1186), (1212), (1253), (1255), % 187.10/29.74 | | | | | | | | | | | | | (1261), (1263), (1265), (1292), (1294), (1302), % 187.10/29.74 | | | | | | | | | | | | | (1314), (1317), (1328), (1332), (1335), (1336), % 187.10/29.74 | | | | | | | | | | | | | (1343), (1345), (1347), (1349), (1350), (1352), % 187.10/29.74 | | | | | | | | | | | | | (1353), (1362), (1371), (1379), (1424), (1426), % 187.10/29.74 | | | | | | | | | | | | | (1428), (1431), (1433), (1434), (1439), (1444), % 187.10/29.74 | | | | | | | | | | | | | (1445), (1450), (1452), (1459), (1460), (1462), % 187.10/29.74 | | | | | | | | | | | | | (1464), (1476), (1477), (1482), (1483), (1484), % 187.10/29.74 | | | | | | | | | | | | | (1485), (1488), (1490), (1497), (1501), (1503), % 187.10/29.74 | | | | | | | | | | | | | (1504), (1506), (1519), (1520), (1522), (1524), % 187.10/29.74 | | | | | | | | | | | | | (1526), (1528), (1531), (1533), (1535), (1536), % 187.10/29.74 | | | | | | | | | | | | | (1538), (1540), (1551), (1552), (1554), (1556), % 187.10/29.74 | | | | | | | | | | | | | (1557), (1560), (1561), (1572), (1573), (1580), % 187.10/29.74 | | | | | | | | | | | | | (1585), (1586), (1587), (1591), (1595), (1596), % 187.10/29.74 | | | | | | | | | | | | | (1597), (1598), (1599), (1600), (1603), (1607), % 187.10/29.74 | | | | | | | | | | | | | (1608), (1609), (1611), (1612), (1613), (1614), % 187.10/29.74 | | | | | | | | | | | | | (1615), (1616), (1617), (1619), (1620), (1621), % 187.10/29.74 | | | | | | | | | | | | | (1622), (6442), (6445), (6446), (6448), (6449), % 187.10/29.74 | | | | | | | | | | | | | (6450), (6452), (6461), (6468), (6471), (6472), % 187.10/29.74 | | | | | | | | | | | | | (6473), (6474), (6476), (6478), (6480), (6481), % 187.10/29.74 | | | | | | | | | | | | | (6482), (6483), (6484), (6485), (6486), (6498), % 187.10/29.74 | | | | | | | | | | | | | (6502), (6503), (6506), (function-axioms) are % 187.10/29.74 | | | | | | | | | | | | | inconsistent by sub-proof #4. % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | Case 2: % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | (6507) all_14_2 = e1 % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | COMBINE_EQS: (6467), (6507) imply: % 187.10/29.74 | | | | | | | | | | | | | (6508) all_6_1 = e1 % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | SIMP: (6508) implies: % 187.10/29.74 | | | | | | | | | | | | | (6509) all_6_1 = e1 % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | REDUCE: (6504), (6509) imply: % 187.10/29.74 | | | | | | | | | | | | | (6510) ~ (e3 = e1) % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | REDUCE: (6487), (6509) imply: % 187.10/29.74 | | | | | | | | | | | | | (6511) op(e0, e1) = e4 % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | BETA: splitting (6443) gives: % 187.10/29.74 | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | Case 1: % 187.10/29.74 | | | | | | | | | | | | | | % 187.10/29.74 | | | | | | | | | | | | | | (6512) ~ (all_6_1 = e1) % 187.10/29.74 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (11), (12), (14), % 187.10/29.75 | | | | | | | | | | | | | | (137), (143), (146), (149), (155), (156), (159), % 187.10/29.75 | | | | | | | | | | | | | | (161), (162), (164), (165), (168), (170), (173), % 187.10/29.75 | | | | | | | | | | | | | | (174), (180), (182), (183), (185), (186), (188), % 187.10/29.75 | | | | | | | | | | | | | | (189), (191), (192), (201), (203), (210), (216), % 187.10/29.75 | | | | | | | | | | | | | | (219), (222), (224), (225), (227), (231), (234), % 187.10/29.75 | | | | | | | | | | | | | | (237), (246), (249), (255), (257), (266), (280), % 187.10/29.75 | | | | | | | | | | | | | | (284), (301), (323), (340), (343), (350), (353), % 187.10/29.75 | | | | | | | | | | | | | | (362), (368), (376), (393), (396), (404), (410), % 187.10/29.75 | | | | | | | | | | | | | | (418), (421), (463), (480), (486), (492), (498), % 187.10/29.75 | | | | | | | | | | | | | | (504), (514), (521), (727), (729), (730), (731), % 187.10/29.75 | | | | | | | | | | | | | | (732), (733), (736), (738), (740), (749), (750), % 187.10/29.75 | | | | | | | | | | | | | | (751), (753), (754), (758), (759), (760), (761), % 187.10/29.75 | | | | | | | | | | | | | | (763), (764), (765), (766), (767), (769), (774), % 187.10/29.75 | | | | | | | | | | | | | | (775), (776), (777), (778), (780), (784), (785), % 187.10/29.75 | | | | | | | | | | | | | | (788), (792), (802), (845), (857), (860), (867), % 187.10/29.75 | | | | | | | | | | | | | | (1032), (1148), (1186), (1212), (1253), (1255), % 187.10/29.75 | | | | | | | | | | | | | | (1261), (1263), (1265), (1292), (1294), (1302), % 187.10/29.75 | | | | | | | | | | | | | | (1314), (1317), (1328), (1332), (1335), (1336), % 187.10/29.75 | | | | | | | | | | | | | | (1343), (1345), (1347), (1349), (1350), (1352), % 187.10/29.75 | | | | | | | | | | | | | | (1353), (1362), (1371), (1379), (1424), (1426), % 187.10/29.75 | | | | | | | | | | | | | | (1428), (1431), (1433), (1434), (1439), (1444), % 187.10/29.75 | | | | | | | | | | | | | | (1445), (1450), (1452), (1459), (1460), (1462), % 187.10/29.75 | | | | | | | | | | | | | | (1464), (1476), (1477), (1482), (1483), (1484), % 187.10/29.75 | | | | | | | | | | | | | | (1485), (1488), (1490), (1497), (1501), (1503), % 187.10/29.75 | | | | | | | | | | | | | | (1504), (1506), (1519), (1520), (1522), (1524), % 187.10/29.75 | | | | | | | | | | | | | | (1526), (1528), (1531), (1533), (1535), (1536), % 187.10/29.75 | | | | | | | | | | | | | | (1538), (1540), (1551), (1552), (1554), (1556), % 187.10/29.75 | | | | | | | | | | | | | | (1557), (1560), (1561), (1572), (1573), (1580), % 187.10/29.75 | | | | | | | | | | | | | | (1585), (1586), (1587), (1591), (1595), (1596), % 187.10/29.75 | | | | | | | | | | | | | | (1597), (1598), (1599), (1600), (1603), (1607), % 187.10/29.75 | | | | | | | | | | | | | | (1608), (1609), (1611), (1612), (1613), (1614), % 187.10/29.75 | | | | | | | | | | | | | | (1615), (1616), (1617), (1619), (1620), (1621), % 187.10/29.75 | | | | | | | | | | | | | | (1622), (6442), (6445), (6446), (6448), (6449), % 187.10/29.75 | | | | | | | | | | | | | | (6450), (6452), (6461), (6468), (6471), (6472), % 187.10/29.75 | | | | | | | | | | | | | | (6473), (6474), (6476), (6478), (6480), (6481), % 187.10/29.75 | | | | | | | | | | | | | | (6482), (6483), (6484), (6485), (6486), (6498), % 187.10/29.75 | | | | | | | | | | | | | | (6502), (6503), (6512), (function-axioms) are % 187.10/29.75 | | | | | | | | | | | | | | inconsistent by sub-proof #4. % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | Case 2: % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | (6513) ~ (all_6_0 = e3) & op(e4, e1) = all_6_0 & % 187.10/29.75 | | | | | | | | | | | | | | $i(all_6_0) % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | ALPHA: (6513) implies: % 187.10/29.75 | | | | | | | | | | | | | | (6514) ~ (all_6_0 = e3) % 187.10/29.75 | | | | | | | | | | | | | | (6515) op(e4, e1) = all_6_0 % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, e4, % 187.10/29.75 | | | | | | | | | | | | | | e1, e0, simplifying with (161), (6511) gives: % 187.10/29.75 | | | | | | | | | | | | | | (6516) all_20_2 = e4 % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_2, % 187.10/29.75 | | | | | | | | | | | | | | all_6_0, e1, e4, simplifying with (170), (6515) % 187.10/29.75 | | | | | | | | | | | | | | gives: % 187.10/29.75 | | | | | | | | | | | | | | (6517) all_26_2 = all_6_0 % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | COMBINE_EQS: (1435), (6517) imply: % 187.10/29.75 | | | | | | | | | | | | | | (6518) all_250_3 = all_6_0 % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | REDUCE: (1545), (6516), (6517) imply: % 187.10/29.75 | | | | | | | | | | | | | | (6519) ~ (all_6_0 = e4) % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | REDUCE: (6480), (6517) imply: % 187.10/29.75 | | | | | | | | | | | | | | (6520) ~ (all_6_0 = e2) % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | REDUCE: (6449), (6517) imply: % 187.10/29.75 | | | | | | | | | | | | | | (6521) ~ (all_6_0 = e0) % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | REDUCE: (1588), (6517) imply: % 187.10/29.75 | | | | | | | | | | | | | | (6522) op(all_6_0, all_16_2) = e1 % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | BETA: splitting (744) gives: % 187.10/29.75 | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | Case 1: % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | (6523) all_250_3 = e4 % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | COMBINE_EQS: (6518), (6523) imply: % 187.10/29.75 | | | | | | | | | | | | | | | (6524) all_6_0 = e4 % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | REDUCE: (6519), (6524) imply: % 187.10/29.75 | | | | | | | | | | | | | | | (6525) $false % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | CLOSE: (6525) is inconsistent. % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | Case 2: % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | (6526) ~ (all_250_3 = e4) % 187.10/29.75 | | | | | | | | | | | | | | | (6527) all_250_3 = e3 | all_250_3 = e2 | all_250_3 = e1 | % 187.10/29.75 | | | | | | | | | | | | | | | all_250_3 = e0 % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | BETA: splitting (6527) gives: % 187.10/29.75 | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | Case 1: % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | (6528) all_250_3 = e3 % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | COMBINE_EQS: (6518), (6528) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | (6529) all_6_0 = e3 % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | REDUCE: (6514), (6529) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | (6530) $false % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | CLOSE: (6530) is inconsistent. % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | Case 2: % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | (6531) all_250_3 = e2 | all_250_3 = e1 | all_250_3 = e0 % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | BETA: splitting (6531) gives: % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | Case 1: % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | (6532) all_250_3 = e2 % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | COMBINE_EQS: (6518), (6532) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | (6533) all_6_0 = e2 % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | REDUCE: (6520), (6533) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | (6534) $false % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | CLOSE: (6534) is inconsistent. % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | Case 2: % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | (6535) all_250_3 = e1 | all_250_3 = e0 % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | BETA: splitting (6535) gives: % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | Case 1: % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6536) all_250_3 = e1 % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6518), (6536) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6537) all_6_0 = e1 % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | REDUCE: (6519), (6537) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6538) ~ (e4 = e1) % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | REDUCE: (6522), (6537) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6539) op(e1, all_16_2) = e1 % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, e1, % 187.10/29.75 | | | | | | | | | | | | | | | | | | all_16_2, e1, simplifying with (1614), (6539) % 187.10/29.75 | | | | | | | | | | | | | | | | | | gives: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6540) e4 = e1 % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | REDUCE: (12), (6540) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6541) $false % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | CLOSE: (6541) is inconsistent. % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | Case 2: % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6542) all_250_3 = e0 % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6518), (6542) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6543) all_6_0 = e0 % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | REDUCE: (6521), (6543) imply: % 187.10/29.75 | | | | | | | | | | | | | | | | | | (6544) $false % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | | CLOSE: (6544) is inconsistent. % 187.10/29.75 | | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | | End of split % 187.10/29.75 | | | | | | | | | | | | | | | | | % 187.10/29.75 | | | | | | | | | | | | | | | | End of split % 187.10/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | End of split % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | End of split % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | End of split % 187.58/29.75 | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | End of split % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | (6545) all_12_2 = e3 % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | REF_CLOSE: (146), (164), (257), (746), (989), (1475), (1477), % 187.58/29.75 | | | | | | | | | | | | (1582), (1605), (6458), (6463), (6466), (6475), % 187.58/29.75 | | | | | | | | | | | | (6485), (6487), (6545), (function-axioms) are % 187.58/29.75 | | | | | | | | | | | | inconsistent by sub-proof #3. % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | End of split % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | (6546) all_10_2 = e1 % 187.58/29.75 | | | | | | | | | | | (6547) op(e1, e2) = all_10_1 & $i(all_10_1) & ( ~ % 187.58/29.75 | | | | | | | | | | | (all_10_1 = e4) | ( ~ (all_10_0 = e0) & op(e2, % 187.58/29.75 | | | | | | | | | | | e4) = all_10_0 & $i(all_10_0))) % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | ALPHA: (6547) implies: % 187.58/29.75 | | | | | | | | | | | (6548) op(e1, e2) = all_10_1 % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | COMBINE_EQS: (897), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6549) all_124_2 = e1 % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | REDUCE: (1481), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6550) ~ (all_244_3 = e1) % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | REDUCE: (1475), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6551) ~ (all_84_2 = e1) % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | REDUCE: (1488), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6552) ~ (all_62_2 = e1) % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | REDUCE: (1494), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6553) ~ (all_38_2 = e1) % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | REDUCE: (1490), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6554) ~ (all_22_2 = e1) % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | REDUCE: (1611), (6546) imply: % 187.58/29.75 | | | | | | | | | | | (6555) op(e2, e1) = e3 % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | BETA: splitting (784) gives: % 187.58/29.75 | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | (6556) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 187.58/29.75 | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | REF_CLOSE: (257), (498), (6550), (6551), (6556), % 187.58/29.75 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.58/29.75 | | | | | | | | | | | | #13. % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | (6557) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 187.58/29.75 | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 187.58/29.75 | | | | | | | | | | | | op(e0, e3) = e1) % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | BETA: splitting (6557) gives: % 187.58/29.75 | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | (6558) all_252_7 = e1 & op(e2, e3) = e1 % 187.58/29.75 | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | ALPHA: (6558) implies: % 187.58/29.75 | | | | | | | | | | | | | (6559) all_252_7 = e1 % 187.58/29.75 | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | BETA: splitting (315) gives: % 187.58/29.75 | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | (6560) ~ (all_124_2 = e1) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | REDUCE: (6549), (6560) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6561) $false % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | CLOSE: (6561) is inconsistent. % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | (6562) op(e1, e2) = all_124_1 & $i(all_124_1) & ( ~ % 187.58/29.75 | | | | | | | | | | | | | | (all_124_1 = e0) | ( ~ (all_124_0 = e4) & op(e2, % 187.58/29.75 | | | | | | | | | | | | | | e0) = all_124_0 & $i(all_124_0))) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | ALPHA: (6562) implies: % 187.58/29.75 | | | | | | | | | | | | | | (6563) op(e1, e2) = all_124_1 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, % 187.58/29.75 | | | | | | | | | | | | | | all_124_1, e2, e1, simplifying with (137), (6563) % 187.58/29.75 | | | | | | | | | | | | | | gives: % 187.58/29.75 | | | | | | | | | | | | | | (6564) all_124_1 = all_4_2 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1, % 187.58/29.75 | | | | | | | | | | | | | | all_124_1, e2, e1, simplifying with (6548), (6563) % 187.58/29.75 | | | | | | | | | | | | | | gives: % 187.58/29.75 | | | | | | | | | | | | | | (6565) all_124_1 = all_10_1 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_38_2, e3, % 187.58/29.75 | | | | | | | | | | | | | | e1, e2, simplifying with (188), (6555) gives: % 187.58/29.75 | | | | | | | | | | | | | | (6566) all_38_2 = e3 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | COMBINE_EQS: (6564), (6565) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6567) all_10_1 = all_4_2 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | COMBINE_EQS: (1195), (6566) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6568) all_190_2 = e3 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | COMBINE_EQS: (887), (6566) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6569) all_242_2 = e3 % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | REDUCE: (1556), (6566) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6570) ~ (all_244_15 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | REDUCE: (1549), (6566) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6571) ~ (all_36_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | SIMP: (6571) implies: % 187.58/29.75 | | | | | | | | | | | | | | (6572) ~ (all_36_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | REDUCE: (1542), (6566) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6573) ~ (all_26_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | SIMP: (6573) implies: % 187.58/29.75 | | | | | | | | | | | | | | (6574) ~ (all_26_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | REDUCE: (1557), (6566) imply: % 187.58/29.75 | | | | | | | | | | | | | | (6575) ~ (all_20_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | SIMP: (6575) implies: % 187.58/29.75 | | | | | | | | | | | | | | (6576) ~ (all_20_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | BETA: splitting (478) gives: % 187.58/29.75 | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | (6577) ~ (all_242_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | REDUCE: (6569), (6577) imply: % 187.58/29.75 | | | | | | | | | | | | | | | (6578) $false % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | CLOSE: (6578) is inconsistent. % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | (6579) op(e3, e2) = all_242_1 & $i(all_242_1) & ( ~ % 187.58/29.75 | | | | | | | | | | | | | | | (all_242_1 = e4) | ( ~ (all_242_0 = e0) & op(e2, % 187.58/29.75 | | | | | | | | | | | | | | | e4) = all_242_0 & $i(all_242_0))) % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | ALPHA: (6579) implies: % 187.58/29.75 | | | | | | | | | | | | | | | (6580) op(e3, e2) = all_242_1 % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | BETA: splitting (407) gives: % 187.58/29.75 | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | (6581) ~ (all_190_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | REDUCE: (6568), (6581) imply: % 187.58/29.75 | | | | | | | | | | | | | | | | (6582) $false % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | CLOSE: (6582) is inconsistent. % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | (6583) op(e3, e2) = all_190_1 & $i(all_190_1) & ( ~ % 187.58/29.75 | | | | | | | | | | | | | | | | (all_190_1 = e0) | ( ~ (all_190_0 = e4) & op(e2, % 187.58/29.75 | | | | | | | | | | | | | | | | e0) = all_190_0 & $i(all_190_0))) % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | ALPHA: (6583) implies: % 187.58/29.75 | | | | | | | | | | | | | | | | (6584) op(e3, e2) = all_190_1 % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | BETA: splitting (766) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | (6585) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 187.58/29.75 | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | BETA: splitting (6585) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6586) all_252_9 = e3 & op(e4, e1) = e3 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6574), (6586), (function-axioms) are % 187.58/29.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #299. % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6587) all_252_10 = e3 & op(e3, e1) = e3 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | ALPHA: (6587) implies: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6588) op(e3, e1) = e3 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_2, e3, % 187.58/29.75 | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (185), (6588) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6589) all_36_2 = e3 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | REDUCE: (6572), (6589) imply: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6590) $false % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | CLOSE: (6590) is inconsistent. % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | End of split % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | Case 2: % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | (6591) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 187.58/29.75 | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 187.58/29.75 | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | BETA: splitting (6591) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6592) all_252_11 = e3 & op(e2, e1) = e3 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | ALPHA: (6592) implies: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6593) all_252_11 = e3 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, % 187.58/29.75 | | | | | | | | | | | | | | | | | | all_242_1, e2, e3, simplifying with (143), (6580) % 187.58/29.75 | | | | | | | | | | | | | | | | | | gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6594) all_242_1 = all_8_2 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_190_1, % 187.58/29.75 | | | | | | | | | | | | | | | | | | all_242_1, e2, e3, simplifying with (6580), (6584) % 187.58/29.75 | | | | | | | | | | | | | | | | | | gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6595) all_242_1 = all_190_1 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6594), (6595) imply: % 187.58/29.75 | | | | | | | | | | | | | | | | | | (6596) all_190_1 = all_8_2 % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | BETA: splitting (150) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | (6597) ~ (all_12_2 = e3) % 187.58/29.75 | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | (6598) ~ (all_18_2 = e2) % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | REDUCE: (6468), (6598) imply: % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | (6599) ~ (all_6_1 = e2) % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | | (6600) ~ (all_22_2 = e2) % 187.58/29.75 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (12), (14), (137), (143), (146), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (149), (155), (161), (164), (168), (170), (173), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (174), (182), (183), (185), (186), (188), (189), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (191), (201), (203), (219), (222), (224), (225), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (227), (237), (257), (266), (280), (368), (393), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (404), (410), (463), (480), (486), (498), (504), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (514), (729), (731), (751), (753), (758), (760), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (763), (764), (765), (766), (767), (778), (785), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (792), (802), (845), (1032), (1186), (1253), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1255), (1328), (1335), (1349), (1350), (1353), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1379), (1426), (1439), (1445), (1450), (1452), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1460), (1476), (1482), (1485), (1488), (1497), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1501), (1503), (1504), (1524), (1531), (1533), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1535), (1536), (1538), (1540), (1551), (1552), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1556), (1560), (1572), (1573), (1580), (1591), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1595), (1597), (1598), (1599), (1600), (1608), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1609), (1612), (1613), (1614), (1615), (1617), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (1619), (1621), (1622), (6442), (6448), (6449), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6473), (6478), (6484), (6485), (6576), (6597), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6599), (6600), (function-axioms) are inconsistent % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | by sub-proof #17. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6601) all_22_2 = e2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6602) op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | e1) = all_22_0 & $i(all_22_0))) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6602) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6603) op(e2, e0) = all_22_1 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1347), (6601) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6604) all_68_2 = e2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1619), (6601) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | (6605) op(e0, e2) = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6606) ~ (all_68_2 = e2) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6604), (6606) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6607) $false % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6607) is inconsistent. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6608) op(e2, e0) = all_68_1 & $i(all_68_1) & ( ~ % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (all_68_1 = e4) | ( ~ (all_68_0 = e1) & op(e0, % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | e4) = all_68_0 & $i(all_68_0))) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6608) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6609) op(e2, e0) = all_68_1 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, e3, % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (173), (6605) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6610) all_28_2 = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | all_68_1, e0, e2, simplifying with (191), (6609) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6611) all_68_1 = all_40_2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1, % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | all_68_1, e0, e2, simplifying with (6603), (6609) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6612) all_68_1 = all_22_1 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6611), (6612) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6613) all_40_2 = all_22_1 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6613) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6614) all_40_2 = all_22_1 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1332), (6610) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6615) all_82_2 = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1362), (6610) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6616) all_158_2 = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1597), (6610), (6614) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | (6617) op(e3, all_22_1) = e2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | (6618) ~ (all_64_2 = e0) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | (6619) ~ (all_82_2 = e3) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6615), (6619) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | (6620) $false % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6620) is inconsistent. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | (6621) op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_82_0 & $i(all_82_0))) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6621) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | (6622) op(e3, e0) = all_82_1 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | (6623) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e3) = e0) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6623) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (6624) all_252_6 = e0 & op(e2, e4) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6624) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (6625) op(e2, e4) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (227), (6618), (6625), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #382. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (6626) all_252_7 = e0 & op(e2, e3) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6559), (6626) are inconsistent by sub-proof % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | #302. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | (6627) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e1) = e0) | (all_252_18 = e0 & % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6627) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (6628) all_252_8 = e0 & op(e2, e2) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (362), (480), (492), (521), (6473), (6616), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (6628), (function-axioms) are inconsistent by % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #456. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | (6629) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e2, e0) = e0) % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6629) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6630) all_252_11 = e0 & op(e2, e1) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6630) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6631) all_252_11 = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6593), (6631) are inconsistent by sub-proof % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | #297. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6632) all_252_18 = e0 & op(e2, e0) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6632) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6633) op(e2, e0) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (362), (6476), (6603), (6616), (6617), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6622), (6633), (function-axioms) are inconsistent % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | (6634) all_64_2 = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6452), (6634) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | (6635) op(e0, e0) = e2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (6473), (6635), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #477. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | (6636) all_18_2 = e2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6468), (6636) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | (6637) all_6_1 = e2 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | REDUCE: (6485), (6637) imply: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | (6638) op(e2, e2) = e0 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (492), (6446), (6638), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #448. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (6639) all_12_2 = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (146), (164), (257), (746), (989), (1475), (1477), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (1582), (1605), (6458), (6463), (6466), (6475), % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (6485), (6487), (6639), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #3. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | (6640) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 187.58/29.76 | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 187.58/29.76 | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | BETA: splitting (6640) gives: % 187.58/29.76 | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (6641) all_252_15 = e3 & op(e1, e1) = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | ALPHA: (6641) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (6642) op(e1, e1) = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (6570), (6642), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (6643) all_252_23 = e3 & op(e0, e1) = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | ALPHA: (6643) implies: % 187.58/29.76 | | | | | | | | | | | | | | | | | | | (6644) op(e0, e1) = e3 % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (6576), (6644), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #508. % 187.58/29.76 | | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | (6645) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 187.58/29.76 | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.58/29.76 | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | BETA: splitting (6645) gives: % 187.58/29.76 | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | Case 1: % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | (6646) all_252_13 = e1 & op(e1, e3) = e1 % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | ALPHA: (6646) implies: % 187.58/29.76 | | | | | | | | | | | | | | (6647) op(e1, e3) = e1 % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_62_2, e1, % 187.58/29.76 | | | | | | | | | | | | | | e3, e1, simplifying with (224), (6647) gives: % 187.58/29.76 | | | | | | | | | | | | | | (6648) all_62_2 = e1 % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | REDUCE: (6552), (6648) imply: % 187.58/29.76 | | | | | | | | | | | | | | (6649) $false % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | CLOSE: (6649) is inconsistent. % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | (6650) all_252_21 = e1 & op(e0, e3) = e1 % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | ALPHA: (6650) implies: % 187.58/29.76 | | | | | | | | | | | | | | (6651) op(e0, e3) = e1 % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | | REF_CLOSE: (164), (6554), (6651), (function-axioms) are % 187.58/29.76 | | | | | | | | | | | | | | inconsistent by sub-proof #479. % 187.58/29.76 | | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | | % 187.58/29.76 | | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | (6652) all_252_17 = e2 & op(e3, e0) = e2 % 187.58/29.76 | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | ALPHA: (6652) implies: % 187.58/29.76 | | | | | | | | | | (6653) op(e3, e0) = e2 % 187.58/29.76 | | | | | | | | | | % 187.58/29.76 | | | | | | | | | | REF_CLOSE: (203), (6476), (6653), (function-axioms) are % 187.58/29.76 | | | | | | | | | | inconsistent by sub-proof #470. % 187.58/29.76 | | | | | | | | | | % 187.58/29.76 | | | | | | | | | End of split % 187.58/29.76 | | | | | | | | | % 187.58/29.76 | | | | | | | | Case 2: % 187.58/29.76 | | | | | | | | | % 187.58/29.76 | | | | | | | | | (6654) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = % 187.58/29.76 | | | | | | | | | e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, % 187.58/29.76 | | | | | | | | | e0) = e2) % 187.58/29.76 | | | | | | | | | % 187.58/29.76 | | | | | | | | | REF_CLOSE: (182), (191), (480), (6473), (6477), (6478), % 187.58/29.76 | | | | | | | | | (6654), (function-axioms) are inconsistent by % 187.58/29.76 | | | | | | | | | sub-proof #25. % 187.58/29.76 | | | | | | | | | % 187.58/29.76 | | | | | | | | End of split % 187.58/29.76 | | | | | | | | % 187.58/29.76 | | | | | | | End of split % 187.58/29.76 | | | | | | | % 187.58/29.76 | | | | | | End of split % 187.58/29.76 | | | | | | % 187.58/29.76 | | | | | Case 2: % 187.58/29.76 | | | | | | % 187.58/29.76 | | | | | | (6655) all_252_5 = e0 & op(e3, e2) = e0 % 187.58/29.76 | | | | | | % 187.58/29.76 | | | | | | ALPHA: (6655) implies: % 187.58/29.76 | | | | | | (6656) op(e3, e2) = e0 % 187.58/29.76 | | | | | | % 187.58/29.76 | | | | | | REF_CLOSE: (143), (6450), (6656), (function-axioms) are inconsistent % 187.58/29.76 | | | | | | by sub-proof #547. % 187.58/29.76 | | | | | | % 187.58/29.76 | | | | | End of split % 187.58/29.76 | | | | | % 187.58/29.76 | | | | Case 2: % 187.58/29.76 | | | | | % 187.58/29.76 | | | | | (6657) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & % 187.58/29.76 | | | | | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 187.58/29.76 | | | | | % 187.58/29.76 | | | | | REF_CLOSE: (137), (173), (492), (1622), (6446), (6448), (6657), % 187.58/29.76 | | | | | (function-axioms) are inconsistent by sub-proof #23. % 187.58/29.76 | | | | | % 187.58/29.76 | | | | End of split % 187.58/29.76 | | | | % 187.58/29.76 | | | End of split % 187.58/29.76 | | | % 187.58/29.76 | | End of split % 187.58/29.76 | | % 187.58/29.76 | Case 2: % 187.58/29.76 | | % 187.58/29.76 | | (6658) all_4_2 = e0 % 187.58/29.76 | | (6659) op(e0, e1) = all_4_1 & $i(all_4_1) & ( ~ (all_4_1 = e4) | ( ~ % 187.58/29.76 | | (all_4_0 = e3) & op(e1, e4) = all_4_0 & $i(all_4_0))) % 187.58/29.76 | | % 187.58/29.76 | | ALPHA: (6659) implies: % 187.58/29.76 | | (6660) op(e0, e1) = all_4_1 % 187.58/29.76 | | (6661) ~ (all_4_1 = e4) | ( ~ (all_4_0 = e3) & op(e1, e4) = all_4_0 & % 187.58/29.76 | | $i(all_4_0)) % 187.58/29.76 | | % 187.58/29.76 | | COMBINE_EQS: (1296), (6658) imply: % 187.58/29.76 | | (6662) all_50_2 = e0 % 187.58/29.76 | | % 187.58/29.76 | | REDUCE: (1527), (6658) imply: % 187.58/29.76 | | (6663) ~ (all_244_8 = e0) % 187.58/29.76 | | % 187.58/29.76 | | REDUCE: (1533), (6658) imply: % 187.58/29.76 | | (6664) ~ (all_244_15 = e0) % 187.58/29.76 | | % 187.58/29.76 | | REDUCE: (1531), (6658) imply: % 187.58/29.76 | | (6665) ~ (all_28_2 = e0) % 187.58/29.76 | | % 187.58/29.76 | | REDUCE: (1460), (6658) imply: % 187.58/29.76 | | (6666) ~ (all_16_2 = e0) % 187.58/29.77 | | % 187.58/29.77 | | REDUCE: (1520), (6658) imply: % 187.58/29.77 | | (6667) ~ (all_8_2 = e0) % 187.58/29.77 | | % 187.58/29.77 | | REDUCE: (1511), (6658) imply: % 187.58/29.77 | | (6668) ~ (all_6_2 = e0) % 187.58/29.77 | | % 187.58/29.77 | | REDUCE: (1591), (6658) imply: % 187.58/29.77 | | (6669) op(e0, all_38_2) = e2 % 187.58/29.77 | | % 187.58/29.77 | | REDUCE: (1616), (6658) imply: % 187.58/29.77 | | (6670) op(e1, e0) = e2 % 187.58/29.77 | | % 187.58/29.77 | | BETA: splitting (207) gives: % 187.58/29.77 | | % 187.58/29.77 | | Case 1: % 187.58/29.77 | | | % 187.58/29.77 | | | (6671) ~ (all_50_2 = e0) % 187.58/29.77 | | | % 187.58/29.77 | | | REDUCE: (6662), (6671) imply: % 187.58/29.77 | | | (6672) $false % 187.58/29.77 | | | % 187.58/29.77 | | | CLOSE: (6672) is inconsistent. % 187.58/29.77 | | | % 187.58/29.77 | | Case 2: % 187.58/29.77 | | | % 187.58/29.77 | | | (6673) op(e0, e1) = all_50_1 & $i(all_50_1) & ( ~ (all_50_1 = e3) | ( ~ % 187.58/29.77 | | | (all_50_0 = e4) & op(e1, e3) = all_50_0 & $i(all_50_0))) % 187.58/29.77 | | | % 187.58/29.77 | | | ALPHA: (6673) implies: % 187.58/29.77 | | | (6674) op(e0, e1) = all_50_1 % 187.58/29.77 | | | % 187.58/29.77 | | | BETA: splitting (773) gives: % 187.58/29.77 | | | % 187.58/29.77 | | | Case 1: % 187.58/29.77 | | | | % 187.58/29.77 | | | | (6675) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 187.58/29.77 | | | | e2) = e0) % 187.58/29.77 | | | | % 187.58/29.77 | | | | REF_CLOSE: (140), (143), (6667), (6668), (6675), (function-axioms) are % 187.58/29.77 | | | | inconsistent by sub-proof #546. % 187.58/29.77 | | | | % 187.58/29.77 | | | Case 2: % 187.58/29.77 | | | | % 187.58/29.77 | | | | (6676) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, % 187.58/29.77 | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 187.58/29.77 | | | | % 187.58/29.77 | | | | BETA: splitting (6676) gives: % 187.58/29.77 | | | | % 187.58/29.77 | | | | Case 1: % 187.58/29.77 | | | | | % 187.58/29.77 | | | | | (6677) all_252_8 = e0 & op(e2, e2) = e0 % 187.58/29.77 | | | | | % 187.58/29.77 | | | | | ALPHA: (6677) implies: % 187.58/29.77 | | | | | (6678) op(e2, e2) = e0 % 187.58/29.77 | | | | | % 187.58/29.77 | | | | | REF_CLOSE: (492), (6663), (6678), (function-axioms) are inconsistent % 187.58/29.77 | | | | | by sub-proof #448. % 187.58/29.77 | | | | | % 187.58/29.77 | | | | Case 2: % 187.58/29.77 | | | | | % 187.58/29.77 | | | | | (6679) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 187.58/29.77 | | | | | op(e0, e2) = e0) % 187.58/29.77 | | | | | % 187.58/29.77 | | | | | BETA: splitting (6679) gives: % 187.58/29.77 | | | | | % 187.58/29.77 | | | | | Case 1: % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_2, % 187.58/29.77 | | | | | | all_50_1, e1, e0, simplifying with (161), (6674) gives: % 187.58/29.77 | | | | | | (6680) all_50_1 = all_20_2 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, all_50_1, % 187.58/29.77 | | | | | | e1, e0, simplifying with (6660), (6674) gives: % 187.58/29.77 | | | | | | (6681) all_50_1 = all_4_1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | GROUND_INST: instantiating (function-axioms) with all_34_2, e2, e0, % 187.58/29.77 | | | | | | e1, simplifying with (182), (6670) gives: % 187.58/29.77 | | | | | | (6682) all_34_2 = e2 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | COMBINE_EQS: (6680), (6681) imply: % 187.58/29.77 | | | | | | (6683) all_20_2 = all_4_1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | SIMP: (6683) implies: % 187.58/29.77 | | | | | | (6684) all_20_2 = all_4_1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | COMBINE_EQS: (1358), (6684) imply: % 187.58/29.77 | | | | | | (6685) all_92_2 = all_4_1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | COMBINE_EQS: (1424), (6684) imply: % 187.58/29.77 | | | | | | (6686) all_250_23 = all_4_1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1580), (6682) imply: % 187.58/29.77 | | | | | | (6687) ~ (all_244_24 = e2) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1573), (6682) imply: % 187.58/29.77 | | | | | | (6688) ~ (all_48_2 = e2) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1552), (6684) imply: % 187.58/29.77 | | | | | | (6689) ~ (all_36_2 = all_4_1) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1569), (6682) imply: % 187.58/29.77 | | | | | | (6690) ~ (all_30_2 = e2) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | SIMP: (6690) implies: % 187.58/29.77 | | | | | | (6691) ~ (all_30_2 = e2) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1464), (6682) imply: % 187.58/29.77 | | | | | | (6692) ~ (all_16_2 = e2) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | SIMP: (6692) implies: % 187.58/29.77 | | | | | | (6693) ~ (all_16_2 = e2) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1536), (6684) imply: % 187.58/29.77 | | | | | | (6694) ~ (all_28_2 = all_4_1) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1545), (6684) imply: % 187.58/29.77 | | | | | | (6695) ~ (all_26_2 = all_4_1) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1504), (6684) imply: % 187.58/29.77 | | | | | | (6696) ~ (all_22_2 = all_4_1) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1470), (6684) imply: % 187.58/29.77 | | | | | | (6697) ~ (all_12_2 = all_4_1) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | SIMP: (6697) implies: % 187.58/29.77 | | | | | | (6698) ~ (all_12_2 = all_4_1) % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1600), (6682), (6684) imply: % 187.58/29.77 | | | | | | (6699) op(e2, all_4_1) = e0 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1599), (6682), (6684) imply: % 187.58/29.77 | | | | | | (6700) op(all_4_1, e2) = e1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | REDUCE: (1621), (6684) imply: % 187.58/29.77 | | | | | | (6701) op(e0, all_4_1) = e1 % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | BETA: splitting (153) gives: % 187.58/29.77 | | | | | | % 187.58/29.77 | | | | | | Case 1: % 187.58/29.77 | | | | | | | % 187.58/29.77 | | | | | | | (6702) ~ (all_14_2 = e1) % 187.58/29.77 | | | | | | | % 187.58/29.77 | | | | | | | REDUCE: (1356), (6702) imply: % 187.58/29.77 | | | | | | | (6703) ~ (all_12_2 = e1) % 187.58/29.77 | | | | | | | % 187.58/29.77 | | | | | | | BETA: splitting (159) gives: % 187.58/29.77 | | | | | | | % 187.58/29.77 | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | % 187.58/29.77 | | | | | | | | (6704) ~ (all_18_2 = e2) % 187.58/29.77 | | | | | | | | % 187.58/29.77 | | | | | | | | REDUCE: (1231), (6704) imply: % 187.58/29.77 | | | | | | | | (6705) ~ (all_12_2 = e2) % 187.58/29.77 | | | | | | | | % 187.58/29.77 | | | | | | | | BETA: splitting (165) gives: % 187.58/29.77 | | | | | | | | % 187.58/29.77 | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | (6706) ~ (all_22_2 = e2) % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | BETA: splitting (751) gives: % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | (6707) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 187.58/29.77 | | | | | | | | | | = e2 & op(e0, e3) = e2) % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | REF_CLOSE: (149), (164), (6705), (6706), (6707), % 187.58/29.77 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.58/29.77 | | | | | | | | | | #542. % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | (6708) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 187.58/29.77 | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 187.58/29.77 | | | | | | | | | | op(e0, e0) = e2) % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | BETA: splitting (6708) gives: % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | (6709) all_252_22 = e2 & op(e0, e2) = e2 % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | ALPHA: (6709) implies: % 187.58/29.77 | | | | | | | | | | | (6710) op(e0, e2) = e2 % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | REF_CLOSE: (173), (1597), (1613), (6665), (6710), % 187.58/29.77 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.58/29.77 | | | | | | | | | | | #288. % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | (6711) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 187.58/29.77 | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | BETA: splitting (6711) gives: % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | (6712) all_252_23 = e2 & op(e0, e1) = e2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | ALPHA: (6712) implies: % 187.58/29.77 | | | | | | | | | | | | (6713) op(e0, e1) = e2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e2, % 187.58/29.77 | | | | | | | | | | | | e1, e0, simplifying with (6660), (6713) gives: % 187.58/29.77 | | | | | | | | | | | | (6714) all_4_1 = e2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | REDUCE: (6699), (6714) imply: % 187.58/29.77 | | | | | | | | | | | | (6715) op(e2, e2) = e0 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | REF_CLOSE: (492), (6663), (6715), (function-axioms) are % 187.58/29.77 | | | | | | | | | | | | inconsistent by sub-proof #448. % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | (6716) all_252_24 = e2 & op(e0, e0) = e2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | ALPHA: (6716) implies: % 187.58/29.77 | | | | | | | | | | | | (6717) op(e0, e0) = e2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | REF_CLOSE: (480), (6687), (6717), (function-axioms) are % 187.58/29.77 | | | | | | | | | | | | inconsistent by sub-proof #477. % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | (6718) all_22_2 = e2 % 187.58/29.77 | | | | | | | | | (6719) op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 % 187.58/29.77 | | | | | | | | | = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = % 187.58/29.77 | | | | | | | | | all_22_0 & $i(all_22_0))) % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | ALPHA: (6719) implies: % 187.58/29.77 | | | | | | | | | (6720) op(e2, e0) = all_22_1 % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | COMBINE_EQS: (1347), (6718) imply: % 187.58/29.77 | | | | | | | | | (6721) all_68_2 = e2 % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | REDUCE: (6696), (6718) imply: % 187.58/29.77 | | | | | | | | | (6722) ~ (all_4_1 = e2) % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | SIMP: (6722) implies: % 187.58/29.77 | | | | | | | | | (6723) ~ (all_4_1 = e2) % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | REDUCE: (1619), (6718) imply: % 187.58/29.77 | | | | | | | | | (6724) op(e0, e2) = e3 % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | BETA: splitting (234) gives: % 187.58/29.77 | | | | | | | | | % 187.58/29.77 | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | (6725) ~ (all_68_2 = e2) % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | REDUCE: (6721), (6725) imply: % 187.58/29.77 | | | | | | | | | | (6726) $false % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | CLOSE: (6726) is inconsistent. % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | (6727) op(e2, e0) = all_68_1 & $i(all_68_1) & ( ~ % 187.58/29.77 | | | | | | | | | | (all_68_1 = e4) | ( ~ (all_68_0 = e1) & op(e0, % 187.58/29.77 | | | | | | | | | | e4) = all_68_0 & $i(all_68_0))) % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | ALPHA: (6727) implies: % 187.58/29.77 | | | | | | | | | | (6728) op(e2, e0) = all_68_1 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, e3, % 187.58/29.77 | | | | | | | | | | e2, e0, simplifying with (173), (6724) gives: % 187.58/29.77 | | | | | | | | | | (6729) all_28_2 = e3 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_40_2, % 187.58/29.77 | | | | | | | | | | all_68_1, e0, e2, simplifying with (191), (6728) % 187.58/29.77 | | | | | | | | | | gives: % 187.58/29.77 | | | | | | | | | | (6730) all_68_1 = all_40_2 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1, % 187.58/29.77 | | | | | | | | | | all_68_1, e0, e2, simplifying with (6720), (6728) % 187.58/29.77 | | | | | | | | | | gives: % 187.58/29.77 | | | | | | | | | | (6731) all_68_1 = all_22_1 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | COMBINE_EQS: (6730), (6731) imply: % 187.58/29.77 | | | | | | | | | | (6732) all_40_2 = all_22_1 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | SIMP: (6732) implies: % 187.58/29.77 | | | | | | | | | | (6733) all_40_2 = all_22_1 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | COMBINE_EQS: (1332), (6729) imply: % 187.58/29.77 | | | | | | | | | | (6734) all_82_2 = e3 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | COMBINE_EQS: (1362), (6729) imply: % 187.58/29.77 | | | | | | | | | | (6735) all_158_2 = e3 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | REDUCE: (6694), (6729) imply: % 187.58/29.77 | | | | | | | | | | (6736) ~ (all_4_1 = e3) % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | SIMP: (6736) implies: % 187.58/29.77 | | | | | | | | | | (6737) ~ (all_4_1 = e3) % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | REDUCE: (1597), (6729), (6733) imply: % 187.58/29.77 | | | | | | | | | | (6738) op(e3, all_22_1) = e2 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | REDUCE: (1620), (6729) imply: % 187.58/29.77 | | | | | | | | | | (6739) op(e0, e3) = e2 % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | BETA: splitting (255) gives: % 187.58/29.77 | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | (6740) ~ (all_82_2 = e3) % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | REDUCE: (6734), (6740) imply: % 187.58/29.77 | | | | | | | | | | | (6741) $false % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | CLOSE: (6741) is inconsistent. % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | (6742) op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 187.58/29.77 | | | | | | | | | | | (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, % 187.58/29.77 | | | | | | | | | | | e1) = all_82_0 & $i(all_82_0))) % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | ALPHA: (6742) implies: % 187.58/29.77 | | | | | | | | | | | (6743) op(e3, e0) = all_82_1 % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | BETA: splitting (362) gives: % 187.58/29.77 | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | (6744) ~ (all_158_2 = e3) % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | REDUCE: (6735), (6744) imply: % 187.58/29.77 | | | | | | | | | | | | (6745) $false % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | CLOSE: (6745) is inconsistent. % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | (6746) op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 187.58/29.77 | | | | | | | | | | | | (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, % 187.58/29.77 | | | | | | | | | | | | e4) = all_158_0 & $i(all_158_0))) % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | ALPHA: (6746) implies: % 187.58/29.77 | | | | | | | | | | | | (6747) op(e3, e0) = all_158_1 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_48_2, % 187.58/29.77 | | | | | | | | | | | | all_158_1, e0, e3, simplifying with (203), (6747) % 187.58/29.77 | | | | | | | | | | | | gives: % 187.58/29.77 | | | | | | | | | | | | (6748) all_158_1 = all_48_2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_82_1, % 187.58/29.77 | | | | | | | | | | | | all_158_1, e0, e3, simplifying with (6743), (6747) % 187.58/29.77 | | | | | | | | | | | | gives: % 187.58/29.77 | | | | | | | | | | | | (6749) all_158_1 = all_82_1 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | COMBINE_EQS: (6748), (6749) imply: % 187.58/29.77 | | | | | | | | | | | | (6750) all_82_1 = all_48_2 % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | BETA: splitting (171) gives: % 187.58/29.77 | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | (6751) ~ (all_26_2 = e0) % 187.58/29.77 | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | BETA: splitting (269) gives: % 187.58/29.77 | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | (6752) ~ (all_92_2 = e4) % 187.58/29.77 | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | REDUCE: (6685), (6752) imply: % 187.58/29.77 | | | | | | | | | | | | | | (6753) ~ (all_4_1 = e4) % 187.58/29.77 | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | BETA: splitting (186) gives: % 187.58/29.77 | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | (6754) ~ (all_36_2 = e0) % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | (6755) ~ (all_38_2 = e0) % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | BETA: splitting (763) gives: % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | (6756) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 187.58/29.77 | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (6751), (6754), (6756), % 187.58/29.77 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.58/29.77 | | | | | | | | | | | | | | | | | #451. % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | (6757) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 187.58/29.77 | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 187.58/29.77 | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | BETA: splitting (6757) gives: % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | (6758) all_252_11 = e0 & op(e2, e1) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | ALPHA: (6758) implies: % 187.58/29.77 | | | | | | | | | | | | | | | | | | (6759) op(e2, e1) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (6755), (6759), (function-axioms) are % 187.58/29.77 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | (6760) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 187.58/29.77 | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | BETA: splitting (6760) gives: % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6761) all_252_15 = e0 & op(e1, e1) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | ALPHA: (6761) implies: % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6762) op(e1, e1) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (486), (6664), (6762), (function-axioms) are % 187.58/29.77 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6763) all_252_23 = e0 & op(e0, e1) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | ALPHA: (6763) implies: % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6764) op(e0, e1) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e0, % 187.58/29.77 | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (6660), (6764) gives: % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6765) all_4_1 = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | REDUCE: (6699), (6765) imply: % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6766) op(e2, e0) = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (362), (6688), (6720), (6735), (6738), % 187.58/29.77 | | | | | | | | | | | | | | | | | | | (6743), (6766), (function-axioms) are inconsistent % 187.58/29.77 | | | | | | | | | | | | | | | | | | | by sub-proof #2. % 187.58/29.77 | | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | (6767) all_38_2 = e0 % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | REDUCE: (6669), (6767) imply: % 187.58/29.77 | | | | | | | | | | | | | | | | (6768) op(e0, e0) = e2 % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | | REF_CLOSE: (480), (6687), (6768), (function-axioms) are % 187.58/29.77 | | | | | | | | | | | | | | | | inconsistent by sub-proof #477. % 187.58/29.77 | | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | (6769) all_36_2 = e0 % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | REDUCE: (1549), (6769) imply: % 187.58/29.77 | | | | | | | | | | | | | | | (6770) ~ (all_38_2 = e0) % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | REDUCE: (6689), (6769) imply: % 187.58/29.77 | | | | | | | | | | | | | | | (6771) ~ (all_4_1 = e0) % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | | REF_CLOSE: (188), (727), (6686), (6699), (6723), (6737), % 187.58/29.77 | | | | | | | | | | | | | | | (6753), (6770), (6771), (function-axioms) are % 187.58/29.77 | | | | | | | | | | | | | | | inconsistent by sub-proof #1. % 187.58/29.77 | | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | | End of split % 187.58/29.77 | | | | | | | | | | | | | | % 187.58/29.77 | | | | | | | | | | | | | Case 2: % 187.58/29.77 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | (6772) all_92_2 = e4 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | COMBINE_EQS: (6685), (6772) imply: % 187.58/29.78 | | | | | | | | | | | | | | (6773) all_4_1 = e4 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | SIMP: (6773) implies: % 187.58/29.78 | | | | | | | | | | | | | | (6774) all_4_1 = e4 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | REDUCE: (6701), (6774) imply: % 187.58/29.78 | | | | | | | | | | | | | | (6775) op(e0, e4) = e1 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | REF_CLOSE: (149), (6703), (6775), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | (6776) all_26_2 = e0 % 187.58/29.78 | | | | | | | | | | | | | (6777) op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 187.58/29.78 | | | | | | | | | | | | | (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, % 187.58/29.78 | | | | | | | | | | | | | e3) = all_26_0 & $i(all_26_0))) % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | ALPHA: (6777) implies: % 187.58/29.78 | | | | | | | | | | | | | (6778) op(e0, e4) = all_26_1 % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | COMBINE_EQS: (1341), (6776) imply: % 187.58/29.78 | | | | | | | | | | | | | (6779) all_44_2 = e0 % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | REDUCE: (1542), (6776) imply: % 187.58/29.78 | | | | | | | | | | | | | (6780) ~ (all_38_2 = e0) % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | REDUCE: (1603), (6776) imply: % 187.58/29.78 | | | | | | | | | | | | | (6781) op(e4, e0) = e1 % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | BETA: splitting (198) gives: % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | (6782) ~ (all_44_2 = e0) % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | REDUCE: (6779), (6782) imply: % 187.58/29.78 | | | | | | | | | | | | | | (6783) $false % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | CLOSE: (6783) is inconsistent. % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | (6784) op(e0, e4) = all_44_1 & $i(all_44_1) & ( ~ % 187.58/29.78 | | | | | | | | | | | | | | (all_44_1 = e2) | ( ~ (all_44_0 = e3) & op(e4, % 187.58/29.78 | | | | | | | | | | | | | | e2) = all_44_0 & $i(all_44_0))) % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | ALPHA: (6784) implies: % 187.58/29.78 | | | | | | | | | | | | | | (6785) op(e0, e4) = all_44_1 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_12_2, % 187.58/29.78 | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (149), (6785) % 187.58/29.78 | | | | | | | | | | | | | | gives: % 187.58/29.78 | | | | | | | | | | | | | | (6786) all_44_1 = all_12_2 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_26_1, % 187.58/29.78 | | | | | | | | | | | | | | all_44_1, e4, e0, simplifying with (6778), (6785) % 187.58/29.78 | | | | | | | | | | | | | | gives: % 187.58/29.78 | | | | | | | | | | | | | | (6787) all_44_1 = all_26_1 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_30_2, e1, % 187.58/29.78 | | | | | | | | | | | | | | e0, e4, simplifying with (176), (6781) gives: % 187.58/29.78 | | | | | | | | | | | | | | (6788) all_30_2 = e1 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | COMBINE_EQS: (6786), (6787) imply: % 187.58/29.78 | | | | | | | | | | | | | | (6789) all_26_1 = all_12_2 % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | REDUCE: (1571), (6788) imply: % 187.58/29.78 | | | | | | | | | | | | | | (6790) ~ (all_244_24 = e1) % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | REDUCE: (6691), (6788) imply: % 187.58/29.78 | | | | | | | | | | | | | | (6791) ~ (e2 = e1) % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | (6792) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.58/29.78 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | BETA: splitting (6792) gives: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | (6793) all_252_20 = e1 & op(e0, e4) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | ALPHA: (6793) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | (6794) op(e0, e4) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | REF_CLOSE: (149), (6703), (6794), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | inconsistent by sub-proof #530. % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | (6795) all_252_21 = e1 & op(e0, e3) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | ALPHA: (6795) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | (6796) op(e0, e3) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6739), (6796), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | inconsistent by sub-proof #10. % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | (6797) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.58/29.78 | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.58/29.78 | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | BETA: splitting (6797) gives: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | (6798) all_252_22 = e1 & op(e0, e2) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | ALPHA: (6798) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | (6799) op(e0, e2) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2, % 187.58/29.78 | | | | | | | | | | | | | | | | e0, simplifying with (6724), (6799) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | (6800) e3 = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | REDUCE: (9), (6800) imply: % 187.58/29.78 | | | | | | | | | | | | | | | | (6801) $false % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | CLOSE: (6801) is inconsistent. % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | (6802) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.58/29.78 | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | BETA: splitting (6802) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | (6803) all_252_23 = e1 & op(e0, e1) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | ALPHA: (6803) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | (6804) op(e0, e1) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e1, % 187.58/29.78 | | | | | | | | | | | | | | | | | e1, e0, simplifying with (6660), (6804) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | (6805) all_4_1 = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | REDUCE: (6699), (6805) imply: % 187.58/29.78 | | | | | | | | | | | | | | | | | (6806) op(e2, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (6780), (6806), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | (6807) all_252_24 = e1 & op(e0, e0) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | ALPHA: (6807) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | (6808) op(e0, e0) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (480), (6790), (6808), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #474. % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | % 187.58/29.78 | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | % 187.58/29.78 | | | | | | | | End of split % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | (6809) all_18_2 = e2 % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | COMBINE_EQS: (1231), (6809) imply: % 187.58/29.78 | | | | | | | | (6810) all_12_2 = e2 % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | REDUCE: (6698), (6810) imply: % 187.58/29.78 | | | | | | | | (6811) ~ (all_4_1 = e2) % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | SIMP: (6811) implies: % 187.58/29.78 | | | | | | | | (6812) ~ (all_4_1 = e2) % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | REDUCE: (1618), (6810) imply: % 187.58/29.78 | | | | | | | | (6813) op(e0, e2) = e4 % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_28_2, e4, % 187.58/29.78 | | | | | | | | e2, e0, simplifying with (173), (6813) gives: % 187.58/29.78 | | | | | | | | (6814) all_28_2 = e4 % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | REDUCE: (1538), (6814) imply: % 187.58/29.78 | | | | | | | | (6815) ~ (all_244_24 = e4) % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | REDUCE: (6694), (6814) imply: % 187.58/29.78 | | | | | | | | (6816) ~ (all_4_1 = e4) % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | SIMP: (6816) implies: % 187.58/29.78 | | | | | | | | (6817) ~ (all_4_1 = e4) % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | REDUCE: (1620), (6814) imply: % 187.58/29.78 | | | | | | | | (6818) op(e0, e4) = e2 % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | BETA: splitting (306) gives: % 187.58/29.78 | | | | | | | | % 187.58/29.78 | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | % 187.58/29.78 | | | | | | | | | (6819) ~ (all_118_2 = e1) % 187.58/29.78 | | | | | | | | | % 187.58/29.78 | | | | | | | | | REDUCE: (1359), (6819) imply: % 187.58/29.78 | | | | | | | | | (6820) ~ (all_22_2 = e1) % 187.58/29.78 | | | | | | | | | % 187.58/29.78 | | | | | | | | | BETA: splitting (162) gives: % 187.58/29.78 | | | | | | | | | % 187.58/29.78 | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | (6821) ~ (all_20_2 = e3) % 187.58/29.78 | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | REDUCE: (6684), (6821) imply: % 187.58/29.78 | | | | | | | | | | (6822) ~ (all_4_1 = e3) % 187.58/29.78 | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | BETA: splitting (171) gives: % 187.58/29.78 | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | (6823) ~ (all_26_2 = e0) % 187.58/29.78 | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | BETA: splitting (186) gives: % 187.58/29.78 | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | (6824) ~ (all_36_2 = e0) % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | BETA: splitting (189) gives: % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | (6825) ~ (all_38_2 = e0) % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | BETA: splitting (763) gives: % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | (6826) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 187.58/29.78 | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | REF_CLOSE: (170), (185), (6823), (6824), (6826), % 187.58/29.78 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof % 187.58/29.78 | | | | | | | | | | | | | | #451. % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | (6827) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 187.58/29.78 | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 187.58/29.78 | | | | | | | | | | | | | | op(e0, e1) = e0) % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | BETA: splitting (6827) gives: % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | (6828) all_252_11 = e0 & op(e2, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | ALPHA: (6828) implies: % 187.58/29.78 | | | | | | | | | | | | | | | (6829) op(e2, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | REF_CLOSE: (188), (6825), (6829), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | inconsistent by sub-proof #549. % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | (6830) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 187.58/29.78 | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | BETA: splitting (6830) gives: % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | (6831) all_252_15 = e0 & op(e1, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | ALPHA: (6831) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | (6832) op(e1, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | REF_CLOSE: (486), (6664), (6832), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | inconsistent by sub-proof #440. % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | (6833) all_252_23 = e0 & op(e0, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | ALPHA: (6833) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | (6834) all_252_23 = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | (6835) op(e0, e1) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | BETA: splitting (750) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | (6836) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 187.58/29.78 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | BETA: splitting (6836) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6837) all_252_20 = e1 & op(e0, e4) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | ALPHA: (6837) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6838) op(e0, e4) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6818), (6838), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #323. % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6839) all_252_21 = e1 & op(e0, e3) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | ALPHA: (6839) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6840) op(e0, e3) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6820), (6840), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #479. % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | (6841) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 187.58/29.78 | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.58/29.78 | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | BETA: splitting (6841) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6842) all_252_22 = e1 & op(e0, e2) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | ALPHA: (6842) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6843) op(e0, e2) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (6813), (6843), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | (6844) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 187.58/29.78 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | BETA: splitting (6844) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | (6845) all_252_23 = e1 & op(e0, e1) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | ALPHA: (6845) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | (6846) all_252_23 = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6834), (6846) are inconsistent by sub-proof % 187.58/29.78 | | | | | | | | | | | | | | | | | | | #351. % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | (6847) all_252_24 = e1 & op(e0, e0) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | ALPHA: (6847) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | (6848) all_252_24 = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | (6849) op(e0, e0) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | BETA: splitting (749) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | Case 1: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | (6850) all_252_24 = e0 & op(e0, e0) = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | ALPHA: (6850) implies: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | (6851) all_252_24 = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6848), (6851) are inconsistent by sub-proof % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | #139. % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_244_24, % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | e1, e0, e0, simplifying with (480), (6849) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | (6852) all_244_24 = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e0, % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (6660), (6835) gives: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | (6853) all_4_1 = e0 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | REDUCE: (6815), (6852) imply: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | (6854) ~ (e4 = e1) % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | REDUCE: (6700), (6853) imply: % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | (6855) op(e0, e2) = e1 % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (6813), (6855), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #256. % 187.58/29.78 | | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | (6856) all_38_2 = e0 % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | REDUCE: (6669), (6856) imply: % 187.58/29.78 | | | | | | | | | | | | | (6857) op(e0, e0) = e2 % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | | REF_CLOSE: (480), (6687), (6857), (function-axioms) are % 187.58/29.78 | | | | | | | | | | | | | inconsistent by sub-proof #477. % 187.58/29.78 | | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | End of split % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | Case 2: % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | (6858) all_36_2 = e0 % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.78 | | | | | | | | | | | | REDUCE: (1549), (6858) imply: % 187.58/29.78 | | | | | | | | | | | | (6859) ~ (all_38_2 = e0) % 187.58/29.78 | | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | | REDUCE: (6689), (6858) imply: % 187.58/29.79 | | | | | | | | | | | | (6860) ~ (all_4_1 = e0) % 187.58/29.79 | | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | | REF_CLOSE: (188), (727), (6686), (6699), (6812), (6817), % 187.58/29.79 | | | | | | | | | | | | (6822), (6859), (6860), (function-axioms) are % 187.58/29.79 | | | | | | | | | | | | inconsistent by sub-proof #1. % 187.58/29.79 | | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | End of split % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | (6861) all_26_2 = e0 % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | REDUCE: (1542), (6861) imply: % 187.58/29.79 | | | | | | | | | | | (6862) ~ (all_38_2 = e0) % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | REDUCE: (6695), (6861) imply: % 187.58/29.79 | | | | | | | | | | | (6863) ~ (all_4_1 = e0) % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | REF_CLOSE: (188), (727), (6686), (6699), (6812), (6817), % 187.58/29.79 | | | | | | | | | | | (6822), (6862), (6863), (function-axioms) are % 187.58/29.79 | | | | | | | | | | | inconsistent by sub-proof #1. % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | End of split % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | (6864) all_20_2 = e3 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | COMBINE_EQS: (6684), (6864) imply: % 187.58/29.79 | | | | | | | | | | (6865) all_4_1 = e3 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | REDUCE: (6701), (6865) imply: % 187.58/29.79 | | | | | | | | | | (6866) op(e0, e3) = e1 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | REF_CLOSE: (164), (6820), (6866), (function-axioms) are % 187.58/29.79 | | | | | | | | | | inconsistent by sub-proof #479. % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | End of split % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | (6867) op(e1, e0) = all_118_1 & $i(all_118_1) & ( ~ % 187.58/29.79 | | | | | | | | | (all_118_1 = e2) | ( ~ (all_118_0 = e4) & op(e0, % 187.58/29.79 | | | | | | | | | e2) = all_118_0 & $i(all_118_0))) % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | ALPHA: (6867) implies: % 187.58/29.79 | | | | | | | | | (6868) op(e1, e0) = all_118_1 % 187.58/29.79 | | | | | | | | | (6869) ~ (all_118_1 = e2) | ( ~ (all_118_0 = e4) & op(e0, % 187.58/29.79 | | | | | | | | | e2) = all_118_0 & $i(all_118_0)) % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | BETA: splitting (6869) gives: % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | Case 1: % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | (6870) ~ (all_118_1 = e2) % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, % 187.58/29.79 | | | | | | | | | | all_118_1, e0, e1, simplifying with (6670), (6868) % 187.58/29.79 | | | | | | | | | | gives: % 187.58/29.79 | | | | | | | | | | (6871) all_118_1 = e2 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | REDUCE: (6870), (6871) imply: % 187.58/29.79 | | | | | | | | | | (6872) $false % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | CLOSE: (6872) is inconsistent. % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | (6873) ~ (all_118_0 = e4) & op(e0, e2) = all_118_0 & % 187.58/29.79 | | | | | | | | | | $i(all_118_0) % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | ALPHA: (6873) implies: % 187.58/29.79 | | | | | | | | | | (6874) ~ (all_118_0 = e4) % 187.58/29.79 | | | | | | | | | | (6875) op(e0, e2) = all_118_0 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e4, % 187.58/29.79 | | | | | | | | | | all_118_0, e2, e0, simplifying with (6813), (6875) % 187.58/29.79 | | | | | | | | | | gives: % 187.58/29.79 | | | | | | | | | | (6876) all_118_0 = e4 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | REDUCE: (6874), (6876) imply: % 187.58/29.79 | | | | | | | | | | (6877) $false % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | CLOSE: (6877) is inconsistent. % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | End of split % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | End of split % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | End of split % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | Case 2: % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | (6878) all_14_2 = e1 % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | COMBINE_EQS: (1356), (6878) imply: % 187.58/29.79 | | | | | | | (6879) all_12_2 = e1 % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | COMBINE_EQS: (1357), (6879) imply: % 187.58/29.79 | | | | | | | (6880) all_42_2 = e1 % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | REDUCE: (1457), (6879) imply: % 187.58/29.79 | | | | | | | (6881) ~ (all_16_2 = e1) % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | REDUCE: (1618), (6879) imply: % 187.58/29.79 | | | | | | | (6882) op(e0, e1) = e4 % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | BETA: splitting (195) gives: % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | | Case 1: % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | (6883) ~ (all_42_2 = e1) % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | REDUCE: (6880), (6883) imply: % 187.58/29.79 | | | | | | | | (6884) $false % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | CLOSE: (6884) is inconsistent. % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_1, e4, % 187.58/29.79 | | | | | | | | e1, e0, simplifying with (6660), (6882) gives: % 187.58/29.79 | | | | | | | | (6885) all_4_1 = e4 % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | BETA: splitting (6661) gives: % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | | Case 1: % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | (6886) ~ (all_4_1 = e4) % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | REDUCE: (6885), (6886) imply: % 187.58/29.79 | | | | | | | | | (6887) $false % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | CLOSE: (6887) is inconsistent. % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | (6888) ~ (all_4_0 = e3) & op(e1, e4) = all_4_0 & % 187.58/29.79 | | | | | | | | | $i(all_4_0) % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | ALPHA: (6888) implies: % 187.58/29.79 | | | | | | | | | (6889) ~ (all_4_0 = e3) % 187.58/29.79 | | | | | | | | | (6890) op(e1, e4) = all_4_0 % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_16_2, % 187.58/29.79 | | | | | | | | | all_4_0, e4, e1, simplifying with (155), (6890) % 187.58/29.79 | | | | | | | | | gives: % 187.58/29.79 | | | | | | | | | (6891) all_16_2 = all_4_0 % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | COMBINE_EQS: (1428), (6891) imply: % 187.58/29.79 | | | | | | | | | (6892) all_250_15 = all_4_0 % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | REDUCE: (6881), (6891) imply: % 187.58/29.79 | | | | | | | | | (6893) ~ (all_4_0 = e1) % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | REDUCE: (1587), (6891) imply: % 187.58/29.79 | | | | | | | | | (6894) op(all_4_0, all_26_2) = e4 % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | BETA: splitting (733) gives: % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | | Case 1: % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | (6895) all_250_15 = e4 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | COMBINE_EQS: (6892), (6895) imply: % 187.58/29.79 | | | | | | | | | | (6896) all_4_0 = e4 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | REDUCE: (6894), (6896) imply: % 187.58/29.79 | | | | | | | | | | (6897) op(e4, all_26_2) = e4 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | REF_CLOSE: (12), (1603), (6897), (function-axioms) are % 187.58/29.79 | | | | | | | | | | inconsistent by sub-proof #579. % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | (6898) all_250_15 = e3 | all_250_15 = e2 | all_250_15 = % 187.58/29.79 | | | | | | | | | | e1 | all_250_15 = e0 % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | BETA: splitting (6898) gives: % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | Case 1: % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | (6899) all_250_15 = e3 % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | COMBINE_EQS: (6892), (6899) imply: % 187.58/29.79 | | | | | | | | | | | (6900) all_4_0 = e3 % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | REDUCE: (6889), (6900) imply: % 187.58/29.79 | | | | | | | | | | | (6901) $false % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | CLOSE: (6901) is inconsistent. % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | Case 2: % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | (6902) all_250_15 = e2 | all_250_15 = e1 | all_250_15 = % 187.58/29.79 | | | | | | | | | | | e0 % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | | REF_CLOSE: (1428), (6666), (6693), (6881), (6902) are % 187.58/29.79 | | | | | | | | | | | inconsistent by sub-proof #326. % 187.58/29.79 | | | | | | | | | | | % 187.58/29.79 | | | | | | | | | | End of split % 187.58/29.79 | | | | | | | | | | % 187.58/29.79 | | | | | | | | | End of split % 187.58/29.79 | | | | | | | | | % 187.58/29.79 | | | | | | | | End of split % 187.58/29.79 | | | | | | | | % 187.58/29.79 | | | | | | | End of split % 187.58/29.79 | | | | | | | % 187.58/29.79 | | | | | | End of split % 187.58/29.79 | | | | | | % 187.58/29.79 | | | | | Case 2: % 187.58/29.79 | | | | | | % 187.58/29.79 | | | | | | (6903) all_252_22 = e0 & op(e0, e2) = e0 % 187.58/29.79 | | | | | | % 187.58/29.79 | | | | | | ALPHA: (6903) implies: % 187.58/29.79 | | | | | | (6904) op(e0, e2) = e0 % 187.58/29.79 | | | | | | % 187.58/29.79 | | | | | | REF_CLOSE: (173), (6665), (6904), (function-axioms) are inconsistent % 187.58/29.79 | | | | | | by sub-proof #24. % 187.58/29.79 | | | | | | % 187.58/29.79 | | | | | End of split % 187.58/29.79 | | | | | % 187.58/29.79 | | | | End of split % 187.58/29.79 | | | | % 187.58/29.79 | | | End of split % 187.58/29.79 | | | % 187.58/29.79 | | End of split % 187.58/29.79 | | % 187.58/29.79 | End of split % 187.58/29.79 | % 187.58/29.79 End of proof % 187.58/29.79 % 187.58/29.79 Sub-proof #1 shows that the following formulas are inconsistent: % 187.58/29.79 ---------------------------------------------------------------- % 187.58/29.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.58/29.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.58/29.79 (2) all_250_23 = all_4_1 % 187.58/29.79 (3) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 187.58/29.79 all_250_23 = e0 % 187.58/29.79 (4) ~ (all_4_1 = e0) % 187.58/29.79 (5) ~ (all_4_1 = e4) % 187.58/29.79 (6) ~ (all_4_1 = e3) % 187.58/29.79 (7) ~ (all_38_2 = e0) % 187.58/29.79 (8) ~ (all_4_1 = e2) % 187.58/29.79 (9) op(e2, all_4_1) = e0 % 187.58/29.79 (10) op(e2, e1) = all_38_2 % 187.58/29.79 % 187.58/29.79 Begin of proof % 187.58/29.79 | % 187.58/29.79 | SIMP: (4) implies: % 187.58/29.79 | (11) ~ (all_4_1 = e0) % 187.58/29.79 | % 187.58/29.79 | BETA: splitting (3) gives: % 187.58/29.79 | % 187.58/29.79 | Case 1: % 187.58/29.79 | | % 187.58/29.79 | | (12) all_250_23 = e4 % 187.58/29.79 | | % 187.58/29.79 | | COMBINE_EQS: (2), (12) imply: % 187.58/29.79 | | (13) all_4_1 = e4 % 187.58/29.79 | | % 187.58/29.79 | | SIMP: (13) implies: % 187.58/29.79 | | (14) all_4_1 = e4 % 187.58/29.79 | | % 187.58/29.79 | | REDUCE: (5), (14) imply: % 187.58/29.79 | | (15) $false % 187.58/29.79 | | % 187.58/29.79 | | CLOSE: (15) is inconsistent. % 187.58/29.79 | | % 187.58/29.79 | Case 2: % 187.58/29.79 | | % 187.58/29.79 | | (16) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 187.58/29.79 | | e0 % 187.58/29.79 | | % 187.58/29.79 | | BETA: splitting (16) gives: % 187.58/29.79 | | % 187.58/29.79 | | Case 1: % 187.58/29.79 | | | % 187.58/29.79 | | | (17) all_250_23 = e3 % 187.58/29.79 | | | % 187.58/29.79 | | | COMBINE_EQS: (2), (17) imply: % 187.58/29.79 | | | (18) all_4_1 = e3 % 187.58/29.79 | | | % 187.58/29.79 | | | SIMP: (18) implies: % 187.58/29.79 | | | (19) all_4_1 = e3 % 187.58/29.79 | | | % 187.58/29.79 | | | REDUCE: (6), (19) imply: % 187.58/29.79 | | | (20) $false % 187.58/29.79 | | | % 187.58/29.79 | | | CLOSE: (20) is inconsistent. % 187.58/29.79 | | | % 187.58/29.79 | | Case 2: % 187.58/29.79 | | | % 187.58/29.79 | | | (21) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 187.58/29.79 | | | % 187.58/29.79 | | | BETA: splitting (21) gives: % 187.58/29.79 | | | % 187.58/29.79 | | | Case 1: % 187.58/29.79 | | | | % 187.58/29.79 | | | | (22) all_250_23 = e2 % 187.58/29.79 | | | | % 187.58/29.79 | | | | COMBINE_EQS: (2), (22) imply: % 187.58/29.79 | | | | (23) all_4_1 = e2 % 187.58/29.79 | | | | % 187.58/29.79 | | | | SIMP: (23) implies: % 187.58/29.79 | | | | (24) all_4_1 = e2 % 187.58/29.79 | | | | % 187.58/29.79 | | | | REDUCE: (8), (24) imply: % 187.58/29.79 | | | | (25) $false % 187.58/29.79 | | | | % 187.58/29.79 | | | | CLOSE: (25) is inconsistent. % 187.58/29.79 | | | | % 187.58/29.79 | | | Case 2: % 187.58/29.79 | | | | % 187.58/29.79 | | | | (26) all_250_23 = e1 | all_250_23 = e0 % 187.58/29.79 | | | | % 187.58/29.79 | | | | BETA: splitting (26) gives: % 187.58/29.79 | | | | % 187.58/29.79 | | | | Case 1: % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | (27) all_250_23 = e1 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | COMBINE_EQS: (2), (27) imply: % 187.58/29.79 | | | | | (28) all_4_1 = e1 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | SIMP: (28) implies: % 187.58/29.79 | | | | | (29) all_4_1 = e1 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | REDUCE: (9), (29) imply: % 187.58/29.79 | | | | | (30) op(e2, e1) = e0 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | REF_CLOSE: (1), (7), (10), (30) are inconsistent by sub-proof #549. % 187.58/29.79 | | | | | % 187.58/29.79 | | | | Case 2: % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | (31) all_250_23 = e0 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | COMBINE_EQS: (2), (31) imply: % 187.58/29.79 | | | | | (32) all_4_1 = e0 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | SIMP: (32) implies: % 187.58/29.79 | | | | | (33) all_4_1 = e0 % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | REDUCE: (11), (33) imply: % 187.58/29.79 | | | | | (34) $false % 187.58/29.79 | | | | | % 187.58/29.79 | | | | | CLOSE: (34) is inconsistent. % 187.58/29.79 | | | | | % 187.58/29.79 | | | | End of split % 187.58/29.79 | | | | % 187.58/29.79 | | | End of split % 187.58/29.79 | | | % 187.58/29.79 | | End of split % 187.58/29.79 | | % 187.58/29.79 | End of split % 187.58/29.79 | % 187.58/29.79 End of proof % 187.58/29.79 % 187.58/29.79 Sub-proof #2 shows that the following formulas are inconsistent: % 187.58/29.79 ---------------------------------------------------------------- % 187.58/29.79 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.58/29.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.58/29.79 (2) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 187.58/29.79 (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 187.58/29.79 $i(all_158_0)))) % 187.58/29.79 (3) op(e3, all_22_1) = e2 % 187.58/29.79 (4) all_158_2 = e3 % 187.58/29.79 (5) op(e2, e0) = all_22_1 % 187.58/29.79 (6) op(e3, e0) = all_48_2 % 187.58/29.79 (7) op(e2, e0) = e0 % 187.58/29.79 (8) op(e3, e0) = all_82_1 % 187.58/29.79 (9) ~ (all_48_2 = e2) % 187.58/29.79 % 187.58/29.79 Begin of proof % 187.58/29.79 | % 187.58/29.79 | BETA: splitting (2) gives: % 187.58/29.79 | % 187.58/29.79 | Case 1: % 187.58/29.79 | | % 187.58/29.79 | | (10) ~ (all_158_2 = e3) % 187.58/29.79 | | % 187.58/29.79 | | REDUCE: (4), (10) imply: % 187.58/29.79 | | (11) $false % 187.58/29.79 | | % 187.58/29.79 | | CLOSE: (11) is inconsistent. % 187.58/29.79 | | % 187.58/29.79 | Case 2: % 187.58/29.79 | | % 187.58/29.79 | | (12) op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ (all_158_1 = e4) | ( ~ % 187.58/29.79 | | (all_158_0 = e1) & op(e0, e4) = all_158_0 & $i(all_158_0))) % 187.58/29.80 | | % 187.58/29.80 | | ALPHA: (12) implies: % 187.58/29.80 | | (13) op(e3, e0) = all_158_1 % 187.58/29.80 | | % 187.58/29.80 | | GROUND_INST: instantiating (1) with all_22_1, e0, e0, e2, simplifying with % 187.58/29.80 | | (5), (7) gives: % 187.58/29.80 | | (14) all_22_1 = e0 % 187.58/29.80 | | % 187.58/29.80 | | GROUND_INST: instantiating (1) with all_48_2, all_158_1, e0, e3, simplifying % 187.58/29.80 | | with (6), (13) gives: % 187.58/29.80 | | (15) all_158_1 = all_48_2 % 187.58/29.80 | | % 187.58/29.80 | | GROUND_INST: instantiating (1) with all_82_1, all_158_1, e0, e3, simplifying % 187.58/29.80 | | with (8), (13) gives: % 187.58/29.80 | | (16) all_158_1 = all_82_1 % 187.58/29.80 | | % 187.58/29.80 | | COMBINE_EQS: (15), (16) imply: % 187.58/29.80 | | (17) all_82_1 = all_48_2 % 187.58/29.80 | | % 187.58/29.80 | | REDUCE: (3), (14) imply: % 187.58/29.80 | | (18) op(e3, e0) = e2 % 187.58/29.80 | | % 187.58/29.80 | | REF_CLOSE: (1), (6), (9), (18) are inconsistent by sub-proof #470. % 187.58/29.80 | | % 187.58/29.80 | End of split % 187.58/29.80 | % 187.58/29.80 End of proof % 187.58/29.80 % 187.58/29.80 Sub-proof #3 shows that the following formulas are inconsistent: % 187.58/29.80 ---------------------------------------------------------------- % 187.58/29.80 (1) ~ (all_84_2 = all_22_2) % 187.58/29.80 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.58/29.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.79/29.80 (3) op(e2, all_6_1) = e0 % 187.79/29.80 (4) all_196_1 = all_6_1 % 187.79/29.80 (5) op(e2, e3) = all_10_2 % 187.79/29.80 (6) op(e4, e3) = all_84_2 % 187.79/29.80 (7) op(e3, all_100_2) = e4 % 187.79/29.80 (8) op(e0, e3) = all_22_2 % 187.79/29.80 (9) all_12_2 = all_6_1 % 187.79/29.80 (10) all_250_1 = e4 | all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 | % 187.79/29.80 all_250_1 = e0 % 187.79/29.80 (11) ~ (all_84_2 = e2) % 187.79/29.80 (12) op(e0, all_6_1) = e4 % 187.79/29.80 (13) ~ (all_196_1 = e3) | ( ~ (all_196_0 = e1) & op(e4, e3) = all_196_0 & % 187.79/29.80 $i(all_196_0)) % 187.79/29.80 (14) ~ (all_84_2 = all_10_2) % 187.79/29.80 (15) all_250_1 = all_84_2 % 187.79/29.80 (16) op(all_84_2, all_100_2) = e3 % 187.79/29.80 (17) all_12_2 = e3 % 187.79/29.80 % 187.79/29.80 Begin of proof % 187.79/29.80 | % 187.79/29.80 | COMBINE_EQS: (9), (17) imply: % 187.79/29.80 | (18) all_6_1 = e3 % 187.79/29.80 | % 187.79/29.80 | COMBINE_EQS: (4), (18) imply: % 187.79/29.80 | (19) all_196_1 = e3 % 187.79/29.80 | % 187.79/29.80 | REDUCE: (3), (18) imply: % 187.79/29.80 | (20) op(e2, e3) = e0 % 187.79/29.80 | % 187.79/29.80 | REDUCE: (12), (18) imply: % 187.79/29.80 | (21) op(e0, e3) = e4 % 187.79/29.80 | % 187.79/29.80 | BETA: splitting (13) gives: % 187.79/29.80 | % 187.79/29.80 | Case 1: % 187.79/29.80 | | % 187.79/29.80 | | (22) ~ (all_196_1 = e3) % 187.79/29.80 | | % 187.79/29.80 | | REDUCE: (19), (22) imply: % 187.79/29.80 | | (23) $false % 187.79/29.80 | | % 187.79/29.80 | | CLOSE: (23) is inconsistent. % 187.79/29.80 | | % 187.79/29.80 | Case 2: % 187.79/29.80 | | % 187.79/29.80 | | (24) ~ (all_196_0 = e1) & op(e4, e3) = all_196_0 & $i(all_196_0) % 187.79/29.80 | | % 187.79/29.80 | | ALPHA: (24) implies: % 187.79/29.80 | | (25) ~ (all_196_0 = e1) % 187.79/29.80 | | (26) op(e4, e3) = all_196_0 % 187.79/29.80 | | % 187.79/29.80 | | GROUND_INST: instantiating (2) with all_22_2, e4, e3, e0, simplifying with % 187.79/29.80 | | (8), (21) gives: % 187.79/29.80 | | (27) all_22_2 = e4 % 187.79/29.80 | | % 187.79/29.80 | | GROUND_INST: instantiating (2) with all_10_2, e0, e3, e2, simplifying with % 187.79/29.80 | | (5), (20) gives: % 187.79/29.80 | | (28) all_10_2 = e0 % 187.79/29.80 | | % 187.79/29.80 | | GROUND_INST: instantiating (2) with all_84_2, all_196_0, e3, e4, simplifying % 187.79/29.80 | | with (6), (26) gives: % 187.79/29.80 | | (29) all_196_0 = all_84_2 % 187.79/29.80 | | % 187.79/29.80 | | REDUCE: (25), (29) imply: % 187.79/29.80 | | (30) ~ (all_84_2 = e1) % 187.79/29.80 | | % 187.79/29.80 | | REDUCE: (1), (27) imply: % 187.79/29.80 | | (31) ~ (all_84_2 = e4) % 187.79/29.80 | | % 187.79/29.80 | | REDUCE: (14), (28) imply: % 187.79/29.80 | | (32) ~ (all_84_2 = e0) % 187.79/29.80 | | % 187.79/29.80 | | BETA: splitting (10) gives: % 187.79/29.80 | | % 187.79/29.80 | | Case 1: % 187.79/29.80 | | | % 187.79/29.80 | | | (33) all_250_1 = e4 % 187.79/29.80 | | | % 187.79/29.80 | | | COMBINE_EQS: (15), (33) imply: % 187.79/29.80 | | | (34) all_84_2 = e4 % 187.79/29.80 | | | % 187.79/29.80 | | | REDUCE: (31), (34) imply: % 187.79/29.80 | | | (35) $false % 187.79/29.80 | | | % 187.79/29.80 | | | CLOSE: (35) is inconsistent. % 187.79/29.80 | | | % 187.79/29.80 | | Case 2: % 187.79/29.80 | | | % 187.79/29.80 | | | (36) ~ (all_250_1 = e4) % 187.79/29.80 | | | (37) all_250_1 = e3 | all_250_1 = e2 | all_250_1 = e1 | all_250_1 = e0 % 187.79/29.80 | | | % 187.79/29.80 | | | BETA: splitting (37) gives: % 187.79/29.80 | | | % 187.79/29.80 | | | Case 1: % 187.79/29.80 | | | | % 187.79/29.80 | | | | (38) all_250_1 = e3 % 187.79/29.80 | | | | % 187.79/29.80 | | | | COMBINE_EQS: (15), (38) imply: % 187.79/29.80 | | | | (39) all_84_2 = e3 % 187.79/29.80 | | | | % 187.79/29.80 | | | | REDUCE: (31), (39) imply: % 187.79/29.80 | | | | (40) ~ (e4 = e3) % 187.79/29.80 | | | | % 187.79/29.80 | | | | SIMP: (40) implies: % 187.79/29.80 | | | | (41) ~ (e4 = e3) % 187.79/29.80 | | | | % 187.79/29.80 | | | | REDUCE: (16), (39) imply: % 187.79/29.80 | | | | (42) op(e3, all_100_2) = e3 % 187.79/29.80 | | | | % 187.79/29.80 | | | | GROUND_INST: instantiating (2) with e4, e3, all_100_2, e3, simplifying % 187.79/29.80 | | | | with (7), (42) gives: % 187.79/29.80 | | | | (43) e4 = e3 % 187.79/29.80 | | | | % 187.79/29.80 | | | | REDUCE: (41), (43) imply: % 187.79/29.80 | | | | (44) $false % 187.79/29.80 | | | | % 187.79/29.80 | | | | CLOSE: (44) is inconsistent. % 187.79/29.80 | | | | % 187.79/29.80 | | | Case 2: % 187.79/29.80 | | | | % 187.79/29.80 | | | | (45) all_250_1 = e2 | all_250_1 = e1 | all_250_1 = e0 % 187.79/29.80 | | | | % 187.79/29.80 | | | | BETA: splitting (45) gives: % 187.79/29.80 | | | | % 187.79/29.80 | | | | Case 1: % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | (46) all_250_1 = e2 % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | COMBINE_EQS: (15), (46) imply: % 187.79/29.80 | | | | | (47) all_84_2 = e2 % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | REDUCE: (11), (47) imply: % 187.79/29.80 | | | | | (48) $false % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | CLOSE: (48) is inconsistent. % 187.79/29.80 | | | | | % 187.79/29.80 | | | | Case 2: % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | (49) all_250_1 = e1 | all_250_1 = e0 % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | BETA: splitting (49) gives: % 187.79/29.80 | | | | | % 187.79/29.80 | | | | | Case 1: % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | (50) all_250_1 = e1 % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | COMBINE_EQS: (15), (50) imply: % 187.79/29.80 | | | | | | (51) all_84_2 = e1 % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | REDUCE: (30), (51) imply: % 187.79/29.80 | | | | | | (52) $false % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | CLOSE: (52) is inconsistent. % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | Case 2: % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | (53) all_250_1 = e0 % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | COMBINE_EQS: (15), (53) imply: % 187.79/29.80 | | | | | | (54) all_84_2 = e0 % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | REDUCE: (32), (54) imply: % 187.79/29.80 | | | | | | (55) $false % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | | CLOSE: (55) is inconsistent. % 187.79/29.80 | | | | | | % 187.79/29.80 | | | | | End of split % 187.79/29.80 | | | | | % 187.79/29.80 | | | | End of split % 187.79/29.80 | | | | % 187.79/29.80 | | | End of split % 187.79/29.80 | | | % 187.79/29.80 | | End of split % 187.79/29.80 | | % 187.79/29.80 | End of split % 187.79/29.80 | % 187.79/29.80 End of proof % 187.79/29.80 % 187.79/29.80 Sub-proof #4 shows that the following formulas are inconsistent: % 187.79/29.80 ---------------------------------------------------------------- % 187.79/29.80 (1) ~ (all_244_8 = all_8_2) % 187.79/29.80 (2) ~ (all_244_8 = all_28_2) % 187.79/29.80 (3) ~ (all_62_2 = all_34_2) % 187.79/29.80 (4) ~ (all_48_2 = all_36_2) % 187.79/29.80 (5) ~ (all_144_2 = e3) | (op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ % 187.79/29.80 (all_144_1 = e0) | ( ~ (all_144_0 = e2) & op(e1, e0) = all_144_0 & % 187.79/29.80 $i(all_144_0)))) % 187.79/29.80 (6) ~ (all_26_2 = e2) % 187.79/29.80 (7) ~ (all_244_8 = e0) % 187.79/29.80 (8) ~ (all_52_2 = e2) | (op(e2, e3) = all_52_1 & $i(all_52_1) & ( ~ % 187.79/29.80 (all_52_1 = e4) | ( ~ (all_52_0 = e0) & op(e3, e4) = all_52_0 & % 187.79/29.80 $i(all_52_0)))) % 187.79/29.80 (9) op(e2, e2) = all_244_8 % 187.79/29.80 (10) ~ (all_244_15 = all_16_2) % 187.79/29.80 (11) ~ (all_84_2 = all_22_2) % 187.79/29.80 (12) all_90_2 = all_22_2 % 187.79/29.80 (13) ~ (all_36_2 = e0) | (op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 187.79/29.80 (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 187.79/29.80 $i(all_36_0)))) % 187.79/29.80 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.79/29.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.79/29.80 (15) ~ (all_162_2 = e1) | (op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ % 187.79/29.80 (all_162_1 = e4) | ( ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 187.79/29.80 $i(all_162_0)))) % 187.79/29.80 (16) op(all_48_2, all_22_2) = e0 % 187.79/29.80 (17) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | % 187.79/29.80 all_250_17 = e0 % 187.79/29.80 (18) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 187.79/29.80 (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 187.79/29.80 $i(all_102_0)))) % 187.79/29.80 (19) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 187.79/29.80 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 187.79/29.80 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 187.79/29.80 (20) ~ (all_180_2 = e4) | (op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 187.79/29.80 (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 187.79/29.80 $i(all_180_0)))) % 187.79/29.80 (21) ~ (all_16_2 = e3) | (op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ % 187.79/29.80 (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 & % 187.79/29.80 $i(all_16_0)))) % 187.79/29.80 (22) op(e0, e2) = all_28_2 % 187.79/29.80 (23) ~ (all_244_24 = e2) % 187.79/29.80 (24) op(e3, e1) = all_36_2 % 187.79/29.80 (25) ~ (e2 = e1) % 187.79/29.80 (26) op(e0, all_64_2) = e2 % 187.79/29.80 (27) all_250_21 = all_22_2 % 187.79/29.80 (28) ~ (all_244_3 = all_8_2) % 187.79/29.80 (29) all_130_2 = all_62_2 % 187.79/29.80 (30) ~ (all_100_2 = all_6_1) % 187.79/29.80 (31) op(e3, e3) = all_244_3 % 187.79/29.80 (32) ~ (all_34_2 = all_16_2) % 187.79/29.80 (33) op(e2, all_6_1) = e0 % 187.79/29.80 (34) op(e1, all_34_2) = e0 % 187.79/29.80 (35) ~ (all_62_2 = e2) | (op(e2, e1) = all_62_1 & $i(all_62_1) & ( ~ % 187.79/29.80 (all_62_1 = e4) | ( ~ (all_62_0 = e0) & op(e1, e4) = all_62_0 & % 187.79/29.80 $i(all_62_0)))) % 187.79/29.80 (36) ~ (all_244_24 = all_22_2) % 187.79/29.80 (37) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 187.79/29.80 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 187.79/29.80 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 187.79/29.80 (38) op(e1, e3) = all_62_2 % 187.79/29.80 (39) ~ (all_24_2 = e2) | (op(e2, e1) = all_24_1 & $i(all_24_1) & ( ~ % 187.79/29.80 (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e1, e3) = all_24_0 & % 187.79/29.80 $i(all_24_0)))) % 187.79/29.80 (40) op(e2, all_38_2) = e1 % 187.79/29.80 (41) ~ (all_26_2 = e0) % 187.79/29.80 (42) op(e1, e1) = all_244_15 % 187.79/29.80 (43) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 187.79/29.80 (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 187.79/29.80 $i(all_158_0)))) % 187.79/29.80 (44) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 187.79/29.80 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = % 187.79/29.80 e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 187.79/29.80 (45) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 187.79/29.80 all_250_23 = e0 % 187.79/29.80 (46) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | % 187.79/29.80 all_250_20 = e0 % 187.79/29.80 (47) all_24_2 = all_16_2 % 187.79/29.80 (48) ~ (all_20_2 = e3) | (op(e3, e0) = all_20_1 & $i(all_20_1) & ( ~ % 187.79/29.80 (all_20_1 = e4) | ( ~ (all_20_0 = e2) & op(e0, e4) = all_20_0 & % 187.79/29.80 $i(all_20_0)))) % 187.79/29.80 (49) ~ (all_48_2 = all_34_2) % 187.79/29.80 (50) ~ (e4 = e0) % 187.79/29.80 (51) all_76_2 = all_40_2 % 187.79/29.80 (52) op(e2, e3) = all_10_2 % 187.79/29.80 (53) ~ (all_244_15 = all_36_2) % 187.79/29.80 (54) all_158_2 = all_28_2 % 187.79/29.80 (55) all_152_2 = all_16_2 % 187.79/29.80 (56) ~ (all_18_2 = e2) | (op(e2, e0) = all_18_1 & $i(all_18_1) & ( ~ % 187.79/29.80 (all_18_1 = e3) | ( ~ (all_18_0 = e1) & op(e0, e3) = all_18_0 & % 187.79/29.80 $i(all_18_0)))) % 187.79/29.80 (57) all_60_2 = all_20_2 % 187.79/29.80 (58) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 187.79/29.80 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 187.79/29.80 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 187.79/29.80 (59) op(e4, e3) = all_84_2 % 187.79/29.80 (60) ~ (all_152_2 = e2) | (op(e2, e1) = all_152_1 & $i(all_152_1) & ( ~ % 187.79/29.80 (all_152_1 = e0) | ( ~ (all_152_0 = e3) & op(e1, e0) = all_152_0 & % 187.79/29.80 $i(all_152_0)))) % 187.79/29.80 (61) ~ (e4 = e3) % 187.79/29.80 (62) ~ (all_4_2 = e0) % 187.79/29.80 (63) all_78_2 = all_10_2 % 187.79/29.80 (64) ~ (all_142_2 = e1) | (op(e1, e4) = all_142_1 & $i(all_142_1) & ( ~ % 187.79/29.80 (all_142_1 = e0) | ( ~ (all_142_0 = e2) & op(e4, e0) = all_142_0 & % 187.79/29.80 $i(all_142_0)))) % 187.79/29.80 (65) ~ (all_192_2 = e4) | (op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 187.79/29.80 (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, e3) = all_192_0 & % 187.79/29.80 $i(all_192_0)))) % 187.79/29.80 (66) ~ (all_64_2 = all_16_2) % 187.79/29.80 (67) ~ (all_78_2 = e4) | (op(e4, e2) = all_78_1 & $i(all_78_1) & ( ~ % 187.79/29.80 (all_78_1 = e1) | ( ~ (all_78_0 = e0) & op(e2, e1) = all_78_0 & % 187.79/29.80 $i(all_78_0)))) % 187.79/29.80 (68) ~ (all_200_2 = e1) | (op(e1, e3) = all_200_1 & $i(all_200_1) & ( ~ % 187.79/29.80 (all_200_1 = e2) | ( ~ (all_200_0 = e4) & op(e3, e2) = all_200_0 & % 187.79/29.80 $i(all_200_0)))) % 187.79/29.80 (69) ~ (all_28_2 = all_6_1) % 187.79/29.80 (70) ~ (all_40_2 = e1) | (op(e1, e2) = all_40_1 & $i(all_40_1) & ( ~ % 187.79/29.80 (all_40_1 = e4) | ( ~ (all_40_0 = e3) & op(e2, e4) = all_40_0 & % 187.79/29.80 $i(all_40_0)))) % 187.79/29.80 (71) all_250_19 = all_34_2 % 187.79/29.80 (72) ~ (all_22_2 = e2) | (op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ % 187.79/29.80 (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & % 187.79/29.80 $i(all_22_0)))) % 187.79/29.81 (73) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 187.79/29.81 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 187.79/29.81 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 187.79/29.81 (74) ~ (all_114_2 = e4) | (op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ % 187.79/29.81 (all_114_1 = e0) | ( ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 & % 187.79/29.81 $i(all_114_0)))) % 187.79/29.81 (75) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 187.79/29.81 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 187.79/29.81 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 187.79/29.81 (76) all_252_4 = e0 % 187.79/29.81 (77) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 187.79/29.81 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 187.79/29.81 $i(all_38_0)))) % 187.79/29.81 (78) all_168_2 = all_100_2 % 187.79/29.81 (79) all_200_2 = all_48_2 % 187.79/29.81 (80) ~ (all_150_2 = e3) | (op(e3, e1) = all_150_1 & $i(all_150_1) & ( ~ % 187.79/29.81 (all_150_1 = e0) | ( ~ (all_150_0 = e4) & op(e1, e0) = all_150_0 & % 187.79/29.81 $i(all_150_0)))) % 187.79/29.81 (81) ~ (all_36_2 = all_26_2) % 187.79/29.81 (82) ~ (all_82_2 = e3) | (op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 187.79/29.81 (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, e1) = all_82_0 & % 187.79/29.81 $i(all_82_0)))) % 187.79/29.81 (83) ~ (all_66_2 = e0) | (op(e0, e1) = all_66_1 & $i(all_66_1) & ( ~ % 187.79/29.81 (all_66_1 = e3) | ( ~ (all_66_0 = e2) & op(e1, e3) = all_66_0 & % 187.79/29.81 $i(all_66_0)))) % 187.79/29.81 (84) all_58_2 = all_20_2 % 187.79/29.81 (85) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 187.79/29.81 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 187.79/29.81 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 187.79/29.81 (86) ~ (all_28_2 = all_20_2) % 187.79/29.81 (87) op(all_8_2, all_10_2) = e2 % 187.79/29.81 (88) op(e3, e4) = all_100_2 % 187.79/29.81 (89) ~ (all_46_2 = e0) | (op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ % 187.79/29.81 (all_46_1 = e2) | ( ~ (all_46_0 = e4) & op(e3, e2) = all_46_0 & % 187.79/29.81 $i(all_46_0)))) % 187.79/29.81 (90) ~ (all_20_2 = all_6_1) % 187.79/29.81 (91) ~ (all_8_2 = e0) % 187.79/29.81 (92) ~ (all_36_2 = all_20_2) % 187.79/29.81 (93) ~ (all_90_2 = e4) | (op(e4, e0) = all_90_1 & $i(all_90_1) & ( ~ % 187.79/29.81 (all_90_1 = e2) | ( ~ (all_90_0 = e1) & op(e0, e2) = all_90_0 & % 187.79/29.81 $i(all_90_0)))) % 187.79/29.81 (94) ~ (all_10_2 = e1) % 187.79/29.81 (95) op(e0, e0) = all_244_24 % 187.79/29.81 (96) all_66_2 = all_16_2 % 187.79/29.81 (97) op(e0, e1) = all_20_2 % 187.79/29.81 (98) all_142_2 = all_84_2 % 187.79/29.81 (99) all_182_2 = all_84_2 % 187.79/29.81 (100) ~ (all_8_2 = all_4_2) % 187.79/29.81 (101) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 187.79/29.81 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 187.79/29.81 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 187.79/29.81 (102) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = % 187.79/29.81 e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, % 187.79/29.81 e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 187.79/29.81 (103) op(e0, all_20_2) = e1 % 187.79/29.81 (104) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | % 187.79/29.81 all_250_9 = e0 % 187.79/29.81 (105) all_150_2 = all_4_2 % 187.79/29.81 (106) ~ (all_244_24 = all_34_2) % 187.79/29.81 (107) ~ (all_182_2 = e1) | (op(e1, e4) = all_182_1 & $i(all_182_1) & ( ~ % 187.79/29.81 (all_182_1 = e2) | ( ~ (all_182_0 = e0) & op(e4, e2) = all_182_0 & % 187.79/29.81 $i(all_182_0)))) % 187.79/29.81 (108) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 187.79/29.81 | (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = e2 & op(e3, e1) = % 187.79/29.81 e2) | (all_252_17 = e2 & op(e3, e0) = e2) % 187.79/29.81 (109) all_250_15 = all_16_2 % 187.79/29.81 (110) ~ (all_76_2 = e3) | (op(e3, e2) = all_76_1 & $i(all_76_1) & ( ~ % 187.79/29.81 (all_76_1 = e4) | ( ~ (all_76_0 = e1) & op(e2, e4) = all_76_0 & % 187.79/29.81 $i(all_76_0)))) % 187.79/29.81 (111) ~ (all_100_2 = all_64_2) % 187.79/29.81 (112) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 187.79/29.81 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 187.79/29.81 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 187.79/29.81 (113) op(all_40_2, all_28_2) = e0 % 187.79/29.81 (114) ~ (all_32_2 = e4) | (op(e4, e0) = all_32_1 & $i(all_32_1) & ( ~ % 187.79/29.81 (all_32_1 = e2) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 & % 187.79/29.81 $i(all_32_0)))) % 187.79/29.81 (115) ~ (all_244_15 = all_38_2) % 187.79/29.81 (116) op(e0, all_28_2) = e2 % 187.79/29.81 (117) all_232_2 = all_34_2 % 187.79/29.81 (118) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = % 187.79/29.81 e4) | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, % 187.79/29.81 e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 187.79/29.81 (119) op(e4, e1) = all_26_2 % 187.79/29.81 (120) op(all_4_2, all_38_2) = e2 % 187.79/29.81 (121) ~ (all_198_2 = e3) | (op(e3, e1) = all_198_1 & $i(all_198_1) & ( ~ % 187.79/29.81 (all_198_1 = e2) | ( ~ (all_198_0 = e4) & op(e1, e2) = all_198_0 & % 187.79/29.81 $i(all_198_0)))) % 187.79/29.81 (122) all_250_7 = e4 | all_250_7 = e3 | all_250_7 = e2 | all_250_7 = e1 | % 187.79/29.81 all_250_7 = e0 % 187.79/29.81 (123) op(e0, e3) = all_22_2 % 187.79/29.81 (124) op(e0, all_22_2) = e3 % 187.79/29.81 (125) op(e4, e4) = all_244_0 % 187.79/29.81 (126) ~ (all_60_2 = e2) | (op(e2, e0) = all_60_1 & $i(all_60_1) & ( ~ % 187.79/29.81 (all_60_1 = e4) | ( ~ (all_60_0 = e3) & op(e0, e4) = all_60_0 & % 187.79/29.81 $i(all_60_0)))) % 187.79/29.81 (127) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 | % 187.79/29.81 all_250_15 = e0 % 187.79/29.81 (128) ~ (all_28_2 = all_4_2) % 187.79/29.81 (129) all_192_2 = all_4_2 % 187.79/29.81 (130) op(e0, e4) = all_6_1 % 187.79/29.81 (131) ~ (all_34_2 = all_4_2) % 187.79/29.81 (132) all_250_19 = e4 | all_250_19 = e3 | all_250_19 = e2 | all_250_19 = e1 | % 187.79/29.81 all_250_19 = e0 % 187.79/29.81 (133) all_68_2 = all_22_2 % 187.79/29.81 (134) ~ (all_48_2 = all_8_2) % 187.79/29.81 (135) ~ (e3 = e0) % 187.79/29.81 (136) op(e3, e2) = all_8_2 % 187.79/29.81 (137) op(all_244_8, all_244_8) = e2 % 187.79/29.81 (138) ~ (all_28_2 = e0) % 187.79/29.81 (139) op(all_244_15, all_244_15) = e1 % 187.79/29.81 (140) all_250_9 = all_48_2 % 187.79/29.81 (141) all_250_17 = all_4_2 % 187.79/29.81 (142) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 187.79/29.81 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 187.79/29.81 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 187.79/29.81 (143) ~ (all_244_0 = e2) % 187.79/29.81 (144) op(e3, all_48_2) = e0 % 187.79/29.81 (145) ~ (all_62_2 = all_10_2) % 187.79/29.81 (146) op(e2, all_40_2) = e0 % 187.79/29.81 (147) ~ (all_244_3 = all_36_2) % 187.79/29.81 (148) op(e1, all_4_2) = e2 % 187.79/29.81 (149) op(all_10_2, all_8_2) = e3 % 187.79/29.81 (150) all_252_16 = e2 % 187.79/29.81 (151) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 187.79/29.81 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 187.79/29.81 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 187.79/29.81 (152) ~ (all_22_2 = all_6_1) % 187.79/29.81 (153) all_198_2 = all_34_2 % 187.79/29.81 (154) ~ (all_244_0 = e0) % 187.79/29.81 (155) ~ (all_244_3 = all_22_2) % 187.79/29.81 (156) all_250_20 = all_6_1 % 187.79/29.81 (157) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = % 187.79/29.81 e1) | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, % 187.79/29.81 e1) = e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 187.79/29.81 (158) ~ (all_244_3 = all_62_2) % 187.79/29.81 (159) op(e1, e4) = all_16_2 % 187.79/29.81 (160) op(e1, all_16_2) = e4 % 187.79/29.81 (161) all_114_2 = all_62_2 % 187.79/29.81 (162) ~ (all_244_15 = all_20_2) % 187.79/29.81 (163) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 187.79/29.81 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 187.79/29.81 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 187.79/29.81 (164) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = % 187.79/29.81 e0) | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, % 187.79/29.81 e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 187.79/29.81 (165) ~ (e3 = e2) % 187.79/29.81 (166) ~ (all_48_2 = all_40_2) % 187.79/29.81 (167) ~ (all_232_2 = e4) | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 187.79/29.81 (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 & % 187.79/29.81 $i(all_232_0)))) % 187.79/29.81 (168) ~ (all_130_2 = e4) | (op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ % 187.79/29.81 (all_130_1 = e2) | ( ~ (all_130_0 = e0) & op(e1, e2) = all_130_0 & % 187.79/29.81 $i(all_130_0)))) % 187.79/29.81 (169) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | % 187.79/29.81 all_250_11 = e0 % 187.79/29.81 (170) ~ (all_16_2 = all_4_2) % 187.79/29.81 (171) op(e2, all_10_2) = e3 % 187.79/29.81 (172) ~ (all_244_24 = all_28_2) % 187.79/29.81 (173) ~ (all_100_2 = all_16_2) % 187.79/29.81 (174) all_18_2 = all_6_1 % 187.79/29.81 (175) op(e4, e2) = e0 % 187.79/29.81 (176) op(all_34_2, all_20_2) = e0 % 187.79/29.81 (177) all_56_2 = all_8_2 % 187.79/29.81 (178) op(e2, e4) = all_64_2 % 187.79/29.81 (179) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 187.79/29.81 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.79/29.81 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 187.79/29.81 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 187.79/29.81 = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 187.79/29.81 op(e0, e1) = e0))) % 187.79/29.81 (180) ~ (all_168_2 = e0) | (op(e0, e3) = all_168_1 & $i(all_168_1) & ( ~ % 187.79/29.81 (all_168_1 = e2) | ( ~ (all_168_0 = e1) & op(e3, e2) = all_168_0 & % 187.79/29.81 $i(all_168_0)))) % 187.79/29.81 (181) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 187.79/29.81 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 187.79/29.81 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 187.79/29.81 (182) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2) % 187.79/29.81 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = % 187.79/29.81 e2) | (all_252_20 = e2 & op(e0, e4) = e2) % 187.79/29.81 (183) ~ (all_68_2 = e2) | (op(e2, e0) = all_68_1 & $i(all_68_1) & ( ~ % 187.79/29.81 (all_68_1 = e4) | ( ~ (all_68_0 = e1) & op(e0, e4) = all_68_0 & % 187.79/29.81 $i(all_68_0)))) % 187.79/29.81 (184) op(e2, e0) = all_40_2 % 187.79/29.81 (185) op(all_28_2, all_40_2) = e2 % 187.79/29.81 (186) op(all_22_2, all_48_2) = e3 % 187.79/29.81 (187) ~ (all_36_2 = all_8_2) % 187.79/29.81 (188) op(e4, all_26_2) = e1 % 187.79/29.81 (189) all_82_2 = all_28_2 % 187.79/29.81 (190) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 187.79/29.81 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 187.79/29.81 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 187.79/29.81 (191) op(all_20_2, all_34_2) = e1 % 187.79/29.81 (192) op(e3, e0) = all_48_2 % 187.79/29.81 (193) ~ (e1 = e0) % 187.79/29.81 (194) all_46_2 = all_36_2 % 187.79/29.81 (195) all_102_2 = all_10_2 % 187.79/29.81 (196) all_70_2 = all_62_2 % 187.79/29.81 (197) ~ (all_70_2 = e0) | (op(e0, e1) = all_70_1 & $i(all_70_1) & ( ~ % 187.79/29.81 (all_70_1 = e2) | ( ~ (all_70_0 = e4) & op(e1, e2) = all_70_0 & % 187.79/29.81 $i(all_70_0)))) % 187.79/29.81 (198) all_144_2 = all_16_2 % 187.79/29.81 (199) all_32_2 = all_20_2 % 187.79/29.81 (200) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 187.79/29.81 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 187.79/29.81 $i(all_188_0)))) % 187.79/29.81 (201) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = e4 & op(e3, e2) = e4) % 187.79/29.81 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = e4 & op(e1, e2) = % 187.79/29.81 e4) | (all_252_22 = e4 & op(e0, e2) = e4) % 187.79/29.81 (202) ~ (all_244_15 = all_34_2) % 187.79/29.81 (203) all_250_7 = all_8_2 % 187.79/29.81 (204) all_162_2 = all_28_2 % 187.79/29.81 (205) ~ (all_28_2 = all_8_2) % 187.79/29.81 (206) ~ (all_6_1 = e1) % 187.79/29.81 (207) ~ (all_100_2 = all_36_2) % 187.79/29.81 (208) op(e0, e4) = all_12_2 % 187.79/29.81 (209) op(e1, all_62_2) = e3 % 187.79/29.81 (210) op(e3, all_36_2) = e1 % 187.79/29.81 (211) ~ (all_244_0 = all_16_2) % 187.79/29.81 (212) all_250_23 = all_20_2 % 187.79/29.81 (213) ~ (e3 = e1) % 187.79/29.81 (214) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 187.79/29.81 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 187.79/29.81 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 187.79/29.81 (215) ~ (e2 = e0) % 187.79/29.81 (216) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) % 187.79/29.81 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = % 187.79/29.81 e0) | (all_252_17 = e0 & op(e3, e0) = e0) % 187.79/29.81 (217) op(e1, e0) = all_34_2 % 187.79/29.81 (218) ~ (all_38_2 = all_20_2) % 187.79/29.81 (219) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 187.79/29.81 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 187.79/29.81 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 187.79/29.81 (220) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | % 187.79/29.81 all_250_21 = e0 % 187.79/29.81 (221) ~ (all_28_2 = e1) | (op(e1, e0) = all_28_1 & $i(all_28_1) & ( ~ % 187.79/29.81 (all_28_1 = e3) | ( ~ (all_28_0 = e4) & op(e0, e3) = all_28_0 & % 187.79/29.81 $i(all_28_0)))) % 187.79/29.81 (222) all_188_2 = all_38_2 % 187.79/29.81 (223) ~ (all_28_2 = all_22_2) % 187.79/29.81 (224) ~ (all_84_2 = all_62_2) % 187.79/29.81 (225) ~ (all_16_2 = all_6_1) % 187.79/29.81 (226) op(e3, all_8_2) = e2 % 187.79/29.81 (227) ~ (all_12_2 = e3) % 187.79/29.81 (228) ~ (all_62_2 = all_16_2) % 187.79/29.81 (229) all_180_2 = all_4_2 % 187.79/29.81 (230) ~ (all_34_2 = e2) % 187.79/29.81 (231) ~ (all_56_2 = e4) | (op(e4, e3) = all_56_1 & $i(all_56_1) & ( ~ % 187.79/29.81 (all_56_1 = e0) | ( ~ (all_56_0 = e1) & op(e3, e0) = all_56_0 & % 187.79/29.81 $i(all_56_0)))) % 187.79/29.81 (232) ~ (all_34_2 = e4) | (op(e4, e1) = all_34_1 & $i(all_34_1) & ( ~ % 187.79/29.81 (all_34_1 = e2) | ( ~ (all_34_0 = e3) & op(e1, e2) = all_34_0 & % 187.79/29.81 $i(all_34_0)))) % 187.79/29.81 (233) op(e1, e2) = all_4_2 % 187.79/29.82 (234) ~ (all_22_2 = all_20_2) % 187.79/29.82 (235) ~ (all_62_2 = all_22_2) % 187.79/29.82 (236) ~ (all_244_15 = all_4_2) % 187.79/29.82 (237) op(e2, e1) = all_38_2 % 187.79/29.82 (238) ~ (all_48_2 = e2) % 187.79/29.82 (239) all_52_2 = all_36_2 % 187.79/29.82 (240) all_250_11 = all_10_2 % 187.79/29.82 (241) op(all_16_2, all_26_2) = e4 % 187.79/29.82 (242) ~ (e4 = e1) % 187.79/29.82 (243) ~ (all_22_2 = all_10_2) % 187.79/29.82 (244) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 187.79/29.82 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 187.79/29.82 $i(all_58_0)))) % 187.79/29.82 % 187.79/29.82 Begin of proof % 187.79/29.82 | % 187.79/29.82 | BETA: splitting (21) gives: % 187.79/29.82 | % 187.79/29.82 | Case 1: % 187.79/29.82 | | % 187.79/29.82 | | (245) ~ (all_16_2 = e3) % 187.79/29.82 | | % 187.79/29.82 | | BETA: splitting (56) gives: % 187.79/29.82 | | % 187.79/29.82 | | Case 1: % 187.79/29.82 | | | % 187.79/29.82 | | | (246) ~ (all_18_2 = e2) % 187.79/29.82 | | | % 187.79/29.82 | | | REDUCE: (174), (246) imply: % 187.79/29.82 | | | (247) ~ (all_6_1 = e2) % 187.79/29.82 | | | % 187.79/29.82 | | | BETA: splitting (48) gives: % 187.79/29.82 | | | % 187.79/29.82 | | | Case 1: % 187.79/29.82 | | | | % 187.79/29.82 | | | | (248) ~ (all_20_2 = e3) % 187.79/29.82 | | | | % 187.79/29.82 | | | | BETA: splitting (72) gives: % 187.79/29.82 | | | | % 187.79/29.82 | | | | Case 1: % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | (249) ~ (all_22_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REF_CLOSE: (3), (12), (13), (14), (15), (19), (20), (22), (23), (24), % 187.79/29.82 | | | | | (27), (31), (33), (34), (35), (37), (38), (39), (40), (41), % 187.79/29.82 | | | | | (42), (47), (49), (52), (53), (57), (59), (61), (62), (65), % 187.79/29.82 | | | | | (66), (71), (73), (77), (81), (84), (86), (88), (89), (92), % 187.79/29.82 | | | | | (93), (95), (97), (102), (103), (106), (112), (113), (115), % 187.79/29.82 | | | | | (117), (118), (119), (120), (123), (124), (125), (126), % 187.79/29.82 | | | | | (128), (129), (130), (131), (132), (135), (136), (138), % 187.79/29.82 | | | | | (139), (144), (145), (146), (147), (157), (158), (159), % 187.79/29.82 | | | | | (160), (162), (163), (164), (166), (167), (170), (172), % 187.79/29.82 | | | | | (173), (176), (178), (182), (184), (185), (186), (187), % 187.79/29.82 | | | | | (191), (192), (194), (196), (197), (200), (204), (207), % 187.79/29.82 | | | | | (208), (209), (210), (211), (213), (215), (216), (217), % 187.79/29.82 | | | | | (219), (220), (221), (222), (223), (224), (225), (227), % 187.79/29.82 | | | | | (229), (230), (232), (233), (234), (235), (236), (237), % 187.79/29.82 | | | | | (242), (244), (247), (248), (249) are inconsistent by % 187.79/29.82 | | | | | sub-proof #17. % 187.79/29.82 | | | | | % 187.79/29.82 | | | | Case 2: % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | (250) all_22_2 = e2 % 187.79/29.82 | | | | | (251) op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 = e1) | % 187.79/29.82 | | | | | ( ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & % 187.79/29.82 | | | | | $i(all_22_0))) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | ALPHA: (251) implies: % 187.79/29.82 | | | | | (252) op(e2, e0) = all_22_1 % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | COMBINE_EQS: (133), (250) imply: % 187.79/29.82 | | | | | (253) all_68_2 = e2 % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (155), (250) imply: % 187.79/29.82 | | | | | (254) ~ (all_244_3 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (11), (250) imply: % 187.79/29.82 | | | | | (255) ~ (all_84_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (235), (250) imply: % 187.79/29.82 | | | | | (256) ~ (all_62_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (234), (250) imply: % 187.79/29.82 | | | | | (257) ~ (all_20_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | SIMP: (257) implies: % 187.79/29.82 | | | | | (258) ~ (all_20_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (243), (250) imply: % 187.79/29.82 | | | | | (259) ~ (all_10_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | SIMP: (259) implies: % 187.79/29.82 | | | | | (260) ~ (all_10_2 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (152), (250) imply: % 187.79/29.82 | | | | | (261) ~ (all_6_1 = e2) % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | REDUCE: (124), (250) imply: % 187.79/29.82 | | | | | (262) op(e0, e2) = e3 % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | BETA: splitting (163) gives: % 187.79/29.82 | | | | | % 187.79/29.82 | | | | | Case 1: % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | | (263) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & % 187.79/29.82 | | | | | | op(e3, e3) = e2) % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | | BETA: splitting (263) gives: % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | | Case 1: % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | (264) all_252_1 = e2 & op(e4, e3) = e2 % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | REF_CLOSE: (14), (59), (255), (264) are inconsistent by sub-proof % 187.79/29.82 | | | | | | | #523. % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | Case 2: % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | (265) all_252_3 = e2 & op(e3, e3) = e2 % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | REF_CLOSE: (14), (31), (254), (265) are inconsistent by sub-proof % 187.79/29.82 | | | | | | | #496. % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | End of split % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | Case 2: % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | | (266) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 187.79/29.82 | | | | | | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | | BETA: splitting (266) gives: % 187.79/29.82 | | | | | | % 187.79/29.82 | | | | | | Case 1: % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | (267) all_252_7 = e2 & op(e2, e3) = e2 % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | REF_CLOSE: (14), (52), (260), (267) are inconsistent by sub-proof % 187.79/29.82 | | | | | | | #458. % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | Case 2: % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | (268) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 187.79/29.82 | | | | | | | op(e0, e3) = e2) % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | BETA: splitting (268) gives: % 187.79/29.82 | | | | | | | % 187.79/29.82 | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | (269) all_252_13 = e2 & op(e1, e3) = e2 % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | ALPHA: (269) implies: % 187.79/29.82 | | | | | | | | (270) op(e1, e3) = e2 % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | REF_CLOSE: (14), (38), (256), (270) are inconsistent by % 187.79/29.82 | | | | | | | | sub-proof #572. % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | (271) all_252_21 = e2 & op(e0, e3) = e2 % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | ALPHA: (271) implies: % 187.79/29.82 | | | | | | | | (272) all_252_21 = e2 % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | BETA: splitting (183) gives: % 187.79/29.82 | | | | | | | | % 187.79/29.82 | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | (273) ~ (all_68_2 = e2) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (253), (273) imply: % 187.79/29.82 | | | | | | | | | (274) $false % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | CLOSE: (274) is inconsistent. % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | (275) op(e2, e0) = all_68_1 & $i(all_68_1) & ( ~ (all_68_1 % 187.79/29.82 | | | | | | | | | = e4) | ( ~ (all_68_0 = e1) & op(e0, e4) = % 187.79/29.82 | | | | | | | | | all_68_0 & $i(all_68_0))) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | ALPHA: (275) implies: % 187.79/29.82 | | | | | | | | | (276) op(e2, e0) = all_68_1 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | GROUND_INST: instantiating (14) with all_28_2, e3, e2, e0, % 187.79/29.82 | | | | | | | | | simplifying with (22), (262) gives: % 187.79/29.82 | | | | | | | | | (277) all_28_2 = e3 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | GROUND_INST: instantiating (14) with all_40_2, all_68_1, e0, % 187.79/29.82 | | | | | | | | | e2, simplifying with (184), (276) gives: % 187.79/29.82 | | | | | | | | | (278) all_68_1 = all_40_2 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | GROUND_INST: instantiating (14) with all_22_1, all_68_1, e0, % 187.79/29.82 | | | | | | | | | e2, simplifying with (252), (276) gives: % 187.79/29.82 | | | | | | | | | (279) all_68_1 = all_22_1 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | COMBINE_EQS: (278), (279) imply: % 187.79/29.82 | | | | | | | | | (280) all_40_2 = all_22_1 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | COMBINE_EQS: (189), (277) imply: % 187.79/29.82 | | | | | | | | | (281) all_82_2 = e3 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | COMBINE_EQS: (54), (277) imply: % 187.79/29.82 | | | | | | | | | (282) all_158_2 = e3 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (2), (277) imply: % 187.79/29.82 | | | | | | | | | (283) ~ (all_244_8 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (86), (277) imply: % 187.79/29.82 | | | | | | | | | (284) ~ (all_20_2 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (205), (277) imply: % 187.79/29.82 | | | | | | | | | (285) ~ (all_8_2 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | SIMP: (285) implies: % 187.79/29.82 | | | | | | | | | (286) ~ (all_8_2 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (69), (277) imply: % 187.79/29.82 | | | | | | | | | (287) ~ (all_6_1 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | SIMP: (287) implies: % 187.79/29.82 | | | | | | | | | (288) ~ (all_6_1 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (128), (277) imply: % 187.79/29.82 | | | | | | | | | (289) ~ (all_4_2 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | SIMP: (289) implies: % 187.79/29.82 | | | | | | | | | (290) ~ (all_4_2 = e3) % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (146), (280) imply: % 187.79/29.82 | | | | | | | | | (291) op(e2, all_22_1) = e0 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | REDUCE: (116), (277) imply: % 187.79/29.82 | | | | | | | | | (292) op(e0, e3) = e2 % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | BETA: splitting (114) gives: % 187.79/29.82 | | | | | | | | | % 187.79/29.82 | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | (293) ~ (all_32_2 = e4) % 187.79/29.82 | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | REDUCE: (199), (293) imply: % 187.79/29.82 | | | | | | | | | | (294) ~ (all_20_2 = e4) % 187.79/29.82 | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | BETA: splitting (82) gives: % 187.79/29.82 | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | (295) ~ (all_82_2 = e3) % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | REDUCE: (281), (295) imply: % 187.79/29.82 | | | | | | | | | | | (296) $false % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | CLOSE: (296) is inconsistent. % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | (297) op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 187.79/29.82 | | | | | | | | | | | (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, % 187.79/29.82 | | | | | | | | | | | e1) = all_82_0 & $i(all_82_0))) % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | ALPHA: (297) implies: % 187.79/29.82 | | | | | | | | | | | (298) op(e3, e0) = all_82_1 % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | BETA: splitting (43) gives: % 187.79/29.82 | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | (299) ~ (all_158_2 = e3) % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | REDUCE: (282), (299) imply: % 187.79/29.82 | | | | | | | | | | | | (300) $false % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | CLOSE: (300) is inconsistent. % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | (301) op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 187.79/29.82 | | | | | | | | | | | | (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, % 187.79/29.82 | | | | | | | | | | | | e4) = all_158_0 & $i(all_158_0))) % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | ALPHA: (301) implies: % 187.79/29.82 | | | | | | | | | | | | (302) op(e3, e0) = all_158_1 % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | BETA: splitting (75) gives: % 187.79/29.82 | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | (303) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 187.79/29.82 | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | BETA: splitting (303) gives: % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | (304) all_252_4 = e3 & op(e4, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | ALPHA: (304) implies: % 187.79/29.82 | | | | | | | | | | | | | | (305) all_252_4 = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | COMBINE_EQS: (76), (305) imply: % 187.79/29.82 | | | | | | | | | | | | | | (306) e3 = e0 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | SIMP: (306) implies: % 187.79/29.82 | | | | | | | | | | | | | | (307) e3 = e0 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | REDUCE: (135), (307) imply: % 187.79/29.82 | | | | | | | | | | | | | | (308) $false % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | CLOSE: (308) is inconsistent. % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | (309) all_252_5 = e3 & op(e3, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | ALPHA: (309) implies: % 187.79/29.82 | | | | | | | | | | | | | | (310) op(e3, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_8_2, e3, e2, e3, % 187.79/29.82 | | | | | | | | | | | | | | simplifying with (136), (310) gives: % 187.79/29.82 | | | | | | | | | | | | | | (311) all_8_2 = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | REDUCE: (286), (311) imply: % 187.79/29.82 | | | | | | | | | | | | | | (312) $false % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | CLOSE: (312) is inconsistent. % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | End of split % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | (313) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 187.79/29.82 | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 187.79/29.82 | | | | | | | | | | | | | op(e0, e2) = e3) % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | BETA: splitting (313) gives: % 187.79/29.82 | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | (314) all_252_8 = e3 & op(e2, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | ALPHA: (314) implies: % 187.79/29.82 | | | | | | | | | | | | | | (315) op(e2, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_244_8, e3, e2, e2, % 187.79/29.82 | | | | | | | | | | | | | | simplifying with (9), (315) gives: % 187.79/29.82 | | | | | | | | | | | | | | (316) all_244_8 = e3 % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | REDUCE: (283), (316) imply: % 187.79/29.82 | | | | | | | | | | | | | | (317) $false % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | CLOSE: (317) is inconsistent. % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | (318) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 187.79/29.82 | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | BETA: splitting (318) gives: % 187.79/29.82 | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | (319) all_252_14 = e3 & op(e1, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | REF_CLOSE: (14), (233), (290), (319) are inconsistent by % 187.79/29.82 | | | | | | | | | | | | | | | sub-proof #350. % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | (320) all_252_22 = e3 & op(e0, e2) = e3 % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | ALPHA: (320) implies: % 187.79/29.82 | | | | | | | | | | | | | | | (321) all_252_22 = e3 % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_48_2, all_158_1, e0, % 187.79/29.82 | | | | | | | | | | | | | | | e3, simplifying with (192), (302) gives: % 187.79/29.82 | | | | | | | | | | | | | | | (322) all_158_1 = all_48_2 % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_82_1, all_158_1, e0, % 187.79/29.82 | | | | | | | | | | | | | | | e3, simplifying with (298), (302) gives: % 187.79/29.82 | | | | | | | | | | | | | | | (323) all_158_1 = all_82_1 % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | COMBINE_EQS: (322), (323) imply: % 187.79/29.82 | | | | | | | | | | | | | | | (324) all_82_1 = all_48_2 % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | BETA: splitting (39) gives: % 187.79/29.82 | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | (325) ~ (all_24_2 = e2) % 187.79/29.82 | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | REDUCE: (47), (325) imply: % 187.79/29.82 | | | | | | | | | | | | | | | | (326) ~ (all_16_2 = e2) % 187.79/29.82 | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 187.79/29.82 | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | (327) ~ (all_34_2 = e4) % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (17), (20), (38), (40), (62), (80), (83), % 187.79/29.82 | | | | | | | | | | | | | | | | | (96), (105), (109), (120), (127), (141), (148), % 187.79/29.82 | | | | | | | | | | | | | | | | | (159), (160), (170), (188), (217), (229), (241), % 187.79/29.82 | | | | | | | | | | | | | | | | | (242), (245), (256), (326), (327) are inconsistent % 187.79/29.82 | | | | | | | | | | | | | | | | | by sub-proof #569. % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | Case 2: % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | (328) all_34_2 = e4 % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (328) imply: % 187.79/29.82 | | | | | | | | | | | | | | | | | (329) all_232_2 = e4 % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | REDUCE: (106), (328) imply: % 187.79/29.82 | | | | | | | | | | | | | | | | | (330) ~ (all_244_24 = e4) % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | REDUCE: (230), (328) imply: % 187.79/29.82 | | | | | | | | | | | | | | | | | (331) ~ (e4 = e2) % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | REDUCE: (34), (328) imply: % 187.79/29.82 | | | | | | | | | | | | | | | | | (332) op(e1, e4) = e0 % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 187.79/29.82 | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | | (333) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 187.79/29.82 | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 187.79/29.82 | | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | | BETA: splitting (333) gives: % 187.79/29.82 | | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.82 | | | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | | | (334) all_252_20 = e4 & op(e0, e4) = e4 % 187.79/29.82 | | | | | | | | | | | | | | | | | | | % 187.79/29.82 | | | | | | | | | | | | | | | | | | | ALPHA: (334) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (335) op(e0, e4) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (33), (66), (130), (159), (167), (178), % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (329), (332), (335) are inconsistent by sub-proof % 187.79/29.83 | | | | | | | | | | | | | | | | | | | #19. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (336) all_252_21 = e4 & op(e0, e3) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (337) op(e0, e3) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (292), (331), (337) are inconsistent by % 187.79/29.83 | | | | | | | | | | | | | | | | | | | sub-proof #330. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | (338) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 187.79/29.83 | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 187.79/29.83 | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (339) all_252_22 = e4 & op(e0, e2) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (340) op(e0, e2) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (61), (262), (340) are inconsistent by % 187.79/29.83 | | | | | | | | | | | | | | | | | | | sub-proof #328. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (341) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (342) all_252_23 = e4 & op(e0, e1) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (97), (294), (342) are inconsistent by % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | sub-proof #518. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (343) all_252_24 = e4 & op(e0, e0) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (95), (330), (343) are inconsistent by % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | sub-proof #18. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | (344) all_24_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | (345) op(e2, e1) = all_24_1 & $i(all_24_1) & ( ~ % 187.79/29.83 | | | | | | | | | | | | | | | | (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e1, % 187.79/29.83 | | | | | | | | | | | | | | | | e3) = all_24_0 & $i(all_24_0))) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | ALPHA: (345) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | (346) op(e2, e1) = all_24_1 % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (344) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (347) all_16_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | SIMP: (347) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | (348) all_16_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (55), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (349) all_152_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | REDUCE: (10), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (350) ~ (all_244_15 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | REDUCE: (173), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (351) ~ (all_100_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | REDUCE: (66), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (352) ~ (all_64_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | REDUCE: (170), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (353) ~ (all_4_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | SIMP: (353) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | (354) ~ (all_4_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | REDUCE: (245), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (355) ~ (e3 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | REDUCE: (160), (348) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | (356) op(e1, e2) = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | (357) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = % 187.79/29.83 | | | | | | | | | | | | | | | | | e2 & op(e3, e4) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (88), (125), (143), (351), (357) are % 187.79/29.83 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #325. % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | (358) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = % 187.79/29.83 | | | | | | | | | | | | | | | | | e2 & op(e1, e4) = e2) | (all_252_20 = e2 & % 187.79/29.83 | | | | | | | | | | | | | | | | | op(e0, e4) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | BETA: splitting (358) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | (359) all_252_6 = e2 & op(e2, e4) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (178), (352), (359) are inconsistent by % 187.79/29.83 | | | | | | | | | | | | | | | | | | sub-proof #467. % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | (360) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 % 187.79/29.83 | | | | | | | | | | | | | | | | | | = e2 & op(e0, e4) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (361) all_252_12 = e2 & op(e1, e4) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (362) all_252_12 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | (363) op(e1, e4) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (364) ~ (all_152_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (364) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (365) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | CLOSE: (365) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (366) op(e2, e1) = all_152_1 & $i(all_152_1) & ( ~ % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (all_152_1 = e0) | ( ~ (all_152_0 = e3) & op(e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | e0) = all_152_0 & $i(all_152_0))) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | (367) op(e2, e1) = all_152_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (368) ~ (all_182_2 = e1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (99), (368) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (369) ~ (all_84_2 = e1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_4_2, e4, e2, e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | simplifying with (233), (356) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (370) all_4_2 = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_38_2, all_152_1, e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (237), (367) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (371) all_152_1 = all_38_2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_24_1, all_152_1, e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | e2, simplifying with (346), (367) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (372) all_152_1 = all_24_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (371), (372) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (373) all_38_2 = all_24_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | SIMP: (373) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (374) all_38_2 = all_24_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (229), (370) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (375) all_180_2 = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (129), (370) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (376) all_192_2 = e4 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (115), (374) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (377) ~ (all_244_15 = all_24_1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (236), (370) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (378) ~ (all_244_15 = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (218), (374) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (379) ~ (all_24_1 = all_20_2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (131), (370) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (380) ~ (all_34_2 = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (370) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (381) ~ (all_8_2 = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | REDUCE: (354), (370) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | (382) ~ (e4 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | (383) ~ (all_180_2 = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (383) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | (384) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (384) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | (385) op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | e0) = all_180_0 & $i(all_180_0))) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (385) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | (386) op(e4, e1) = all_180_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (387) ~ (all_192_2 = e4) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (387) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (388) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (388) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (389) op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_192_0 & $i(all_192_0))) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (389) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (390) op(e4, e1) = all_192_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_26_2, all_192_1, e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | e4, simplifying with (119), (390) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (391) all_192_1 = all_26_2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_180_1, all_192_1, e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | e4, simplifying with (386), (390) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (392) all_192_1 = all_180_1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (391), (392) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | (393) all_180_1 = all_26_2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | (394) ~ (all_36_2 = e0) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | (395) ~ (all_38_2 = e0) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (396) ~ (all_40_2 = e1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) ~ (all_52_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (239), (397) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) ~ (all_36_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (88), (254), (351), (399) are % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #465. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 & % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (400) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_252_5 = e2 & op(e3, e2) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (401) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) op(e3, e2) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (24), (119), (398), (403) are % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #556. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (404) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) all_252_11 = e2 & op(e2, e1) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (406) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_252_4 = e1 & op(e4, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (407) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) all_252_4 = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (408) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) e1 = e0 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (409) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) e1 = e0 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (193), (410) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (411) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_252_5 = e1 & op(e3, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) op(e3, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (136), (402), (413) are inconsistent % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #464. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (414) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) all_252_8 = e1 & op(e2, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (415) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) op(e2, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (405) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) op(e2, e1) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_24_1, e2, e1, e2, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (346), (417) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (418) all_24_1 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_244_8, e1, e2, e2, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (9), (416) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (419) all_244_8 = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (137), (419) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (420) op(e1, e1) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (350), (420) are inconsistent by % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #515. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (421) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (421) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_252_14 = e1 & op(e1, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (422) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (423) op(e1, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with e4, e1, e2, e1, % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (356), (423) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (424) e4 = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (242), (424) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (425) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (425) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426) all_252_22 = e1 & op(e0, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (426) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_252_22 = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (321), (427) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) e3 = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (428) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (429) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (97), (258), (350), (430) are % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (192), (238), (398), (431) are % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #469. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) all_52_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (239), (432) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (433) all_36_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (433) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (434) all_36_2 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (81), (434) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (435) ~ (all_26_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (187), (434) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (436) ~ (all_8_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (436) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (437) ~ (all_8_2 = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (210), (434) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | (438) op(e3, e2) = e1 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (439) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e2) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (439) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (440) all_252_4 = e2 & op(e4, e2) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (440) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_252_4 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (76), (441) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) e2 = e0 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (442) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (443) e2 = e0 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (443) imply: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) $false % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (444) is inconsistent. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) all_252_5 = e2 & op(e3, e2) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) op(e3, e2) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (136), (438), (446) are inconsistent % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #464. % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e2) = e2) | (all_252_22 = e2 & % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e2) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (447) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_252_8 = e2 & op(e2, e2) = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (448) implies: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) all_252_8 = e2 % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (121) gives: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) ~ (all_198_2 = e3) % 187.79/29.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (153), (450) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) ~ (all_34_2 = e3) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_252_9 = e2 & op(e4, e1) = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (119), (453) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #558. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_252_10 = e2 & op(e3, e1) = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_252_10 = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) all_250_7 = e4 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (381), (456) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #16. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) ~ (all_250_7 = e4) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) all_250_7 = e3 | all_250_7 = e2 | all_250_7 = e1 | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_250_7 = e3 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (286), (459) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #15. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) ~ (all_250_7 = e3) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) all_250_7 = e2 | all_250_7 = e1 | all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_250_7 = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (437), (462) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #14. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) ~ (all_250_7 = e2) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_250_7 = e1 | all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (464) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) all_250_7 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (465) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_8_2 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (466) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_8_2 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (467) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) ~ (all_244_3 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (467) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) ~ (all_244_8 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (467) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) ~ (e4 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (286), (467) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) ~ (e3 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (467) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) ~ (e2 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (59), (369), (468), (473) are % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (474) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_252_7 = e1 & op(e2, e3) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) op(e2, e3) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (52), (94), (476) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (477) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_252_13 = e1 & op(e1, e3) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_252_13 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) ~ (all_168_2 = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (480) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) ~ (all_100_2 = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (41), (119), (394), (482) are % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #451. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_252_11 = e0 & op(e2, e1) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) op(e2, e1) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (237), (395), (485) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #549. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_252_15 = e0 & op(e1, e1) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) all_252_15 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (135), (142), (159), (213), (217), (233), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245), (290), (451), (479), (488) are inconsistent % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #12. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_252_23 = e0 & op(e0, e1) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (489) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) op(e0, e1) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_252_0 = e0 & op(e4, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (125), (154), (492) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #343. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_252_2 = e0 & op(e3, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (88), (481), (493) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (494) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_252_6 = e0 & op(e2, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (23), (26), (37), (42), (44), (50), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (61), (94), (95), (118), (119), (135), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (178), (184), (193), (213), (237), (242), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378), (382), (396), (455), (469), (490), (495) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #11. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (496) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) all_252_12 = e0 & op(e1, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (362), (497) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #320. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) all_252_20 = e0 & op(e0, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (25), (31), (41), (50), (52), (59), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (94), (97), (101), (102), (119), (135), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (142), (151), (159), (164), (193), (213), (217), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (242), (245), (262), (290), (292), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (321), (369), (382), (394), (395), (451), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468), (498) are inconsistent by sub-proof #9. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_168_2 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (33), (46), (78), (111), (156), (178), % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (247), (288), (499) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_252_21 = e1 & op(e0, e3) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) op(e0, e3) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (292), (501) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (203), (502) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (503) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_252_11 = e2 & op(e2, e1) = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (504) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_252_11 = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) all_250_7 = e4 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (381), (506) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #16. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) ~ (all_250_7 = e4) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_250_7 = e3 | all_250_7 = e2 | all_250_7 = e1 | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_250_7 = e3 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (286), (509) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #15. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) ~ (all_250_7 = e3) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_250_7 = e2 | all_250_7 = e1 | all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (511) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_250_7 = e2 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (437), (512) are inconsistent by sub-proof % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #14. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) ~ (all_250_7 = e2) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) all_250_7 = e1 | all_250_7 = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (515) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_252_6 = e1 & op(e2, e4) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (516) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) op(e2, e4) = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (514) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_250_7 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (518) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) all_8_2 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (519) implies: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) all_8_2 = e1 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (520) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) ~ (all_244_3 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (520) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) ~ (e4 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (286), (520) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) ~ (e3 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (520) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) ~ (e2 = e1) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) ~ (all_168_2 = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (525) imply: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_100_2 = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (527) gives: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_252_0 = e0 & op(e4, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (125), (154), (528) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #343. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_252_2 = e0 & op(e3, e4) = e0 % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (88), (526), (529) are inconsistent by % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.79/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (530) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (530) gives: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (531) all_252_6 = e0 & op(e2, e4) = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (531) implies: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (532) op(e2, e4) = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (193), (517), (532) are inconsistent by % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #360. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (533) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (533) gives: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_252_12 = e0 & op(e1, e4) = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_252_12 = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (362), (535) are inconsistent by sub-proof % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #81. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) all_252_20 = e0 & op(e0, e4) = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (25), (31), (41), (50), (52), (59), % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (94), (97), (101), (102), (119), (135), % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (142), (151), (159), (164), (193), (213), (217), % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (237), (242), (245), (262), (290), (292), % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294), (321), (369), (382), (394), (395), (451), % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521), (536) are inconsistent by sub-proof #9. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_168_2 = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (33), (46), (78), (111), (156), (178), % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (247), (288), (537) are inconsistent by % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_250_7 = e0 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (203), (538) are inconsistent by sub-proof % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_252_7 = e1 & op(e2, e3) = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) op(e2, e3) = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (52), (94), (540) are inconsistent by % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (541) gives: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_252_8 = e1 & op(e2, e2) = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_252_8 = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (449), (543) imply: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) e2 = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (544) imply: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) $false % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (545) is inconsistent. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (546) gives: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) all_252_11 = e1 & op(e2, e1) = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (505), (547) are inconsistent by sub-proof % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #357. % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_252_18 = e1 & op(e2, e0) = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies: % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) op(e2, e0) = e1 % 187.99/29.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (184), (396), (549) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #516. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (97), (258), (350), (550) are % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_198_2 = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (153), (551) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_34_2 = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (552) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) all_34_2 = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (202), (553) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) ~ (all_244_15 = e3) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (380), (553) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) ~ (e4 = e3) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_250_7 = e4 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (381), (556) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #16. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) ~ (all_250_7 = e4) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_250_7 = e3 | all_250_7 = e2 | all_250_7 = e1 | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_250_7 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (558) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) all_250_7 = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (286), (559) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #15. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) ~ (all_250_7 = e3) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_250_7 = e2 | all_250_7 = e1 | all_250_7 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (561) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_250_7 = e2 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (203), (437), (562) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #14. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) ~ (all_250_7 = e2) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_250_7 = e1 | all_250_7 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (565) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) all_252_12 = e3 & op(e1, e4) = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (159), (245), (566) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #513. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (567) all_252_13 = e3 & op(e1, e3) = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_252_13 = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (564) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_250_7 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (569) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_8_2 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (570) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (571) all_8_2 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (28), (571) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (572) ~ (all_244_3 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (286), (571) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (573) ~ (e3 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (571) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (574) ~ (e2 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (575) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (59), (369), (572), (575) are % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #13. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (576) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (576) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_252_7 = e1 & op(e2, e3) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (577) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (578) op(e2, e3) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (52), (94), (578) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (579) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (579) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_252_13 = e1 & op(e1, e3) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (213), (568), (580) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #175. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_252_21 = e1 & op(e0, e3) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (581) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) op(e0, e3) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (292), (582) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #10. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) all_250_7 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (203), (583) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (584) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_252_14 = e3 & op(e1, e2) = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (233), (290), (585) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #350. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_252_15 = e3 & op(e1, e1) = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) op(e1, e1) = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (554), (588) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #443. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_252_19 = e3 & op(e1, e0) = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (589) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) all_252_19 = e3 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (564) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (591) all_250_7 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (203), (591) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (592) all_8_2 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (592) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (593) all_8_2 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (593) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (594) ~ (all_244_8 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (593) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (595) ~ (all_48_2 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (381), (593) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (596) ~ (e4 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (286), (593) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (597) ~ (e3 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (437), (593) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (598) ~ (e2 = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (599) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (599) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (600) all_252_16 = e1 & op(e4, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (600) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (601) all_252_16 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (601) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (602) e2 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (602) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (603) $false % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (603) is inconsistent. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (604) all_252_17 = e1 & op(e3, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (604) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (605) op(e3, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_48_2, e1, e0, e3, % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (192), (605) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_48_2 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (595), (606) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (607) $false % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (607) is inconsistent. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (608) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (608) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_252_18 = e1 & op(e2, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) op(e2, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (184), (396), (610) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #516. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_252_19 = e1 & op(e1, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_252_19 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (590), (613) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) e3 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (213), (614) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) $false % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (615) is inconsistent. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_252_24 = e1 & op(e0, e0) = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_252_24 = e1 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (618) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_252_20 = e4 & op(e0, e4) = e4 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (619) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_252_20 = e4 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) ~ (all_168_2 = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (78), (621) imply: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) ~ (all_100_2 = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_252_24 = e0 & op(e0, e0) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (623) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_252_24 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (617), (624) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #139. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (627) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_252_20 = e0 & op(e0, e4) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (628) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_252_20 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (620), (629) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #525. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) all_252_21 = e0 & op(e0, e3) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (630) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) all_252_21 = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (272), (631) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #27. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) all_252_22 = e0 & op(e0, e2) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (633) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) op(e0, e2) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (138), (634) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_252_23 = e0 & op(e0, e1) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (635) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) op(e0, e1) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (31), (88), (254), (351), (637) are % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #465. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_252_5 = e2 & op(e3, e2) = e2) | (all_252_10 = % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) | (all_252_17 = e2 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e2) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_252_5 = e2 & op(e3, e2) = e2 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) op(e3, e2) = e2 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (136), (438), (640) are inconsistent % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #464. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e3, e0) = e2) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_252_10 = e2 & op(e3, e1) = e2 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (642) implies: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_252_10 = e2 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e4) = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (644) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_252_0 = e0 & op(e4, e4) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (125), (154), (645) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #343. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_252_2 = e0 & op(e3, e4) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (88), (622), (646) are inconsistent by % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (647) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_252_6 = e0 & op(e2, e4) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (14), (23), (26), (37), (42), (44), (50), % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (61), (94), (95), (118), (119), (135), % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (178), (184), (193), (213), (237), (242), % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (378), (382), (396), (594), (636), (643), (648) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #11. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e4) = e0) % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (649) gives: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_252_12 = e0 & op(e1, e4) = e0 % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (215), (362), (650) are inconsistent by sub-proof % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #320. % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_252_20 = e0 & op(e0, e4) = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (651) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_252_20 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (620), (652) are inconsistent by sub-proof % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #525. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_252_17 = e2 & op(e3, e0) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) op(e3, e0) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (192), (238), (654) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #470. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_168_2 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (30), (33), (46), (78), (111), (156), (178), % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (247), (288), (655) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #8. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_252_21 = e4 & op(e0, e3) = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) op(e0, e3) = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (292), (382), (657) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #330. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e4) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (658) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_252_22 = e4 & op(e0, e2) = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (659) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) op(e0, e2) = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (61), (262), (660) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #328. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (661) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_252_23 = e4 & op(e0, e1) = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (97), (294), (662) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #518. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_252_24 = e4 & op(e0, e0) = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (663) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_252_24 = e4 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (617), (664) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) e4 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (242), (665) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) $false % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (666) is inconsistent. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_250_7 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (203), (667) are inconsistent by sub-proof % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #7. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e2) = e2) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (668) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_252_14 = e2 & op(e1, e2) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (669) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) op(e1, e2) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_4_2, e2, e2, e1, % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (233), (670) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_4_2 = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (370), (671) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) e4 = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (382), (672) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) $false % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (673) is inconsistent. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_252_22 = e2 & op(e0, e2) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (674) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) op(e0, e2) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (138), (146), (185), (675) are % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #288. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (676) all_40_2 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (280), (676) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (677) all_22_1 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (677) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_22_1 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (291), (678) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (679) op(e2, e1) = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (237), (395), (679) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #549. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_38_2 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (374), (680) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_24_1 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (681) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_24_1 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (379), (682) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | (683) ~ (all_20_2 = e0) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (683) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | (684) ~ (all_20_2 = e0) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (34), (45), (191), (212), (248), (258), % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | (294), (684) are inconsistent by sub-proof #485. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | (685) all_36_2 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (92), (685) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | (686) ~ (all_20_2 = e0) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (686) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | (687) ~ (all_20_2 = e0) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (34), (45), (191), (212), (248), (258), % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | (294), (687) are inconsistent by sub-proof #485. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (688) all_182_2 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (689) op(e1, e4) = all_182_1 & $i(all_182_1) & ( ~ % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (all_182_1 = e2) | ( ~ (all_182_0 = e0) & op(e4, % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | e2) = all_182_0 & $i(all_182_0))) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | ALPHA: (689) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (690) op(e1, e4) = all_182_1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (691) ~ (all_182_1 = e2) | ( ~ (all_182_0 = e0) & % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | op(e4, e2) = all_182_0 & $i(all_182_0)) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (688) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (692) all_84_2 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | SIMP: (692) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (693) all_84_2 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (693) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | (694) all_142_2 = e1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (691) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | (695) ~ (all_182_1 = e2) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (696) ~ (all_142_2 = e1) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (694), (696) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (697) $false % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (697) is inconsistent. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (698) op(e1, e4) = all_142_1 & $i(all_142_1) & ( ~ % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (all_142_1 = e0) | ( ~ (all_142_0 = e2) & op(e4, % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_142_0 & $i(all_142_0))) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (698) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (699) op(e1, e4) = all_142_1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_142_1, all_182_1, e4, % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (690), (699) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (700) all_182_1 = all_142_1 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with e2, all_182_1, e4, e1, % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | simplifying with (363), (690) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (701) all_182_1 = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (700), (701) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (702) all_142_1 = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (695), (701) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | (703) $false % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (703) is inconsistent. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | (704) ~ (all_182_0 = e0) & op(e4, e2) = all_182_0 & % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_182_0) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (704) implies: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | (705) ~ (all_182_0 = e0) % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | (706) op(e4, e2) = all_182_0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with e0, all_182_0, e2, e4, % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | simplifying with (175), (706) gives: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | (707) all_182_0 = e0 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (705), (707) imply: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | (708) $false % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (708) is inconsistent. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | (709) all_252_20 = e2 & op(e0, e4) = e2 % 187.99/29.86 | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (130), (247), (709) are inconsistent by % 187.99/29.86 | | | | | | | | | | | | | | | | | | | sub-proof #22. % 187.99/29.86 | | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | (710) all_32_2 = e4 % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | COMBINE_EQS: (199), (710) imply: % 187.99/29.86 | | | | | | | | | | (711) all_20_2 = e4 % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REF_CLOSE: (14), (46), (90), (103), (130), (156), (206), % 187.99/29.86 | | | | | | | | | | (247), (288), (711) are inconsistent by sub-proof % 187.99/29.86 | | | | | | | | | | #6. % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | End of split % 187.99/29.86 | | | | | | | | | % 187.99/29.86 | | | | | | | | End of split % 187.99/29.86 | | | | | | | | % 187.99/29.86 | | | | | | | End of split % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | End of split % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | End of split % 187.99/29.86 | | | | | % 187.99/29.86 | | | | End of split % 187.99/29.86 | | | | % 187.99/29.86 | | | Case 2: % 187.99/29.86 | | | | % 187.99/29.86 | | | | (712) all_20_2 = e3 % 187.99/29.86 | | | | % 187.99/29.86 | | | | REF_CLOSE: (14), (22), (23), (25), (95), (103), (123), (124), (130), % 187.99/29.86 | | | | (138), (146), (165), (185), (219), (247), (712) are % 187.99/29.86 | | | | inconsistent by sub-proof #5. % 187.99/29.86 | | | | % 187.99/29.86 | | | End of split % 187.99/29.86 | | | % 187.99/29.86 | | Case 2: % 187.99/29.86 | | | % 187.99/29.86 | | | (713) all_18_2 = e2 % 187.99/29.86 | | | % 187.99/29.86 | | | COMBINE_EQS: (174), (713) imply: % 187.99/29.86 | | | (714) all_6_1 = e2 % 187.99/29.86 | | | % 187.99/29.86 | | | REDUCE: (33), (714) imply: % 187.99/29.86 | | | (715) op(e2, e2) = e0 % 187.99/29.86 | | | % 187.99/29.86 | | | REF_CLOSE: (7), (9), (14), (715) are inconsistent by sub-proof #448. % 187.99/29.86 | | | % 187.99/29.86 | | End of split % 187.99/29.86 | | % 187.99/29.86 | Case 2: % 187.99/29.86 | | % 187.99/29.86 | | (716) all_16_2 = e3 % 187.99/29.86 | | (717) op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e2) | ( ~ % 187.99/29.86 | | (all_16_0 = e0) & op(e1, e2) = all_16_0 & $i(all_16_0))) % 187.99/29.86 | | % 187.99/29.86 | | ALPHA: (717) implies: % 187.99/29.86 | | (718) op(e3, e1) = all_16_1 % 187.99/29.86 | | % 187.99/29.86 | | COMBINE_EQS: (198), (716) imply: % 187.99/29.86 | | (719) all_144_2 = e3 % 187.99/29.86 | | % 187.99/29.86 | | REDUCE: (10), (716) imply: % 187.99/29.86 | | (720) ~ (all_244_15 = e3) % 187.99/29.86 | | % 187.99/29.86 | | REDUCE: (228), (716) imply: % 187.99/29.86 | | (721) ~ (all_62_2 = e3) % 187.99/29.86 | | % 187.99/29.86 | | REDUCE: (32), (716) imply: % 187.99/29.86 | | (722) ~ (all_34_2 = e3) % 187.99/29.86 | | % 187.99/29.86 | | REDUCE: (170), (716) imply: % 187.99/29.86 | | (723) ~ (all_4_2 = e3) % 187.99/29.86 | | % 187.99/29.86 | | SIMP: (723) implies: % 187.99/29.86 | | (724) ~ (all_4_2 = e3) % 187.99/29.86 | | % 187.99/29.86 | | REDUCE: (160), (716) imply: % 187.99/29.86 | | (725) op(e1, e3) = e4 % 187.99/29.86 | | % 187.99/29.86 | | BETA: splitting (142) gives: % 187.99/29.86 | | % 187.99/29.86 | | Case 1: % 187.99/29.86 | | | % 187.99/29.86 | | | (726) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, % 187.99/29.86 | | | e3) = e3) % 187.99/29.86 | | | % 187.99/29.86 | | | BETA: splitting (726) gives: % 187.99/29.86 | | | % 187.99/29.86 | | | Case 1: % 187.99/29.86 | | | | % 187.99/29.86 | | | | (727) all_252_12 = e3 & op(e1, e4) = e3 % 187.99/29.86 | | | | % 187.99/29.86 | | | | ALPHA: (727) implies: % 187.99/29.86 | | | | (728) all_252_12 = e3 % 187.99/29.86 | | | | % 187.99/29.86 | | | | BETA: splitting (5) gives: % 187.99/29.86 | | | | % 187.99/29.86 | | | | Case 1: % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | (729) ~ (all_144_2 = e3) % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | REDUCE: (719), (729) imply: % 187.99/29.86 | | | | | (730) $false % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | CLOSE: (730) is inconsistent. % 187.99/29.86 | | | | | % 187.99/29.86 | | | | Case 2: % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | (731) op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ (all_144_1 = e0) % 187.99/29.86 | | | | | | ( ~ (all_144_0 = e2) & op(e1, e0) = all_144_0 & % 187.99/29.86 | | | | | $i(all_144_0))) % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | ALPHA: (731) implies: % 187.99/29.86 | | | | | (732) op(e3, e1) = all_144_1 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | GROUND_INST: instantiating (14) with all_62_2, e4, e3, e1, simplifying % 187.99/29.86 | | | | | with (38), (725) gives: % 187.99/29.86 | | | | | (733) all_62_2 = e4 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | GROUND_INST: instantiating (14) with all_36_2, all_144_1, e1, e3, % 187.99/29.86 | | | | | simplifying with (24), (732) gives: % 187.99/29.86 | | | | | (734) all_144_1 = all_36_2 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | GROUND_INST: instantiating (14) with all_16_1, all_144_1, e1, e3, % 187.99/29.86 | | | | | simplifying with (718), (732) gives: % 187.99/29.86 | | | | | (735) all_144_1 = all_16_1 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | COMBINE_EQS: (734), (735) imply: % 187.99/29.86 | | | | | (736) all_36_2 = all_16_1 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | SIMP: (736) implies: % 187.99/29.86 | | | | | (737) all_36_2 = all_16_1 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | COMBINE_EQS: (161), (733) imply: % 187.99/29.86 | | | | | (738) all_114_2 = e4 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | COMBINE_EQS: (29), (733) imply: % 187.99/29.86 | | | | | (739) all_130_2 = e4 % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | REDUCE: (235), (733) imply: % 187.99/29.86 | | | | | (740) ~ (all_22_2 = e4) % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | SIMP: (740) implies: % 187.99/29.86 | | | | | (741) ~ (all_22_2 = e4) % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | REDUCE: (92), (737) imply: % 187.99/29.86 | | | | | (742) ~ (all_20_2 = all_16_1) % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | SIMP: (742) implies: % 187.99/29.86 | | | | | (743) ~ (all_20_2 = all_16_1) % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | BETA: splitting (74) gives: % 187.99/29.86 | | | | | % 187.99/29.86 | | | | | Case 1: % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | (744) ~ (all_114_2 = e4) % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | REDUCE: (738), (744) imply: % 187.99/29.86 | | | | | | (745) $false % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | CLOSE: (745) is inconsistent. % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | Case 2: % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | (746) op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ (all_114_1 = % 187.99/29.86 | | | | | | e0) | ( ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 & % 187.99/29.86 | | | | | | $i(all_114_0))) % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | ALPHA: (746) implies: % 187.99/29.86 | | | | | | (747) op(e4, e1) = all_114_1 % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | BETA: splitting (168) gives: % 187.99/29.86 | | | | | | % 187.99/29.86 | | | | | | Case 1: % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | (748) ~ (all_130_2 = e4) % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | REDUCE: (739), (748) imply: % 187.99/29.86 | | | | | | | (749) $false % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | CLOSE: (749) is inconsistent. % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | Case 2: % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | (750) op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ (all_130_1 = % 187.99/29.86 | | | | | | | e2) | ( ~ (all_130_0 = e0) & op(e1, e2) = all_130_0 & % 187.99/29.86 | | | | | | | $i(all_130_0))) % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | ALPHA: (750) implies: % 187.99/29.86 | | | | | | | (751) op(e4, e1) = all_130_1 % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | GROUND_INST: instantiating (14) with all_26_2, all_130_1, e1, e4, % 187.99/29.86 | | | | | | | simplifying with (119), (751) gives: % 187.99/29.86 | | | | | | | (752) all_130_1 = all_26_2 % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | GROUND_INST: instantiating (14) with all_114_1, all_130_1, e1, e4, % 187.99/29.86 | | | | | | | simplifying with (747), (751) gives: % 187.99/29.86 | | | | | | | (753) all_130_1 = all_114_1 % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | COMBINE_EQS: (752), (753) imply: % 187.99/29.86 | | | | | | | (754) all_114_1 = all_26_2 % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | BETA: splitting (56) gives: % 187.99/29.86 | | | | | | | % 187.99/29.86 | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | % 187.99/29.86 | | | | | | | | (755) ~ (all_18_2 = e2) % 187.99/29.86 | | | | | | | | % 187.99/29.86 | | | | | | | | REDUCE: (174), (755) imply: % 187.99/29.86 | | | | | | | | (756) ~ (all_6_1 = e2) % 187.99/29.86 | | | | | | | | % 187.99/29.86 | | | | | | | | BETA: splitting (48) gives: % 187.99/29.86 | | | | | | | | % 187.99/29.86 | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | % 187.99/29.86 | | | | | | | | | (757) ~ (all_20_2 = e3) % 187.99/29.86 | | | | | | | | | % 187.99/29.86 | | | | | | | | | BETA: splitting (72) gives: % 187.99/29.86 | | | | | | | | | % 187.99/29.86 | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | (758) ~ (all_22_2 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REF_CLOSE: (3), (12), (13), (14), (15), (19), (20), (22), % 187.99/29.86 | | | | | | | | | | (23), (24), (27), (31), (33), (34), (35), (37), % 187.99/29.86 | | | | | | | | | | (38), (39), (40), (41), (42), (47), (49), (52), % 187.99/29.86 | | | | | | | | | | (53), (57), (59), (61), (62), (65), (66), (71), % 187.99/29.86 | | | | | | | | | | (73), (77), (81), (84), (86), (88), (89), (92), % 187.99/29.86 | | | | | | | | | | (93), (95), (97), (102), (103), (106), (112), % 187.99/29.86 | | | | | | | | | | (113), (115), (117), (118), (119), (120), (123), % 187.99/29.86 | | | | | | | | | | (124), (125), (126), (128), (129), (130), (131), % 187.99/29.86 | | | | | | | | | | (132), (135), (136), (138), (139), (144), (145), % 187.99/29.86 | | | | | | | | | | (146), (147), (157), (158), (159), (160), (162), % 187.99/29.86 | | | | | | | | | | (163), (164), (166), (167), (170), (172), (173), % 187.99/29.86 | | | | | | | | | | (176), (178), (182), (184), (185), (186), (187), % 187.99/29.86 | | | | | | | | | | (191), (192), (194), (196), (197), (200), (204), % 187.99/29.86 | | | | | | | | | | (207), (208), (209), (210), (211), (213), (215), % 187.99/29.86 | | | | | | | | | | (216), (217), (219), (220), (221), (222), (223), % 187.99/29.86 | | | | | | | | | | (224), (225), (227), (229), (230), (232), (233), % 187.99/29.86 | | | | | | | | | | (234), (235), (236), (237), (242), (244), (756), % 187.99/29.86 | | | | | | | | | | (757), (758) are inconsistent by sub-proof #17. % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | Case 2: % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | (759) all_22_2 = e2 % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (223), (759) imply: % 187.99/29.86 | | | | | | | | | | (760) ~ (all_28_2 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (234), (759) imply: % 187.99/29.86 | | | | | | | | | | (761) ~ (all_20_2 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | SIMP: (761) implies: % 187.99/29.86 | | | | | | | | | | (762) ~ (all_20_2 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (243), (759) imply: % 187.99/29.86 | | | | | | | | | | (763) ~ (all_10_2 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | SIMP: (763) implies: % 187.99/29.86 | | | | | | | | | | (764) ~ (all_10_2 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (152), (759) imply: % 187.99/29.86 | | | | | | | | | | (765) ~ (all_6_1 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (741), (759) imply: % 187.99/29.86 | | | | | | | | | | (766) ~ (e4 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | SIMP: (766) implies: % 187.99/29.86 | | | | | | | | | | (767) ~ (e4 = e2) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (124), (759) imply: % 187.99/29.86 | | | | | | | | | | (768) op(e0, e2) = e3 % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | GROUND_INST: instantiating (14) with all_28_2, e3, e2, e0, % 187.99/29.86 | | | | | | | | | | simplifying with (22), (768) gives: % 187.99/29.86 | | | | | | | | | | (769) all_28_2 = e3 % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (86), (769) imply: % 187.99/29.86 | | | | | | | | | | (770) ~ (all_20_2 = e3) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | REDUCE: (69), (769) imply: % 187.99/29.86 | | | | | | | | | | (771) ~ (all_6_1 = e3) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | SIMP: (771) implies: % 187.99/29.86 | | | | | | | | | | (772) ~ (all_6_1 = e3) % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | BETA: splitting (114) gives: % 187.99/29.86 | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | Case 1: % 187.99/29.86 | | | | | | | | | | | % 187.99/29.86 | | | | | | | | | | | (773) ~ (all_32_2 = e4) % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | REDUCE: (199), (773) imply: % 187.99/29.87 | | | | | | | | | | | (774) ~ (all_20_2 = e4) % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | BETA: splitting (13) gives: % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | Case 1: % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | (775) ~ (all_36_2 = e0) % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | BETA: splitting (231) gives: % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | Case 1: % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | (776) ~ (all_56_2 = e4) % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | REDUCE: (177), (776) imply: % 187.99/29.87 | | | | | | | | | | | | | (777) ~ (all_8_2 = e4) % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | BETA: splitting (201) gives: % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | Case 1: % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | (778) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_5 = % 187.99/29.87 | | | | | | | | | | | | | | e4 & op(e3, e2) = e4) % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | BETA: splitting (778) gives: % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | Case 1: % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | (779) all_252_4 = e4 & op(e4, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | ALPHA: (779) implies: % 187.99/29.87 | | | | | | | | | | | | | | | (780) all_252_4 = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | COMBINE_EQS: (76), (780) imply: % 187.99/29.87 | | | | | | | | | | | | | | | (781) e4 = e0 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | SIMP: (781) implies: % 187.99/29.87 | | | | | | | | | | | | | | | (782) e4 = e0 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | REDUCE: (50), (782) imply: % 187.99/29.87 | | | | | | | | | | | | | | | (783) $false % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | CLOSE: (783) is inconsistent. % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | (784) all_252_5 = e4 & op(e3, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | ALPHA: (784) implies: % 187.99/29.87 | | | | | | | | | | | | | | | (785) op(e3, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | REF_CLOSE: (14), (136), (777), (785) are inconsistent by % 187.99/29.87 | | | | | | | | | | | | | | | sub-proof #521. % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | (786) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_14 = % 187.99/29.87 | | | | | | | | | | | | | | e4 & op(e1, e2) = e4) | (all_252_22 = e4 & % 187.99/29.87 | | | | | | | | | | | | | | op(e0, e2) = e4) % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | BETA: splitting (786) gives: % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | Case 1: % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | (787) all_252_8 = e4 & op(e2, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | ALPHA: (787) implies: % 187.99/29.87 | | | | | | | | | | | | | | | (788) op(e2, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_244_8, e4, e2, e2, % 187.99/29.87 | | | | | | | | | | | | | | | simplifying with (9), (788) gives: % 187.99/29.87 | | | | | | | | | | | | | | | (789) all_244_8 = e4 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | REDUCE: (137), (789) imply: % 187.99/29.87 | | | | | | | | | | | | | | | (790) op(e4, e4) = e2 % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | REF_CLOSE: (14), (125), (143), (790) are inconsistent by % 187.99/29.87 | | | | | | | | | | | | | | | sub-proof #500. % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | (791) (all_252_14 = e4 & op(e1, e2) = e4) | (all_252_22 % 187.99/29.87 | | | | | | | | | | | | | | | = e4 & op(e0, e2) = e4) % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | BETA: splitting (791) gives: % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | Case 1: % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | | (792) all_252_14 = e4 & op(e1, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (50), (73), (112), (135), (165), % 187.99/29.87 | | | | | | | | | | | | | | | | (190), (193), (213), (215), (217), (230), (242), % 187.99/29.87 | | | | | | | | | | | | | | | | (725), (728), (767), (792) are inconsistent by % 187.99/29.87 | | | | | | | | | | | | | | | | sub-proof #412. % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | | (793) all_252_22 = e4 & op(e0, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | | ALPHA: (793) implies: % 187.99/29.87 | | | | | | | | | | | | | | | | (794) op(e0, e2) = e4 % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (61), (768), (794) are inconsistent by % 187.99/29.87 | | | | | | | | | | | | | | | | sub-proof #328. % 187.99/29.87 | | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | (795) all_56_2 = e4 % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | COMBINE_EQS: (177), (795) imply: % 187.99/29.87 | | | | | | | | | | | | | (796) all_8_2 = e4 % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | REDUCE: (134), (796) imply: % 187.99/29.87 | | | | | | | | | | | | | (797) ~ (all_48_2 = e4) % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | REDUCE: (87), (796) imply: % 187.99/29.87 | | | | | | | | | | | | | (798) op(e4, all_10_2) = e2 % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | | REF_CLOSE: (14), (16), (18), (24), (51), (63), (67), (68), % 187.99/29.87 | | | | | | | | | | | | | (79), (94), (104), (110), (124), (125), (140), % 187.99/29.87 | | | | | | | | | | | | | (143), (144), (149), (166), (169), (171), (184), % 187.99/29.87 | | | | | | | | | | | | | (195), (226), (238), (240), (764), (775), (797), % 187.99/29.87 | | | | | | | | | | | | | (798) are inconsistent by sub-proof #497. % 187.99/29.87 | | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | (799) all_36_2 = e0 % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | COMBINE_EQS: (737), (799) imply: % 187.99/29.87 | | | | | | | | | | | | (800) all_16_1 = e0 % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | SIMP: (800) implies: % 187.99/29.87 | | | | | | | | | | | | (801) all_16_1 = e0 % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | REDUCE: (743), (801) imply: % 187.99/29.87 | | | | | | | | | | | | (802) ~ (all_20_2 = e0) % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | | REF_CLOSE: (14), (34), (45), (191), (212), (757), (762), % 187.99/29.87 | | | | | | | | | | | | (774), (802) are inconsistent by sub-proof #485. % 187.99/29.87 | | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | (803) all_32_2 = e4 % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | COMBINE_EQS: (199), (803) imply: % 187.99/29.87 | | | | | | | | | | | (804) all_20_2 = e4 % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | SIMP: (804) implies: % 187.99/29.87 | | | | | | | | | | | (805) all_20_2 = e4 % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | | REF_CLOSE: (14), (46), (90), (103), (130), (156), (206), % 187.99/29.87 | | | | | | | | | | | (756), (772), (805) are inconsistent by sub-proof % 187.99/29.87 | | | | | | | | | | | #6. % 187.99/29.87 | | | | | | | | | | | % 187.99/29.87 | | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | | % 187.99/29.87 | | | | | | | | | End of split % 187.99/29.87 | | | | | | | | | % 187.99/29.87 | | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | | % 187.99/29.87 | | | | | | | | | (806) all_20_2 = e3 % 187.99/29.87 | | | | | | | | | % 187.99/29.87 | | | | | | | | | REF_CLOSE: (14), (22), (23), (25), (95), (103), (123), (124), % 187.99/29.87 | | | | | | | | | (130), (138), (146), (165), (185), (219), (756), % 187.99/29.87 | | | | | | | | | (806) are inconsistent by sub-proof #5. % 187.99/29.87 | | | | | | | | | % 187.99/29.87 | | | | | | | | End of split % 187.99/29.87 | | | | | | | | % 187.99/29.87 | | | | | | | Case 2: % 187.99/29.87 | | | | | | | | % 187.99/29.87 | | | | | | | | (807) all_18_2 = e2 % 187.99/29.87 | | | | | | | | % 187.99/29.87 | | | | | | | | COMBINE_EQS: (174), (807) imply: % 187.99/29.87 | | | | | | | | (808) all_6_1 = e2 % 187.99/29.87 | | | | | | | | % 187.99/29.87 | | | | | | | | REDUCE: (33), (808) imply: % 187.99/29.87 | | | | | | | | (809) op(e2, e2) = e0 % 187.99/29.87 | | | | | | | | % 187.99/29.87 | | | | | | | | REF_CLOSE: (7), (9), (14), (809) are inconsistent by sub-proof % 187.99/29.87 | | | | | | | | #448. % 187.99/29.87 | | | | | | | | % 187.99/29.87 | | | | | | | End of split % 187.99/29.87 | | | | | | | % 187.99/29.87 | | | | | | End of split % 187.99/29.87 | | | | | | % 187.99/29.87 | | | | | End of split % 187.99/29.87 | | | | | % 187.99/29.87 | | | | End of split % 187.99/29.87 | | | | % 187.99/29.87 | | | Case 2: % 187.99/29.87 | | | | % 187.99/29.87 | | | | (810) all_252_13 = e3 & op(e1, e3) = e3 % 187.99/29.87 | | | | % 187.99/29.87 | | | | REF_CLOSE: (14), (38), (61), (725), (810) are inconsistent by sub-proof % 187.99/29.87 | | | | #336. % 187.99/29.87 | | | | % 187.99/29.87 | | | End of split % 187.99/29.87 | | | % 187.99/29.87 | | Case 2: % 187.99/29.87 | | | % 187.99/29.87 | | | (811) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 187.99/29.87 | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 187.99/29.87 | | | % 187.99/29.87 | | | BETA: splitting (811) gives: % 187.99/29.87 | | | % 187.99/29.87 | | | Case 1: % 187.99/29.87 | | | | % 187.99/29.87 | | | | (812) all_252_14 = e3 & op(e1, e2) = e3 % 187.99/29.87 | | | | % 187.99/29.87 | | | | REF_CLOSE: (14), (233), (724), (812) are inconsistent by sub-proof #350. % 187.99/29.87 | | | | % 187.99/29.87 | | | Case 2: % 187.99/29.87 | | | | % 187.99/29.87 | | | | (813) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, % 187.99/29.87 | | | | e0) = e3) % 187.99/29.87 | | | | % 187.99/29.87 | | | | BETA: splitting (813) gives: % 187.99/29.87 | | | | % 187.99/29.87 | | | | Case 1: % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | (814) all_252_15 = e3 & op(e1, e1) = e3 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | ALPHA: (814) implies: % 187.99/29.87 | | | | | (815) op(e1, e1) = e3 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | REF_CLOSE: (14), (42), (720), (815) are inconsistent by sub-proof % 187.99/29.87 | | | | | #443. % 187.99/29.87 | | | | | % 187.99/29.87 | | | | Case 2: % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | (816) all_252_19 = e3 & op(e1, e0) = e3 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | REF_CLOSE: (14), (217), (722), (816) are inconsistent by sub-proof % 187.99/29.87 | | | | | #536. % 187.99/29.87 | | | | | % 187.99/29.87 | | | | End of split % 187.99/29.87 | | | | % 187.99/29.87 | | | End of split % 187.99/29.87 | | | % 187.99/29.87 | | End of split % 187.99/29.87 | | % 187.99/29.87 | End of split % 187.99/29.87 | % 187.99/29.87 End of proof % 187.99/29.87 % 187.99/29.87 Sub-proof #5 shows that the following formulas are inconsistent: % 187.99/29.87 ---------------------------------------------------------------- % 187.99/29.87 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.87 (2) op(e0, e2) = all_28_2 % 187.99/29.87 (3) ~ (all_244_24 = e2) % 187.99/29.87 (4) ~ (e2 = e1) % 187.99/29.87 (5) all_20_2 = e3 % 187.99/29.87 (6) op(e0, e0) = all_244_24 % 187.99/29.87 (7) op(e0, all_20_2) = e1 % 187.99/29.87 (8) op(e0, e3) = all_22_2 % 187.99/29.87 (9) ~ (all_6_1 = e2) % 187.99/29.87 (10) op(e0, all_22_2) = e3 % 187.99/29.87 (11) op(e0, e4) = all_6_1 % 187.99/29.87 (12) ~ (all_28_2 = e0) % 187.99/29.87 (13) op(e2, all_40_2) = e0 % 187.99/29.87 (14) ~ (e3 = e2) % 187.99/29.87 (15) op(all_28_2, all_40_2) = e2 % 187.99/29.87 (16) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 187.99/29.87 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 187.99/29.87 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 187.99/29.87 % 187.99/29.87 Begin of proof % 187.99/29.87 | % 187.99/29.87 | REDUCE: (5), (7) imply: % 187.99/29.87 | (17) op(e0, e3) = e1 % 187.99/29.87 | % 187.99/29.87 | GROUND_INST: instantiating (1) with all_22_2, e1, e3, e0, simplifying with % 187.99/29.87 | (8), (17) gives: % 187.99/29.87 | (18) all_22_2 = e1 % 187.99/29.87 | % 187.99/29.87 | REDUCE: (10), (18) imply: % 187.99/29.87 | (19) op(e0, e1) = e3 % 187.99/29.87 | % 187.99/29.87 | BETA: splitting (16) gives: % 187.99/29.87 | % 187.99/29.87 | Case 1: % 187.99/29.87 | | % 187.99/29.87 | | (20) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) % 187.99/29.87 | | = e2) % 187.99/29.87 | | % 187.99/29.87 | | BETA: splitting (20) gives: % 187.99/29.87 | | % 187.99/29.87 | | Case 1: % 187.99/29.87 | | | % 187.99/29.87 | | | (21) all_252_20 = e2 & op(e0, e4) = e2 % 187.99/29.87 | | | % 187.99/29.87 | | | REF_CLOSE: (1), (9), (11), (21) are inconsistent by sub-proof #22. % 187.99/29.87 | | | % 187.99/29.87 | | Case 2: % 187.99/29.87 | | | % 187.99/29.87 | | | (22) all_252_21 = e2 & op(e0, e3) = e2 % 187.99/29.87 | | | % 187.99/29.87 | | | ALPHA: (22) implies: % 187.99/29.87 | | | (23) op(e0, e3) = e2 % 187.99/29.87 | | | % 187.99/29.87 | | | REF_CLOSE: (1), (4), (17), (23) are inconsistent by sub-proof #10. % 187.99/29.87 | | | % 187.99/29.87 | | End of split % 187.99/29.87 | | % 187.99/29.87 | Case 2: % 187.99/29.87 | | % 187.99/29.87 | | (24) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) % 187.99/29.87 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 187.99/29.87 | | % 187.99/29.87 | | REF_CLOSE: (1), (2), (3), (6), (12), (13), (14), (15), (19), (24) are % 187.99/29.87 | | inconsistent by sub-proof #259. % 187.99/29.87 | | % 187.99/29.87 | End of split % 187.99/29.87 | % 187.99/29.87 End of proof % 187.99/29.87 % 187.99/29.87 Sub-proof #6 shows that the following formulas are inconsistent: % 187.99/29.87 ---------------------------------------------------------------- % 187.99/29.87 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.87 (2) all_20_2 = e4 % 187.99/29.87 (3) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | % 187.99/29.87 all_250_20 = e0 % 187.99/29.87 (4) ~ (all_20_2 = all_6_1) % 187.99/29.87 (5) ~ (all_6_1 = e3) % 187.99/29.87 (6) op(e0, all_20_2) = e1 % 187.99/29.87 (7) ~ (all_6_1 = e2) % 187.99/29.87 (8) op(e0, e4) = all_6_1 % 187.99/29.87 (9) all_250_20 = all_6_1 % 187.99/29.87 (10) ~ (all_6_1 = e1) % 187.99/29.87 % 187.99/29.87 Begin of proof % 187.99/29.87 | % 187.99/29.87 | REDUCE: (2), (4) imply: % 187.99/29.87 | (11) ~ (all_6_1 = e4) % 187.99/29.87 | % 187.99/29.87 | SIMP: (11) implies: % 187.99/29.87 | (12) ~ (all_6_1 = e4) % 187.99/29.87 | % 187.99/29.87 | REDUCE: (2), (6) imply: % 187.99/29.87 | (13) op(e0, e4) = e1 % 187.99/29.87 | % 187.99/29.87 | BETA: splitting (3) gives: % 187.99/29.87 | % 187.99/29.87 | Case 1: % 187.99/29.87 | | % 187.99/29.87 | | (14) all_250_20 = e4 % 187.99/29.87 | | % 187.99/29.87 | | COMBINE_EQS: (9), (14) imply: % 187.99/29.87 | | (15) all_6_1 = e4 % 187.99/29.87 | | % 187.99/29.87 | | REDUCE: (12), (15) imply: % 187.99/29.87 | | (16) $false % 187.99/29.87 | | % 187.99/29.87 | | CLOSE: (16) is inconsistent. % 187.99/29.87 | | % 187.99/29.87 | Case 2: % 187.99/29.87 | | % 187.99/29.87 | | (17) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 = % 187.99/29.87 | | e0 % 187.99/29.87 | | % 187.99/29.87 | | BETA: splitting (17) gives: % 187.99/29.87 | | % 187.99/29.87 | | Case 1: % 187.99/29.87 | | | % 187.99/29.87 | | | (18) all_250_20 = e3 % 187.99/29.87 | | | % 187.99/29.87 | | | COMBINE_EQS: (9), (18) imply: % 187.99/29.87 | | | (19) all_6_1 = e3 % 187.99/29.87 | | | % 187.99/29.87 | | | REDUCE: (5), (19) imply: % 187.99/29.87 | | | (20) $false % 187.99/29.87 | | | % 187.99/29.87 | | | CLOSE: (20) is inconsistent. % 187.99/29.87 | | | % 187.99/29.87 | | Case 2: % 187.99/29.87 | | | % 187.99/29.87 | | | (21) all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0 % 187.99/29.87 | | | % 187.99/29.87 | | | BETA: splitting (21) gives: % 187.99/29.87 | | | % 187.99/29.87 | | | Case 1: % 187.99/29.87 | | | | % 187.99/29.87 | | | | (22) all_250_20 = e2 % 187.99/29.87 | | | | % 187.99/29.87 | | | | COMBINE_EQS: (9), (22) imply: % 187.99/29.87 | | | | (23) all_6_1 = e2 % 187.99/29.87 | | | | % 187.99/29.87 | | | | REDUCE: (7), (23) imply: % 187.99/29.87 | | | | (24) $false % 187.99/29.87 | | | | % 187.99/29.87 | | | | CLOSE: (24) is inconsistent. % 187.99/29.87 | | | | % 187.99/29.87 | | | Case 2: % 187.99/29.87 | | | | % 187.99/29.87 | | | | (25) all_250_20 = e1 | all_250_20 = e0 % 187.99/29.87 | | | | % 187.99/29.87 | | | | BETA: splitting (25) gives: % 187.99/29.87 | | | | % 187.99/29.87 | | | | Case 1: % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | (26) all_250_20 = e1 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | COMBINE_EQS: (9), (26) imply: % 187.99/29.87 | | | | | (27) all_6_1 = e1 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | REDUCE: (10), (27) imply: % 187.99/29.87 | | | | | (28) $false % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | CLOSE: (28) is inconsistent. % 187.99/29.87 | | | | | % 187.99/29.87 | | | | Case 2: % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | (29) all_250_20 = e0 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | COMBINE_EQS: (9), (29) imply: % 187.99/29.87 | | | | | (30) all_6_1 = e0 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | REDUCE: (10), (30) imply: % 187.99/29.87 | | | | | (31) ~ (e1 = e0) % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | SIMP: (31) implies: % 187.99/29.87 | | | | | (32) ~ (e1 = e0) % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | REDUCE: (8), (30) imply: % 187.99/29.87 | | | | | (33) op(e0, e4) = e0 % 187.99/29.87 | | | | | % 187.99/29.87 | | | | | REF_CLOSE: (1), (13), (32), (33) are inconsistent by sub-proof #318. % 187.99/29.87 | | | | | % 187.99/29.87 | | | | End of split % 187.99/29.87 | | | | % 187.99/29.87 | | | End of split % 187.99/29.87 | | | % 187.99/29.87 | | End of split % 187.99/29.87 | | % 187.99/29.87 | End of split % 187.99/29.87 | % 187.99/29.87 End of proof % 187.99/29.87 % 187.99/29.87 Sub-proof #7 shows that the following formulas are inconsistent: % 187.99/29.87 ---------------------------------------------------------------- % 187.99/29.87 (1) all_250_7 = all_8_2 % 187.99/29.87 (2) all_250_7 = e0 % 187.99/29.87 (3) ~ (all_8_2 = e0) % 187.99/29.87 % 187.99/29.87 Begin of proof % 187.99/29.87 | % 187.99/29.87 | COMBINE_EQS: (1), (2) imply: % 187.99/29.87 | (4) all_8_2 = e0 % 187.99/29.87 | % 187.99/29.87 | SIMP: (4) implies: % 187.99/29.87 | (5) all_8_2 = e0 % 187.99/29.87 | % 187.99/29.87 | REDUCE: (3), (5) imply: % 187.99/29.87 | (6) $false % 187.99/29.87 | % 187.99/29.87 | CLOSE: (6) is inconsistent. % 187.99/29.87 | % 187.99/29.87 End of proof % 187.99/29.87 % 187.99/29.87 Sub-proof #8 shows that the following formulas are inconsistent: % 187.99/29.87 ---------------------------------------------------------------- % 187.99/29.87 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.87 (2) ~ (all_100_2 = all_6_1) % 187.99/29.87 (3) op(e2, all_6_1) = e0 % 187.99/29.87 (4) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | % 187.99/29.87 all_250_20 = e0 % 187.99/29.87 (5) all_168_2 = all_100_2 % 187.99/29.87 (6) ~ (all_6_1 = e3) % 187.99/29.87 (7) ~ (all_100_2 = all_64_2) % 187.99/29.87 (8) all_168_2 = e0 % 187.99/29.87 (9) ~ (all_6_1 = e2) % 187.99/29.87 (10) all_250_20 = all_6_1 % 187.99/29.87 (11) op(e2, e4) = all_64_2 % 187.99/29.87 (12) ~ (all_6_1 = e1) % 187.99/29.87 % 187.99/29.87 Begin of proof % 187.99/29.87 | % 187.99/29.87 | COMBINE_EQS: (5), (8) imply: % 187.99/29.87 | (13) all_100_2 = e0 % 187.99/29.87 | % 187.99/29.87 | SIMP: (13) implies: % 187.99/29.87 | (14) all_100_2 = e0 % 187.99/29.87 | % 187.99/29.87 | REDUCE: (7), (14) imply: % 187.99/29.87 | (15) ~ (all_64_2 = e0) % 187.99/29.87 | % 187.99/29.87 | SIMP: (15) implies: % 187.99/29.87 | (16) ~ (all_64_2 = e0) % 187.99/29.87 | % 187.99/29.87 | REDUCE: (2), (14) imply: % 187.99/29.87 | (17) ~ (all_6_1 = e0) % 187.99/29.87 | % 187.99/29.87 | SIMP: (17) implies: % 187.99/29.87 | (18) ~ (all_6_1 = e0) % 187.99/29.87 | % 187.99/29.87 | BETA: splitting (4) gives: % 187.99/29.87 | % 187.99/29.87 | Case 1: % 187.99/29.87 | | % 187.99/29.87 | | (19) all_250_20 = e4 % 187.99/29.87 | | % 187.99/29.87 | | COMBINE_EQS: (10), (19) imply: % 187.99/29.87 | | (20) all_6_1 = e4 % 187.99/29.87 | | % 187.99/29.87 | | SIMP: (20) implies: % 187.99/29.87 | | (21) all_6_1 = e4 % 187.99/29.87 | | % 187.99/29.87 | | REDUCE: (3), (21) imply: % 187.99/29.87 | | (22) op(e2, e4) = e0 % 187.99/29.88 | | % 187.99/29.88 | | REF_CLOSE: (1), (11), (16), (22) are inconsistent by sub-proof #382. % 187.99/29.88 | | % 187.99/29.88 | Case 2: % 187.99/29.88 | | % 187.99/29.88 | | (23) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 = % 187.99/29.88 | | e0 % 187.99/29.88 | | % 187.99/29.88 | | BETA: splitting (23) gives: % 187.99/29.88 | | % 187.99/29.88 | | Case 1: % 187.99/29.88 | | | % 187.99/29.88 | | | (24) all_250_20 = e3 % 187.99/29.88 | | | % 187.99/29.88 | | | COMBINE_EQS: (10), (24) imply: % 187.99/29.88 | | | (25) all_6_1 = e3 % 187.99/29.88 | | | % 187.99/29.88 | | | SIMP: (25) implies: % 187.99/29.88 | | | (26) all_6_1 = e3 % 187.99/29.88 | | | % 187.99/29.88 | | | REDUCE: (6), (26) imply: % 187.99/29.88 | | | (27) $false % 187.99/29.88 | | | % 187.99/29.88 | | | CLOSE: (27) is inconsistent. % 187.99/29.88 | | | % 187.99/29.88 | | Case 2: % 187.99/29.88 | | | % 187.99/29.88 | | | (28) all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0 % 187.99/29.88 | | | % 187.99/29.88 | | | BETA: splitting (28) gives: % 187.99/29.88 | | | % 187.99/29.88 | | | Case 1: % 187.99/29.88 | | | | % 187.99/29.88 | | | | (29) all_250_20 = e2 % 187.99/29.88 | | | | % 187.99/29.88 | | | | COMBINE_EQS: (10), (29) imply: % 187.99/29.88 | | | | (30) all_6_1 = e2 % 187.99/29.88 | | | | % 187.99/29.88 | | | | SIMP: (30) implies: % 187.99/29.88 | | | | (31) all_6_1 = e2 % 187.99/29.88 | | | | % 187.99/29.88 | | | | REDUCE: (9), (31) imply: % 187.99/29.88 | | | | (32) $false % 187.99/29.88 | | | | % 187.99/29.88 | | | | CLOSE: (32) is inconsistent. % 187.99/29.88 | | | | % 187.99/29.88 | | | Case 2: % 187.99/29.88 | | | | % 187.99/29.88 | | | | (33) all_250_20 = e1 | all_250_20 = e0 % 187.99/29.88 | | | | % 187.99/29.88 | | | | BETA: splitting (33) gives: % 187.99/29.88 | | | | % 187.99/29.88 | | | | Case 1: % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | (34) all_250_20 = e1 % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | COMBINE_EQS: (10), (34) imply: % 187.99/29.88 | | | | | (35) all_6_1 = e1 % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | REDUCE: (12), (35) imply: % 187.99/29.88 | | | | | (36) $false % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | CLOSE: (36) is inconsistent. % 187.99/29.88 | | | | | % 187.99/29.88 | | | | Case 2: % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | (37) all_250_20 = e0 % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | COMBINE_EQS: (10), (37) imply: % 187.99/29.88 | | | | | (38) all_6_1 = e0 % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | REDUCE: (18), (38) imply: % 187.99/29.88 | | | | | (39) $false % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | CLOSE: (39) is inconsistent. % 187.99/29.88 | | | | | % 187.99/29.88 | | | | End of split % 187.99/29.88 | | | | % 187.99/29.88 | | | End of split % 187.99/29.88 | | | % 187.99/29.88 | | End of split % 187.99/29.88 | | % 187.99/29.88 | End of split % 187.99/29.88 | % 187.99/29.88 End of proof % 187.99/29.88 % 187.99/29.88 Sub-proof #9 shows that the following formulas are inconsistent: % 187.99/29.88 ---------------------------------------------------------------- % 187.99/29.88 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.88 (2) ~ (all_20_2 = e4) % 187.99/29.88 (3) ~ (all_36_2 = e0) % 187.99/29.88 (4) op(e3, e1) = all_36_2 % 187.99/29.88 (5) ~ (e2 = e1) % 187.99/29.88 (6) op(e3, e3) = all_244_3 % 187.99/29.88 (7) ~ (all_26_2 = e0) % 187.99/29.88 (8) ~ (e4 = e0) % 187.99/29.88 (9) op(e2, e3) = all_10_2 % 187.99/29.88 (10) op(e4, e3) = all_84_2 % 187.99/29.88 (11) ~ (e4 = e3) % 187.99/29.88 (12) ~ (all_16_2 = e3) % 187.99/29.88 (13) ~ (all_84_2 = e1) % 187.99/29.88 (14) ~ (all_244_3 = e1) % 187.99/29.88 (15) ~ (all_10_2 = e1) % 187.99/29.88 (16) op(e0, e1) = all_20_2 % 187.99/29.88 (17) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 187.99/29.88 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 187.99/29.88 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 187.99/29.88 (18) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = % 187.99/29.88 e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, % 187.99/29.88 e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 187.99/29.88 (19) ~ (all_38_2 = e0) % 187.99/29.88 (20) op(e4, e1) = all_26_2 % 187.99/29.88 (21) ~ (e3 = e0) % 187.99/29.88 (22) op(e0, e3) = e2 % 187.99/29.88 (23) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 187.99/29.88 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 187.99/29.88 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 187.99/29.88 (24) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 187.99/29.88 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 187.99/29.88 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 187.99/29.88 (25) op(e1, e4) = all_16_2 % 187.99/29.88 (26) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 187.99/29.88 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 187.99/29.88 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 187.99/29.88 (27) ~ (e4 = e2) % 187.99/29.88 (28) ~ (e1 = e0) % 187.99/29.88 (29) op(e0, e2) = e3 % 187.99/29.88 (30) all_252_20 = e0 & op(e0, e4) = e0 % 187.99/29.88 (31) ~ (all_4_2 = e3) % 187.99/29.88 (32) ~ (e3 = e1) % 187.99/29.88 (33) op(e1, e0) = all_34_2 % 187.99/29.88 (34) ~ (all_34_2 = e3) % 187.99/29.88 (35) op(e1, e2) = all_4_2 % 187.99/29.88 (36) op(e2, e1) = all_38_2 % 187.99/29.88 (37) all_252_22 = e3 % 187.99/29.88 (38) ~ (e4 = e1) % 187.99/29.88 % 187.99/29.88 Begin of proof % 187.99/29.88 | % 187.99/29.88 | ALPHA: (30) implies: % 187.99/29.88 | (39) all_252_20 = e0 % 187.99/29.88 | (40) op(e0, e4) = e0 % 187.99/29.88 | % 187.99/29.88 | BETA: splitting (18) gives: % 187.99/29.88 | % 187.99/29.88 | Case 1: % 187.99/29.88 | | % 187.99/29.88 | | (41) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) % 187.99/29.88 | | = e4) % 187.99/29.88 | | % 187.99/29.88 | | REF_CLOSE: (1), (8), (22), (27), (39), (41) are inconsistent by sub-proof % 187.99/29.88 | | #329. % 187.99/29.88 | | % 187.99/29.88 | Case 2: % 187.99/29.88 | | % 187.99/29.88 | | (42) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, e1) % 187.99/29.88 | | = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 187.99/29.88 | | % 187.99/29.88 | | BETA: splitting (42) gives: % 187.99/29.88 | | % 187.99/29.88 | | Case 1: % 187.99/29.88 | | | % 187.99/29.88 | | | (43) all_252_22 = e4 & op(e0, e2) = e4 % 187.99/29.88 | | | % 187.99/29.88 | | | ALPHA: (43) implies: % 187.99/29.88 | | | (44) op(e0, e2) = e4 % 187.99/29.88 | | | % 187.99/29.88 | | | REF_CLOSE: (1), (11), (29), (44) are inconsistent by sub-proof #328. % 187.99/29.88 | | | % 187.99/29.88 | | Case 2: % 187.99/29.88 | | | % 187.99/29.88 | | | (45) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, % 187.99/29.88 | | | e0) = e4) % 187.99/29.88 | | | % 187.99/29.88 | | | BETA: splitting (45) gives: % 187.99/29.88 | | | % 187.99/29.88 | | | Case 1: % 187.99/29.88 | | | | % 187.99/29.88 | | | | (46) all_252_23 = e4 & op(e0, e1) = e4 % 187.99/29.88 | | | | % 187.99/29.88 | | | | REF_CLOSE: (1), (2), (16), (46) are inconsistent by sub-proof #518. % 187.99/29.88 | | | | % 187.99/29.88 | | | Case 2: % 187.99/29.88 | | | | % 187.99/29.88 | | | | (47) all_252_24 = e4 & op(e0, e0) = e4 % 187.99/29.88 | | | | % 187.99/29.88 | | | | ALPHA: (47) implies: % 187.99/29.88 | | | | (48) all_252_24 = e4 % 187.99/29.88 | | | | % 187.99/29.88 | | | | BETA: splitting (17) gives: % 187.99/29.88 | | | | % 187.99/29.88 | | | | Case 1: % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | (49) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & % 187.99/29.88 | | | | | op(e0, e3) = e1) % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | BETA: splitting (49) gives: % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | Case 1: % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | (50) all_252_20 = e1 & op(e0, e4) = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | ALPHA: (50) implies: % 187.99/29.88 | | | | | | (51) op(e0, e4) = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | REF_CLOSE: (1), (28), (40), (51) are inconsistent by sub-proof #318. % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | Case 2: % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | (52) all_252_21 = e1 & op(e0, e3) = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | ALPHA: (52) implies: % 187.99/29.88 | | | | | | (53) op(e0, e3) = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | REF_CLOSE: (1), (5), (22), (53) are inconsistent by sub-proof #10. % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | End of split % 187.99/29.88 | | | | | % 187.99/29.88 | | | | Case 2: % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | (54) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & % 187.99/29.88 | | | | | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | BETA: splitting (54) gives: % 187.99/29.88 | | | | | % 187.99/29.88 | | | | | Case 1: % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | (55) all_252_22 = e1 & op(e0, e2) = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | ALPHA: (55) implies: % 187.99/29.88 | | | | | | (56) all_252_22 = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | COMBINE_EQS: (37), (56) imply: % 187.99/29.88 | | | | | | (57) e3 = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | SIMP: (57) implies: % 187.99/29.88 | | | | | | (58) e3 = e1 % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | REDUCE: (32), (58) imply: % 187.99/29.88 | | | | | | (59) $false % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | CLOSE: (59) is inconsistent. % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | Case 2: % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | (60) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 187.99/29.88 | | | | | | op(e0, e0) = e1) % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | BETA: splitting (60) gives: % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | | Case 1: % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | (61) all_252_23 = e1 & op(e0, e1) = e1 % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | ALPHA: (61) implies: % 187.99/29.88 | | | | | | | (62) all_252_23 = e1 % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | BETA: splitting (24) gives: % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | Case 1: % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | | (63) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & % 187.99/29.88 | | | | | | | | op(e3, e3) = e1) % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | | REF_CLOSE: (1), (6), (10), (13), (14), (63) are inconsistent by % 187.99/29.88 | | | | | | | | sub-proof #13. % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | Case 2: % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | | (64) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & % 187.99/29.88 | | | | | | | | op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | | BETA: splitting (64) gives: % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | | Case 1: % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | | (65) all_252_7 = e1 & op(e2, e3) = e1 % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | | ALPHA: (65) implies: % 187.99/29.88 | | | | | | | | | (66) op(e2, e3) = e1 % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | | REF_CLOSE: (1), (9), (15), (66) are inconsistent by sub-proof % 187.99/29.88 | | | | | | | | | #554. % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | Case 2: % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | | (67) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 % 187.99/29.88 | | | | | | | | | & op(e0, e3) = e1) % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | | BETA: splitting (67) gives: % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | | Case 1: % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | (68) all_252_13 = e1 & op(e1, e3) = e1 % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | ALPHA: (68) implies: % 187.99/29.88 | | | | | | | | | | (69) all_252_13 = e1 % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | BETA: splitting (26) gives: % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | Case 1: % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | (70) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 187.99/29.88 | | | | | | | | | | | e0 & op(e3, e1) = e0) % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (20), (70) are inconsistent by % 187.99/29.88 | | | | | | | | | | | sub-proof #451. % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | Case 2: % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | (71) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 187.99/29.88 | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 187.99/29.88 | | | | | | | | | | | op(e0, e1) = e0) % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | BETA: splitting (71) gives: % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | Case 1: % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | (72) all_252_11 = e0 & op(e2, e1) = e0 % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | ALPHA: (72) implies: % 187.99/29.88 | | | | | | | | | | | | (73) op(e2, e1) = e0 % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | REF_CLOSE: (1), (19), (36), (73) are inconsistent by % 187.99/29.88 | | | | | | | | | | | | sub-proof #549. % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | Case 2: % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | (74) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 187.99/29.88 | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | BETA: splitting (74) gives: % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | Case 1: % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | | (75) all_252_15 = e0 & op(e1, e1) = e0 % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | | ALPHA: (75) implies: % 187.99/29.88 | | | | | | | | | | | | | (76) all_252_15 = e0 % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | | REF_CLOSE: (1), (12), (21), (23), (25), (31), (32), (33), % 187.99/29.88 | | | | | | | | | | | | | (34), (35), (69), (76) are inconsistent by % 187.99/29.88 | | | | | | | | | | | | | sub-proof #12. % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | Case 2: % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | | (77) all_252_23 = e0 & op(e0, e1) = e0 % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | | ALPHA: (77) implies: % 187.99/29.88 | | | | | | | | | | | | | (78) all_252_23 = e0 % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | | REF_CLOSE: (28), (62), (78) are inconsistent by sub-proof % 187.99/29.88 | | | | | | | | | | | | | #351. % 187.99/29.88 | | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | | End of split % 187.99/29.88 | | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | | End of split % 187.99/29.88 | | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | End of split % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | Case 2: % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | (79) all_252_21 = e1 & op(e0, e3) = e1 % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | ALPHA: (79) implies: % 187.99/29.88 | | | | | | | | | | (80) op(e0, e3) = e1 % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | | REF_CLOSE: (1), (5), (22), (80) are inconsistent by sub-proof % 187.99/29.88 | | | | | | | | | | #10. % 187.99/29.88 | | | | | | | | | | % 187.99/29.88 | | | | | | | | | End of split % 187.99/29.88 | | | | | | | | | % 187.99/29.88 | | | | | | | | End of split % 187.99/29.88 | | | | | | | | % 187.99/29.88 | | | | | | | End of split % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | Case 2: % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | (81) all_252_24 = e1 & op(e0, e0) = e1 % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | ALPHA: (81) implies: % 187.99/29.88 | | | | | | | (82) all_252_24 = e1 % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | COMBINE_EQS: (48), (82) imply: % 187.99/29.88 | | | | | | | (83) e4 = e1 % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | SIMP: (83) implies: % 187.99/29.88 | | | | | | | (84) e4 = e1 % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | REDUCE: (38), (84) imply: % 187.99/29.88 | | | | | | | (85) $false % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | | CLOSE: (85) is inconsistent. % 187.99/29.88 | | | | | | | % 187.99/29.88 | | | | | | End of split % 187.99/29.88 | | | | | | % 187.99/29.88 | | | | | End of split % 187.99/29.88 | | | | | % 187.99/29.88 | | | | End of split % 187.99/29.88 | | | | % 187.99/29.88 | | | End of split % 187.99/29.88 | | | % 187.99/29.88 | | End of split % 187.99/29.88 | | % 187.99/29.88 | End of split % 187.99/29.88 | % 187.99/29.88 End of proof % 187.99/29.88 % 187.99/29.88 Sub-proof #10 shows that the following formulas are inconsistent: % 187.99/29.88 ---------------------------------------------------------------- % 187.99/29.88 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.88 (2) op(e0, e3) = e2 % 187.99/29.88 (3) op(e0, e3) = e1 % 187.99/29.88 (4) ~ (e2 = e1) % 187.99/29.88 % 187.99/29.88 Begin of proof % 187.99/29.88 | % 187.99/29.88 | GROUND_INST: instantiating (1) with e1, e2, e3, e0, simplifying with (2), (3) % 187.99/29.88 | gives: % 187.99/29.88 | (5) e2 = e1 % 187.99/29.88 | % 187.99/29.88 | REDUCE: (4), (5) imply: % 187.99/29.88 | (6) $false % 187.99/29.88 | % 187.99/29.88 | CLOSE: (6) is inconsistent. % 187.99/29.88 | % 187.99/29.88 End of proof % 187.99/29.88 % 187.99/29.88 Sub-proof #11 shows that the following formulas are inconsistent: % 187.99/29.88 ---------------------------------------------------------------- % 187.99/29.88 (1) op(e2, e2) = all_244_8 % 187.99/29.88 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.88 (3) ~ (all_244_24 = e2) % 187.99/29.88 (4) op(e0, all_64_2) = e2 % 187.99/29.88 (5) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 187.99/29.88 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 187.99/29.88 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 187.99/29.88 (6) op(e1, e1) = all_244_15 % 187.99/29.88 (7) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) | % 187.99/29.88 (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = e1) % 187.99/29.88 | (all_252_18 = e1 & op(e2, e0) = e1) % 187.99/29.88 (8) ~ (e4 = e0) % 187.99/29.88 (9) op(e2, e3) = all_10_2 % 187.99/29.88 (10) ~ (e4 = e3) % 187.99/29.88 (11) all_252_6 = e0 & op(e2, e4) = e0 % 187.99/29.88 (12) ~ (all_244_15 = e4) % 187.99/29.88 (13) ~ (all_10_2 = e1) % 187.99/29.88 (14) op(e0, e0) = all_244_24 % 187.99/29.88 (15) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 187.99/29.88 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 187.99/29.88 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 187.99/29.88 (16) op(e4, e1) = all_26_2 % 187.99/29.88 (17) ~ (e3 = e0) % 187.99/29.88 (18) ~ (all_244_8 = e1) % 187.99/29.88 (19) ~ (e3 = e2) % 187.99/29.88 (20) op(e2, e4) = all_64_2 % 187.99/29.88 (21) ~ (e4 = e2) % 187.99/29.88 (22) op(e2, e0) = all_40_2 % 187.99/29.88 (23) all_252_10 = e2 % 187.99/29.88 (24) ~ (e1 = e0) % 187.99/29.88 (25) op(e0, e1) = e0 % 187.99/29.88 (26) ~ (e3 = e1) % 187.99/29.88 (27) ~ (all_40_2 = e1) % 187.99/29.88 (28) op(e2, e1) = all_38_2 % 187.99/29.88 (29) ~ (e4 = e1) % 187.99/29.88 % 187.99/29.88 Begin of proof % 187.99/29.88 | % 187.99/29.88 | ALPHA: (11) implies: % 187.99/29.88 | (30) op(e2, e4) = e0 % 187.99/29.88 | % 187.99/29.88 | BETA: splitting (7) gives: % 187.99/29.88 | % 187.99/29.88 | Case 1: % 187.99/29.88 | | % 187.99/29.88 | | (31) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = % 187.99/29.88 | | e1) % 187.99/29.88 | | % 187.99/29.88 | | BETA: splitting (31) gives: % 187.99/29.88 | | % 187.99/29.88 | | Case 1: % 187.99/29.88 | | | % 187.99/29.88 | | | (32) all_252_6 = e1 & op(e2, e4) = e1 % 187.99/29.88 | | | % 187.99/29.88 | | | ALPHA: (32) implies: % 187.99/29.88 | | | (33) op(e2, e4) = e1 % 187.99/29.88 | | | % 187.99/29.88 | | | REF_CLOSE: (2), (24), (30), (33) are inconsistent by sub-proof #360. % 187.99/29.88 | | | % 187.99/29.88 | | Case 2: % 187.99/29.88 | | | % 187.99/29.88 | | | (34) all_252_7 = e1 & op(e2, e3) = e1 % 187.99/29.88 | | | % 187.99/29.88 | | | ALPHA: (34) implies: % 187.99/29.88 | | | (35) op(e2, e3) = e1 % 187.99/29.88 | | | % 187.99/29.88 | | | REF_CLOSE: (2), (9), (13), (35) are inconsistent by sub-proof #554. % 187.99/29.88 | | | % 187.99/29.88 | | End of split % 187.99/29.88 | | % 187.99/29.88 | Case 2: % 187.99/29.88 | | % 187.99/29.89 | | (36) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = % 187.99/29.89 | | e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 187.99/29.89 | | % 187.99/29.89 | | BETA: splitting (36) gives: % 187.99/29.89 | | % 187.99/29.89 | | Case 1: % 187.99/29.89 | | | % 187.99/29.89 | | | (37) all_252_8 = e1 & op(e2, e2) = e1 % 187.99/29.89 | | | % 187.99/29.89 | | | ALPHA: (37) implies: % 187.99/29.89 | | | (38) op(e2, e2) = e1 % 187.99/29.89 | | | % 187.99/29.89 | | | REF_CLOSE: (1), (2), (18), (38) are inconsistent by sub-proof #490. % 187.99/29.89 | | | % 187.99/29.89 | | Case 2: % 187.99/29.89 | | | % 187.99/29.89 | | | (39) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 = e1 & op(e2, % 187.99/29.89 | | | e0) = e1) % 187.99/29.89 | | | % 187.99/29.89 | | | BETA: splitting (39) gives: % 187.99/29.89 | | | % 187.99/29.89 | | | Case 1: % 187.99/29.89 | | | | % 187.99/29.89 | | | | (40) all_252_11 = e1 & op(e2, e1) = e1 % 187.99/29.89 | | | | % 187.99/29.89 | | | | ALPHA: (40) implies: % 187.99/29.89 | | | | (41) all_252_11 = e1 % 187.99/29.89 | | | | (42) op(e2, e1) = e1 % 187.99/29.89 | | | | % 187.99/29.89 | | | | BETA: splitting (15) gives: % 187.99/29.89 | | | | % 187.99/29.89 | | | | Case 1: % 187.99/29.89 | | | | | % 187.99/29.89 | | | | | (43) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, % 187.99/29.89 | | | | | e1) = e4) % 187.99/29.89 | | | | | % 187.99/29.89 | | | | | BETA: splitting (43) gives: % 187.99/29.89 | | | | | % 187.99/29.89 | | | | | Case 1: % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | (44) all_252_9 = e4 & op(e4, e1) = e4 % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | ALPHA: (44) implies: % 187.99/29.89 | | | | | | (45) op(e4, e1) = e4 % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | BETA: splitting (5) gives: % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | Case 1: % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | (46) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & % 187.99/29.89 | | | | | | | op(e3, e1) = e3) % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | BETA: splitting (46) gives: % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | Case 1: % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | (47) all_252_9 = e3 & op(e4, e1) = e3 % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | ALPHA: (47) implies: % 187.99/29.89 | | | | | | | | (48) op(e4, e1) = e3 % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | REF_CLOSE: (2), (10), (16), (45), (48) are inconsistent by % 187.99/29.89 | | | | | | | | sub-proof #463. % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | Case 2: % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | (49) all_252_10 = e3 & op(e3, e1) = e3 % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | REF_CLOSE: (19), (23), (49) are inconsistent by sub-proof #365. % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | End of split % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | Case 2: % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | (50) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 187.99/29.89 | | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | BETA: splitting (50) gives: % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | Case 1: % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | (51) all_252_11 = e3 & op(e2, e1) = e3 % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | ALPHA: (51) implies: % 187.99/29.89 | | | | | | | | (52) op(e2, e1) = e3 % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | REF_CLOSE: (2), (26), (28), (42), (52) are inconsistent by % 187.99/29.89 | | | | | | | | sub-proof #290. % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | Case 2: % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | (53) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 187.99/29.89 | | | | | | | | op(e0, e1) = e3) % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | BETA: splitting (53) gives: % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | | Case 1: % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | GROUND_INST: instantiating (2) with all_64_2, e0, e4, e2, % 187.99/29.89 | | | | | | | | | simplifying with (20), (30) gives: % 187.99/29.89 | | | | | | | | | (54) all_64_2 = e0 % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | REDUCE: (4), (54) imply: % 187.99/29.89 | | | | | | | | | (55) op(e0, e0) = e2 % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | REF_CLOSE: (2), (3), (14), (55) are inconsistent by sub-proof % 187.99/29.89 | | | | | | | | | #477. % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | Case 2: % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | (56) all_252_23 = e3 & op(e0, e1) = e3 % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | ALPHA: (56) implies: % 187.99/29.89 | | | | | | | | | (57) op(e0, e1) = e3 % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | | REF_CLOSE: (2), (17), (25), (57) are inconsistent by sub-proof % 187.99/29.89 | | | | | | | | | #449. % 187.99/29.89 | | | | | | | | | % 187.99/29.89 | | | | | | | | End of split % 187.99/29.89 | | | | | | | | % 187.99/29.89 | | | | | | | End of split % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | End of split % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | Case 2: % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | (58) all_252_10 = e4 & op(e3, e1) = e4 % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | REF_CLOSE: (21), (23), (58) are inconsistent by sub-proof #462. % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | End of split % 187.99/29.89 | | | | | % 187.99/29.89 | | | | Case 2: % 187.99/29.89 | | | | | % 187.99/29.89 | | | | | (59) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & % 187.99/29.89 | | | | | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 187.99/29.89 | | | | | % 187.99/29.89 | | | | | BETA: splitting (59) gives: % 187.99/29.89 | | | | | % 187.99/29.89 | | | | | Case 1: % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | (60) all_252_11 = e4 & op(e2, e1) = e4 % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | ALPHA: (60) implies: % 187.99/29.89 | | | | | | (61) all_252_11 = e4 % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | REF_CLOSE: (29), (41), (61) are inconsistent by sub-proof #461. % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | Case 2: % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | (62) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 187.99/29.89 | | | | | | op(e0, e1) = e4) % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | BETA: splitting (62) gives: % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | | Case 1: % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | (63) all_252_15 = e4 & op(e1, e1) = e4 % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | ALPHA: (63) implies: % 187.99/29.89 | | | | | | | (64) op(e1, e1) = e4 % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | REF_CLOSE: (2), (6), (12), (64) are inconsistent by sub-proof % 187.99/29.89 | | | | | | | #460. % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | Case 2: % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | (65) all_252_23 = e4 & op(e0, e1) = e4 % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | ALPHA: (65) implies: % 187.99/29.89 | | | | | | | (66) op(e0, e1) = e4 % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | | REF_CLOSE: (2), (8), (25), (66) are inconsistent by sub-proof % 187.99/29.89 | | | | | | | #324. % 187.99/29.89 | | | | | | | % 187.99/29.89 | | | | | | End of split % 187.99/29.89 | | | | | | % 187.99/29.89 | | | | | End of split % 187.99/29.89 | | | | | % 187.99/29.89 | | | | End of split % 187.99/29.89 | | | | % 187.99/29.89 | | | Case 2: % 187.99/29.89 | | | | % 187.99/29.89 | | | | (67) all_252_18 = e1 & op(e2, e0) = e1 % 187.99/29.89 | | | | % 187.99/29.89 | | | | ALPHA: (67) implies: % 187.99/29.89 | | | | (68) op(e2, e0) = e1 % 187.99/29.89 | | | | % 187.99/29.89 | | | | REF_CLOSE: (2), (22), (27), (68) are inconsistent by sub-proof #516. % 187.99/29.89 | | | | % 187.99/29.89 | | | End of split % 187.99/29.89 | | | % 187.99/29.89 | | End of split % 187.99/29.89 | | % 187.99/29.89 | End of split % 187.99/29.89 | % 187.99/29.89 End of proof % 187.99/29.89 % 187.99/29.89 Sub-proof #12 shows that the following formulas are inconsistent: % 187.99/29.89 ---------------------------------------------------------------- % 187.99/29.89 (1) all_252_15 = e0 % 187.99/29.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.89 (3) ~ (all_16_2 = e3) % 187.99/29.89 (4) ~ (e3 = e0) % 187.99/29.89 (5) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = e3) % 187.99/29.89 | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) = % 187.99/29.89 e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 187.99/29.89 (6) op(e1, e4) = all_16_2 % 187.99/29.89 (7) ~ (all_4_2 = e3) % 187.99/29.89 (8) ~ (e3 = e1) % 187.99/29.89 (9) op(e1, e0) = all_34_2 % 187.99/29.89 (10) ~ (all_34_2 = e3) % 187.99/29.89 (11) all_252_13 = e1 % 187.99/29.89 (12) op(e1, e2) = all_4_2 % 187.99/29.89 % 187.99/29.89 Begin of proof % 187.99/29.89 | % 187.99/29.89 | BETA: splitting (5) gives: % 187.99/29.89 | % 187.99/29.89 | Case 1: % 187.99/29.89 | | % 187.99/29.89 | | (13) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) % 187.99/29.89 | | = e3) % 187.99/29.89 | | % 187.99/29.89 | | BETA: splitting (13) gives: % 187.99/29.89 | | % 187.99/29.89 | | Case 1: % 187.99/29.89 | | | % 187.99/29.89 | | | (14) all_252_12 = e3 & op(e1, e4) = e3 % 187.99/29.89 | | | % 187.99/29.89 | | | REF_CLOSE: (2), (3), (6), (14) are inconsistent by sub-proof #513. % 187.99/29.89 | | | % 187.99/29.89 | | Case 2: % 187.99/29.89 | | | % 187.99/29.89 | | | (15) all_252_13 = e3 & op(e1, e3) = e3 % 187.99/29.89 | | | % 187.99/29.89 | | | REF_CLOSE: (8), (11), (15) are inconsistent by sub-proof #87. % 187.99/29.89 | | | % 187.99/29.89 | | End of split % 187.99/29.89 | | % 187.99/29.89 | Case 2: % 187.99/29.89 | | % 187.99/29.89 | | (16) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) % 187.99/29.89 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 187.99/29.89 | | % 187.99/29.89 | | BETA: splitting (16) gives: % 187.99/29.89 | | % 187.99/29.89 | | Case 1: % 187.99/29.89 | | | % 187.99/29.89 | | | (17) all_252_14 = e3 & op(e1, e2) = e3 % 187.99/29.89 | | | % 187.99/29.89 | | | REF_CLOSE: (2), (7), (12), (17) are inconsistent by sub-proof #350. % 187.99/29.89 | | | % 187.99/29.89 | | Case 2: % 187.99/29.89 | | | % 187.99/29.89 | | | (18) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, % 187.99/29.89 | | | e0) = e3) % 187.99/29.89 | | | % 187.99/29.89 | | | BETA: splitting (18) gives: % 187.99/29.89 | | | % 187.99/29.89 | | | Case 1: % 187.99/29.89 | | | | % 187.99/29.89 | | | | (19) all_252_15 = e3 & op(e1, e1) = e3 % 187.99/29.89 | | | | % 187.99/29.89 | | | | ALPHA: (19) implies: % 187.99/29.89 | | | | (20) all_252_15 = e3 % 187.99/29.89 | | | | % 187.99/29.89 | | | | COMBINE_EQS: (1), (20) imply: % 187.99/29.89 | | | | (21) e3 = e0 % 187.99/29.89 | | | | % 187.99/29.89 | | | | SIMP: (21) implies: % 187.99/29.89 | | | | (22) e3 = e0 % 187.99/29.89 | | | | % 187.99/29.89 | | | | REDUCE: (4), (22) imply: % 187.99/29.89 | | | | (23) $false % 187.99/29.89 | | | | % 187.99/29.89 | | | | CLOSE: (23) is inconsistent. % 187.99/29.89 | | | | % 187.99/29.89 | | | Case 2: % 187.99/29.89 | | | | % 187.99/29.89 | | | | (24) all_252_19 = e3 & op(e1, e0) = e3 % 187.99/29.89 | | | | % 187.99/29.89 | | | | REF_CLOSE: (2), (9), (10), (24) are inconsistent by sub-proof #536. % 187.99/29.89 | | | | % 187.99/29.89 | | | End of split % 187.99/29.89 | | | % 187.99/29.89 | | End of split % 187.99/29.89 | | % 187.99/29.89 | End of split % 187.99/29.89 | % 187.99/29.89 End of proof % 187.99/29.89 % 187.99/29.89 Sub-proof #13 shows that the following formulas are inconsistent: % 187.99/29.89 ---------------------------------------------------------------- % 187.99/29.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.89 (2) op(e3, e3) = all_244_3 % 187.99/29.89 (3) op(e4, e3) = all_84_2 % 187.99/29.89 (4) ~ (all_84_2 = e1) % 187.99/29.89 (5) ~ (all_244_3 = e1) % 187.99/29.89 (6) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 187.99/29.89 % 187.99/29.89 Begin of proof % 187.99/29.89 | % 187.99/29.89 | BETA: splitting (6) gives: % 187.99/29.89 | % 187.99/29.89 | Case 1: % 187.99/29.89 | | % 187.99/29.89 | | (7) all_252_1 = e1 & op(e4, e3) = e1 % 187.99/29.89 | | % 187.99/29.89 | | ALPHA: (7) implies: % 187.99/29.89 | | (8) op(e4, e3) = e1 % 187.99/29.89 | | % 187.99/29.89 | | GROUND_INST: instantiating (1) with all_84_2, e1, e3, e4, simplifying with % 187.99/29.89 | | (3), (8) gives: % 187.99/29.89 | | (9) all_84_2 = e1 % 187.99/29.89 | | % 187.99/29.89 | | REDUCE: (4), (9) imply: % 187.99/29.89 | | (10) $false % 187.99/29.89 | | % 187.99/29.89 | | CLOSE: (10) is inconsistent. % 187.99/29.89 | | % 187.99/29.89 | Case 2: % 187.99/29.89 | | % 187.99/29.89 | | (11) all_252_3 = e1 & op(e3, e3) = e1 % 187.99/29.89 | | % 187.99/29.89 | | ALPHA: (11) implies: % 187.99/29.89 | | (12) op(e3, e3) = e1 % 187.99/29.89 | | % 187.99/29.89 | | REF_CLOSE: (1), (2), (5), (12) are inconsistent by sub-proof #305. % 187.99/29.89 | | % 187.99/29.89 | End of split % 187.99/29.89 | % 187.99/29.89 End of proof % 187.99/29.89 % 187.99/29.89 Sub-proof #14 shows that the following formulas are inconsistent: % 187.99/29.89 ---------------------------------------------------------------- % 187.99/29.89 (1) all_250_7 = all_8_2 % 187.99/29.89 (2) all_250_7 = e2 % 187.99/29.89 (3) ~ (all_8_2 = e2) % 187.99/29.89 % 187.99/29.89 Begin of proof % 187.99/29.89 | % 187.99/29.89 | COMBINE_EQS: (1), (2) imply: % 187.99/29.89 | (4) all_8_2 = e2 % 187.99/29.89 | % 187.99/29.89 | SIMP: (4) implies: % 187.99/29.89 | (5) all_8_2 = e2 % 187.99/29.89 | % 187.99/29.89 | REDUCE: (3), (5) imply: % 187.99/29.89 | (6) $false % 187.99/29.89 | % 187.99/29.89 | CLOSE: (6) is inconsistent. % 187.99/29.89 | % 187.99/29.89 End of proof % 187.99/29.89 % 187.99/29.89 Sub-proof #15 shows that the following formulas are inconsistent: % 187.99/29.89 ---------------------------------------------------------------- % 187.99/29.89 (1) all_250_7 = all_8_2 % 187.99/29.89 (2) all_250_7 = e3 % 187.99/29.89 (3) ~ (all_8_2 = e3) % 187.99/29.89 % 187.99/29.89 Begin of proof % 187.99/29.89 | % 187.99/29.89 | COMBINE_EQS: (1), (2) imply: % 187.99/29.89 | (4) all_8_2 = e3 % 187.99/29.89 | % 187.99/29.89 | SIMP: (4) implies: % 187.99/29.89 | (5) all_8_2 = e3 % 187.99/29.89 | % 187.99/29.89 | REDUCE: (3), (5) imply: % 187.99/29.89 | (6) $false % 187.99/29.89 | % 187.99/29.89 | CLOSE: (6) is inconsistent. % 187.99/29.89 | % 187.99/29.89 End of proof % 187.99/29.89 % 187.99/29.89 Sub-proof #16 shows that the following formulas are inconsistent: % 187.99/29.89 ---------------------------------------------------------------- % 187.99/29.89 (1) all_250_7 = all_8_2 % 187.99/29.89 (2) all_250_7 = e4 % 187.99/29.89 (3) ~ (all_8_2 = e4) % 187.99/29.89 % 187.99/29.89 Begin of proof % 187.99/29.89 | % 187.99/29.89 | COMBINE_EQS: (1), (2) imply: % 187.99/29.89 | (4) all_8_2 = e4 % 187.99/29.89 | % 187.99/29.89 | SIMP: (4) implies: % 187.99/29.89 | (5) all_8_2 = e4 % 187.99/29.89 | % 187.99/29.89 | REDUCE: (3), (5) imply: % 187.99/29.89 | (6) $false % 187.99/29.89 | % 187.99/29.89 | CLOSE: (6) is inconsistent. % 187.99/29.89 | % 187.99/29.89 End of proof % 187.99/29.89 % 187.99/29.89 Sub-proof #17 shows that the following formulas are inconsistent: % 187.99/29.89 ---------------------------------------------------------------- % 187.99/29.89 (1) ~ (all_62_2 = all_34_2) % 187.99/29.89 (2) all_90_2 = all_22_2 % 187.99/29.89 (3) ~ (all_36_2 = e0) | (op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 187.99/29.89 (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 187.99/29.89 $i(all_36_0)))) % 187.99/29.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 187.99/29.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 187.99/29.89 (5) ~ (all_162_2 = e1) | (op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ % 187.99/29.89 (all_162_1 = e4) | ( ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 187.99/29.89 $i(all_162_0)))) % 187.99/29.89 (6) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 187.99/29.89 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 187.99/29.89 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 187.99/29.89 (7) ~ (all_180_2 = e4) | (op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 187.99/29.89 (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 187.99/29.89 $i(all_180_0)))) % 187.99/29.89 (8) op(e0, e2) = all_28_2 % 187.99/29.89 (9) ~ (all_244_24 = e2) % 187.99/29.89 (10) op(e3, e1) = all_36_2 % 187.99/29.89 (11) all_250_21 = all_22_2 % 187.99/29.89 (12) op(e3, e3) = all_244_3 % 187.99/29.89 (13) op(e2, all_6_1) = e0 % 187.99/29.89 (14) op(e1, all_34_2) = e0 % 187.99/29.89 (15) ~ (all_62_2 = e2) | (op(e2, e1) = all_62_1 & $i(all_62_1) & ( ~ % 187.99/29.89 (all_62_1 = e4) | ( ~ (all_62_0 = e0) & op(e1, e4) = all_62_0 & % 187.99/29.89 $i(all_62_0)))) % 187.99/29.89 (16) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 187.99/29.89 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 187.99/29.89 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 187.99/29.89 (17) op(e1, e3) = all_62_2 % 187.99/29.89 (18) ~ (all_24_2 = e2) | (op(e2, e1) = all_24_1 & $i(all_24_1) & ( ~ % 187.99/29.89 (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e1, e3) = all_24_0 & % 187.99/29.89 $i(all_24_0)))) % 187.99/29.89 (19) op(e2, all_38_2) = e1 % 187.99/29.89 (20) ~ (all_26_2 = e0) % 187.99/29.89 (21) op(e1, e1) = all_244_15 % 187.99/29.89 (22) all_24_2 = all_16_2 % 187.99/29.89 (23) ~ (all_48_2 = all_34_2) % 187.99/29.89 (24) op(e2, e3) = all_10_2 % 187.99/29.89 (25) ~ (all_244_15 = all_36_2) % 187.99/29.89 (26) all_60_2 = all_20_2 % 187.99/29.89 (27) op(e4, e3) = all_84_2 % 187.99/29.89 (28) ~ (e4 = e3) % 187.99/29.89 (29) ~ (all_4_2 = e0) % 187.99/29.89 (30) ~ (all_192_2 = e4) | (op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 187.99/29.89 (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, e3) = all_192_0 & % 187.99/29.89 $i(all_192_0)))) % 187.99/29.89 (31) ~ (all_64_2 = all_16_2) % 187.99/29.89 (32) all_250_19 = all_34_2 % 187.99/29.89 (33) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 187.99/29.89 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 187.99/29.89 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 187.99/29.89 (34) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 187.99/29.89 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 187.99/29.89 $i(all_38_0)))) % 187.99/29.89 (35) ~ (all_36_2 = all_26_2) % 187.99/29.89 (36) all_58_2 = all_20_2 % 187.99/29.89 (37) ~ (all_28_2 = all_20_2) % 187.99/29.89 (38) op(e3, e4) = all_100_2 % 187.99/29.89 (39) ~ (all_20_2 = e3) % 187.99/29.90 (40) ~ (all_46_2 = e0) | (op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ % 187.99/29.90 (all_46_1 = e2) | ( ~ (all_46_0 = e4) & op(e3, e2) = all_46_0 & % 187.99/29.90 $i(all_46_0)))) % 187.99/29.90 (41) ~ (all_36_2 = all_20_2) % 187.99/29.90 (42) ~ (all_90_2 = e4) | (op(e4, e0) = all_90_1 & $i(all_90_1) & ( ~ % 187.99/29.90 (all_90_1 = e2) | ( ~ (all_90_0 = e1) & op(e0, e2) = all_90_0 & % 187.99/29.90 $i(all_90_0)))) % 187.99/29.90 (43) op(e0, e0) = all_244_24 % 187.99/29.90 (44) op(e0, e1) = all_20_2 % 187.99/29.90 (45) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = % 187.99/29.90 e4) | (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 = e4 & op(e0, % 187.99/29.90 e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 187.99/29.90 (46) op(e0, all_20_2) = e1 % 187.99/29.90 (47) ~ (all_244_24 = all_34_2) % 187.99/29.90 (48) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 187.99/29.90 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 187.99/29.90 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 187.99/29.90 (49) op(all_40_2, all_28_2) = e0 % 187.99/29.90 (50) ~ (all_244_15 = all_38_2) % 187.99/29.90 (51) all_232_2 = all_34_2 % 187.99/29.90 (52) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 187.99/29.90 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 187.99/29.90 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 187.99/29.90 (53) op(e4, e1) = all_26_2 % 187.99/29.90 (54) op(all_4_2, all_38_2) = e2 % 187.99/29.90 (55) op(e0, e3) = all_22_2 % 187.99/29.90 (56) ~ (all_6_1 = e2) % 187.99/29.90 (57) op(e0, all_22_2) = e3 % 187.99/29.90 (58) op(e4, e4) = all_244_0 % 187.99/29.90 (59) ~ (all_60_2 = e2) | (op(e2, e0) = all_60_1 & $i(all_60_1) & ( ~ % 187.99/29.90 (all_60_1 = e4) | ( ~ (all_60_0 = e3) & op(e0, e4) = all_60_0 & % 187.99/29.90 $i(all_60_0)))) % 187.99/29.90 (60) ~ (all_28_2 = all_4_2) % 187.99/29.90 (61) all_192_2 = all_4_2 % 187.99/29.90 (62) op(e0, e4) = all_6_1 % 187.99/29.90 (63) ~ (all_34_2 = all_4_2) % 187.99/29.90 (64) all_250_19 = e4 | all_250_19 = e3 | all_250_19 = e2 | all_250_19 = e1 | % 187.99/29.90 all_250_19 = e0 % 187.99/29.90 (65) ~ (e3 = e0) % 187.99/29.90 (66) op(e3, e2) = all_8_2 % 187.99/29.90 (67) ~ (all_28_2 = e0) % 187.99/29.90 (68) op(all_244_15, all_244_15) = e1 % 187.99/29.90 (69) op(e3, all_48_2) = e0 % 187.99/29.90 (70) ~ (all_62_2 = all_10_2) % 187.99/29.90 (71) op(e2, all_40_2) = e0 % 187.99/29.90 (72) ~ (all_244_3 = all_36_2) % 187.99/29.90 (73) ~ (all_22_2 = e2) % 187.99/29.90 (74) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 187.99/29.90 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 187.99/29.90 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 187.99/29.90 (75) ~ (all_244_3 = all_62_2) % 187.99/29.90 (76) op(e1, e4) = all_16_2 % 187.99/29.90 (77) op(e1, all_16_2) = e4 % 187.99/29.90 (78) ~ (all_244_15 = all_20_2) % 187.99/29.90 (79) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 187.99/29.90 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 187.99/29.90 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 187.99/29.90 (80) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 187.99/29.90 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 187.99/29.90 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 187.99/29.90 (81) ~ (all_48_2 = all_40_2) % 187.99/29.90 (82) ~ (all_232_2 = e4) | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 187.99/29.90 (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 & % 187.99/29.90 $i(all_232_0)))) % 187.99/29.90 (83) ~ (all_16_2 = all_4_2) % 187.99/29.90 (84) ~ (all_244_24 = all_28_2) % 187.99/29.90 (85) ~ (all_100_2 = all_16_2) % 187.99/29.90 (86) op(all_34_2, all_20_2) = e0 % 187.99/29.90 (87) op(e2, e4) = all_64_2 % 187.99/29.90 (88) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2) % 187.99/29.90 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = % 187.99/29.90 e2) | (all_252_20 = e2 & op(e0, e4) = e2) % 187.99/29.90 (89) op(e2, e0) = all_40_2 % 187.99/29.90 (90) op(all_28_2, all_40_2) = e2 % 187.99/29.90 (91) op(all_22_2, all_48_2) = e3 % 187.99/29.90 (92) ~ (all_36_2 = all_8_2) % 187.99/29.90 (93) op(all_20_2, all_34_2) = e1 % 187.99/29.90 (94) op(e3, e0) = all_48_2 % 187.99/29.90 (95) all_46_2 = all_36_2 % 187.99/29.90 (96) all_70_2 = all_62_2 % 187.99/29.90 (97) ~ (all_70_2 = e0) | (op(e0, e1) = all_70_1 & $i(all_70_1) & ( ~ % 187.99/29.90 (all_70_1 = e2) | ( ~ (all_70_0 = e4) & op(e1, e2) = all_70_0 & % 187.99/29.90 $i(all_70_0)))) % 187.99/29.90 (98) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 187.99/29.90 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 187.99/29.90 $i(all_188_0)))) % 187.99/29.90 (99) all_162_2 = all_28_2 % 187.99/29.90 (100) ~ (all_100_2 = all_36_2) % 187.99/29.90 (101) op(e0, e4) = all_12_2 % 187.99/29.90 (102) op(e1, all_62_2) = e3 % 187.99/29.90 (103) op(e3, all_36_2) = e1 % 187.99/29.90 (104) ~ (all_244_0 = all_16_2) % 187.99/29.90 (105) ~ (e3 = e1) % 187.99/29.90 (106) ~ (e2 = e0) % 187.99/29.90 (107) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) % 187.99/29.90 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = % 187.99/29.90 e0) | (all_252_17 = e0 & op(e3, e0) = e0) % 187.99/29.90 (108) op(e1, e0) = all_34_2 % 187.99/29.90 (109) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 187.99/29.90 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 187.99/29.90 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 187.99/29.90 (110) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | % 187.99/29.90 all_250_21 = e0 % 187.99/29.90 (111) ~ (all_28_2 = e1) | (op(e1, e0) = all_28_1 & $i(all_28_1) & ( ~ % 187.99/29.90 (all_28_1 = e3) | ( ~ (all_28_0 = e4) & op(e0, e3) = all_28_0 & % 187.99/29.90 $i(all_28_0)))) % 187.99/29.90 (112) all_188_2 = all_38_2 % 187.99/29.90 (113) ~ (all_28_2 = all_22_2) % 187.99/29.90 (114) ~ (all_84_2 = all_62_2) % 187.99/29.90 (115) ~ (all_16_2 = all_6_1) % 187.99/29.90 (116) ~ (all_12_2 = e3) % 187.99/29.90 (117) all_180_2 = all_4_2 % 187.99/29.90 (118) ~ (all_34_2 = e2) % 187.99/29.90 (119) ~ (all_34_2 = e4) | (op(e4, e1) = all_34_1 & $i(all_34_1) & ( ~ % 187.99/29.90 (all_34_1 = e2) | ( ~ (all_34_0 = e3) & op(e1, e2) = all_34_0 & % 187.99/29.90 $i(all_34_0)))) % 187.99/29.90 (120) op(e1, e2) = all_4_2 % 187.99/29.90 (121) ~ (all_22_2 = all_20_2) % 187.99/29.90 (122) ~ (all_62_2 = all_22_2) % 187.99/29.90 (123) ~ (all_244_15 = all_4_2) % 187.99/29.90 (124) op(e2, e1) = all_38_2 % 187.99/29.90 (125) ~ (e4 = e1) % 187.99/29.90 (126) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 187.99/29.90 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 187.99/29.90 $i(all_58_0)))) % 187.99/29.90 % 187.99/29.90 Begin of proof % 187.99/29.90 | % 187.99/29.90 | BETA: splitting (18) gives: % 187.99/29.90 | % 187.99/29.90 | Case 1: % 187.99/29.90 | | % 187.99/29.90 | | (127) ~ (all_24_2 = e2) % 187.99/29.90 | | % 187.99/29.90 | | REDUCE: (22), (127) imply: % 187.99/29.90 | | (128) ~ (all_16_2 = e2) % 187.99/29.90 | | % 187.99/29.90 | | BETA: splitting (111) gives: % 187.99/29.90 | | % 187.99/29.90 | | Case 1: % 187.99/29.90 | | | % 187.99/29.90 | | | (129) ~ (all_28_2 = e1) % 187.99/29.90 | | | % 187.99/29.90 | | | REF_CLOSE: (4), (8), (9), (36), (43), (44), (46), (55), (56), (62), (67), % 187.99/29.90 | | | (71), (73), (90), (109), (126), (129) are inconsistent by % 187.99/29.90 | | | sub-proof #20. % 187.99/29.90 | | | % 187.99/29.90 | | Case 2: % 187.99/29.90 | | | % 187.99/29.90 | | | (130) all_28_2 = e1 % 187.99/29.90 | | | (131) op(e1, e0) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = e3) | ( ~ % 187.99/29.90 | | | (all_28_0 = e4) & op(e0, e3) = all_28_0 & $i(all_28_0))) % 187.99/29.90 | | | % 187.99/29.90 | | | ALPHA: (131) implies: % 187.99/29.90 | | | (132) op(e1, e0) = all_28_1 % 187.99/29.90 | | | % 187.99/29.90 | | | COMBINE_EQS: (99), (130) imply: % 187.99/29.90 | | | (133) all_162_2 = e1 % 187.99/29.90 | | | % 187.99/29.90 | | | REDUCE: (84), (130) imply: % 187.99/29.90 | | | (134) ~ (all_244_24 = e1) % 187.99/29.90 | | | % 187.99/29.90 | | | REDUCE: (60), (130) imply: % 187.99/29.90 | | | (135) ~ (all_4_2 = e1) % 187.99/29.90 | | | % 187.99/29.90 | | | SIMP: (135) implies: % 187.99/29.90 | | | (136) ~ (all_4_2 = e1) % 187.99/29.90 | | | % 187.99/29.90 | | | REDUCE: (49), (130) imply: % 187.99/29.90 | | | (137) op(all_40_2, e1) = e0 % 187.99/29.90 | | | % 187.99/29.90 | | | BETA: splitting (5) gives: % 187.99/29.90 | | | % 187.99/29.90 | | | Case 1: % 187.99/29.90 | | | | % 187.99/29.90 | | | | (138) ~ (all_162_2 = e1) % 187.99/29.90 | | | | % 187.99/29.90 | | | | REDUCE: (133), (138) imply: % 187.99/29.90 | | | | (139) $false % 187.99/29.90 | | | | % 187.99/29.90 | | | | CLOSE: (139) is inconsistent. % 187.99/29.90 | | | | % 187.99/29.90 | | | Case 2: % 187.99/29.90 | | | | % 187.99/29.90 | | | | (140) op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ (all_162_1 = e4) | % 187.99/29.90 | | | | ( ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 187.99/29.90 | | | | $i(all_162_0))) % 187.99/29.90 | | | | % 187.99/29.90 | | | | ALPHA: (140) implies: % 187.99/29.90 | | | | (141) op(e1, e0) = all_162_1 % 187.99/29.90 | | | | % 187.99/29.90 | | | | BETA: splitting (109) gives: % 187.99/29.90 | | | | % 187.99/29.90 | | | | Case 1: % 187.99/29.90 | | | | | % 187.99/29.90 | | | | | (142) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & % 187.99/29.90 | | | | | op(e0, e3) = e2) % 187.99/29.90 | | | | | % 187.99/29.90 | | | | | REF_CLOSE: (4), (55), (56), (62), (73), (142) are inconsistent by % 187.99/29.90 | | | | | sub-proof #21. % 187.99/29.90 | | | | | % 187.99/29.90 | | | | Case 2: % 187.99/29.90 | | | | | % 187.99/29.90 | | | | | (143) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & % 187.99/29.90 | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 187.99/29.90 | | | | | % 187.99/29.90 | | | | | BETA: splitting (143) gives: % 187.99/29.90 | | | | | % 187.99/29.90 | | | | | Case 1: % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | | (144) all_252_22 = e2 & op(e0, e2) = e2 % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | | ALPHA: (144) implies: % 187.99/29.90 | | | | | | (145) op(e0, e2) = e2 % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | | REF_CLOSE: (4), (8), (67), (71), (90), (145) are inconsistent by % 187.99/29.90 | | | | | | sub-proof #288. % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | Case 2: % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | | (146) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 187.99/29.90 | | | | | | op(e0, e0) = e2) % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | | BETA: splitting (146) gives: % 187.99/29.90 | | | | | | % 187.99/29.90 | | | | | | Case 1: % 187.99/29.90 | | | | | | | % 187.99/29.90 | | | | | | | (147) all_252_23 = e2 & op(e0, e1) = e2 % 187.99/29.90 | | | | | | | % 187.99/29.90 | | | | | | | ALPHA: (147) implies: % 187.99/29.90 | | | | | | | (148) all_252_23 = e2 % 187.99/29.90 | | | | | | | (149) op(e0, e1) = e2 % 187.99/29.90 | | | | | | | % 187.99/29.90 | | | | | | | BETA: splitting (42) gives: % 187.99/29.90 | | | | | | | % 187.99/29.90 | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | (150) ~ (all_90_2 = e4) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (2), (150) imply: % 187.99/29.90 | | | | | | | | (151) ~ (all_22_2 = e4) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | GROUND_INST: instantiating (4) with all_20_2, e2, e1, e0, % 187.99/29.90 | | | | | | | | simplifying with (44), (149) gives: % 187.99/29.90 | | | | | | | | (152) all_20_2 = e2 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | GROUND_INST: instantiating (4) with all_34_2, all_162_1, e0, e1, % 187.99/29.90 | | | | | | | | simplifying with (108), (141) gives: % 187.99/29.90 | | | | | | | | (153) all_162_1 = all_34_2 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | GROUND_INST: instantiating (4) with all_28_1, all_162_1, e0, e1, % 187.99/29.90 | | | | | | | | simplifying with (132), (141) gives: % 187.99/29.90 | | | | | | | | (154) all_162_1 = all_28_1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | COMBINE_EQS: (153), (154) imply: % 187.99/29.90 | | | | | | | | (155) all_34_2 = all_28_1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | SIMP: (155) implies: % 187.99/29.90 | | | | | | | | (156) all_34_2 = all_28_1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | COMBINE_EQS: (36), (152) imply: % 187.99/29.90 | | | | | | | | (157) all_58_2 = e2 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | COMBINE_EQS: (26), (152) imply: % 187.99/29.90 | | | | | | | | (158) all_60_2 = e2 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | COMBINE_EQS: (51), (156) imply: % 187.99/29.90 | | | | | | | | (159) all_232_2 = all_28_1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | COMBINE_EQS: (32), (156) imply: % 187.99/29.90 | | | | | | | | (160) all_250_19 = all_28_1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (78), (152) imply: % 187.99/29.90 | | | | | | | | (161) ~ (all_244_15 = e2) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (47), (156) imply: % 187.99/29.90 | | | | | | | | (162) ~ (all_244_24 = all_28_1) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (1), (156) imply: % 187.99/29.90 | | | | | | | | (163) ~ (all_62_2 = all_28_1) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (23), (156) imply: % 187.99/29.90 | | | | | | | | (164) ~ (all_48_2 = all_28_1) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (63), (156) imply: % 187.99/29.90 | | | | | | | | (165) ~ (all_28_1 = all_4_2) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (118), (156) imply: % 187.99/29.90 | | | | | | | | (166) ~ (all_28_1 = e2) % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (93), (152), (156) imply: % 187.99/29.90 | | | | | | | | (167) op(e2, all_28_1) = e1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (14), (156) imply: % 187.99/29.90 | | | | | | | | (168) op(e1, all_28_1) = e0 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | REDUCE: (46), (152) imply: % 187.99/29.90 | | | | | | | | (169) op(e0, e2) = e1 % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | BETA: splitting (126) gives: % 187.99/29.90 | | | | | | | | % 187.99/29.90 | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | (170) ~ (all_58_2 = e2) % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | REDUCE: (157), (170) imply: % 187.99/29.90 | | | | | | | | | (171) $false % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | CLOSE: (171) is inconsistent. % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | Case 2: % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | (172) op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ (all_58_1 % 187.99/29.90 | | | | | | | | | = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = % 187.99/29.90 | | | | | | | | | all_58_0 & $i(all_58_0))) % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | ALPHA: (172) implies: % 187.99/29.90 | | | | | | | | | (173) op(e2, e0) = all_58_1 % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | BETA: splitting (59) gives: % 187.99/29.90 | | | | | | | | | % 187.99/29.90 | | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | (174) ~ (all_60_2 = e2) % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | REDUCE: (158), (174) imply: % 187.99/29.90 | | | | | | | | | | (175) $false % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | CLOSE: (175) is inconsistent. % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | Case 2: % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | (176) op(e2, e0) = all_60_1 & $i(all_60_1) & ( ~ % 187.99/29.90 | | | | | | | | | | (all_60_1 = e4) | ( ~ (all_60_0 = e3) & op(e0, % 187.99/29.90 | | | | | | | | | | e4) = all_60_0 & $i(all_60_0))) % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | ALPHA: (176) implies: % 187.99/29.90 | | | | | | | | | | (177) op(e2, e0) = all_60_1 % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | GROUND_INST: instantiating (4) with all_40_2, all_60_1, e0, e2, % 187.99/29.90 | | | | | | | | | | simplifying with (89), (177) gives: % 187.99/29.90 | | | | | | | | | | (178) all_60_1 = all_40_2 % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | GROUND_INST: instantiating (4) with all_58_1, all_60_1, e0, e2, % 187.99/29.90 | | | | | | | | | | simplifying with (173), (177) gives: % 187.99/29.90 | | | | | | | | | | (179) all_60_1 = all_58_1 % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | COMBINE_EQS: (178), (179) imply: % 187.99/29.90 | | | | | | | | | | (180) all_58_1 = all_40_2 % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | SIMP: (180) implies: % 187.99/29.90 | | | | | | | | | | (181) all_58_1 = all_40_2 % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | BETA: splitting (119) gives: % 187.99/29.90 | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | (182) ~ (all_34_2 = e4) % 187.99/29.90 | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | REDUCE: (156), (182) imply: % 187.99/29.90 | | | | | | | | | | | (183) ~ (all_28_1 = e4) % 187.99/29.90 | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | BETA: splitting (3) gives: % 187.99/29.90 | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | (184) ~ (all_36_2 = e0) % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | REF_CLOSE: (4), (10), (19), (20), (21), (34), (43), (50), % 187.99/29.90 | | | | | | | | | | | | (53), (68), (80), (89), (98), (106), (112), (124), % 187.99/29.90 | | | | | | | | | | | | (134), (137), (148), (184) are inconsistent by % 187.99/29.90 | | | | | | | | | | | | sub-proof #284. % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | Case 2: % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | (185) all_36_2 = e0 % 187.99/29.90 | | | | | | | | | | | | (186) op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 187.99/29.90 | | | | | | | | | | | | (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, % 187.99/29.90 | | | | | | | | | | | | e4) = all_36_0 & $i(all_36_0))) % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | ALPHA: (186) implies: % 187.99/29.90 | | | | | | | | | | | | (187) op(e0, e3) = all_36_1 % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | COMBINE_EQS: (95), (185) imply: % 187.99/29.90 | | | | | | | | | | | | (188) all_46_2 = e0 % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | REDUCE: (103), (185) imply: % 187.99/29.90 | | | | | | | | | | | | (189) op(e3, e0) = e1 % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | BETA: splitting (40) gives: % 187.99/29.90 | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | (190) ~ (all_46_2 = e0) % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | REDUCE: (188), (190) imply: % 187.99/29.90 | | | | | | | | | | | | | (191) $false % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | CLOSE: (191) is inconsistent. % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | Case 2: % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | (192) op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ % 187.99/29.90 | | | | | | | | | | | | | (all_46_1 = e2) | ( ~ (all_46_0 = e4) & op(e3, % 187.99/29.90 | | | | | | | | | | | | | e2) = all_46_0 & $i(all_46_0))) % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | ALPHA: (192) implies: % 187.99/29.90 | | | | | | | | | | | | | (193) op(e0, e3) = all_46_1 % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_22_2, all_46_1, e3, e0, % 187.99/29.90 | | | | | | | | | | | | | simplifying with (55), (193) gives: % 187.99/29.90 | | | | | | | | | | | | | (194) all_46_1 = all_22_2 % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_36_1, all_46_1, e3, e0, % 187.99/29.90 | | | | | | | | | | | | | simplifying with (187), (193) gives: % 187.99/29.90 | | | | | | | | | | | | | (195) all_46_1 = all_36_1 % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_48_2, e1, e0, e3, % 187.99/29.90 | | | | | | | | | | | | | simplifying with (94), (189) gives: % 187.99/29.90 | | | | | | | | | | | | | (196) all_48_2 = e1 % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | COMBINE_EQS: (194), (195) imply: % 187.99/29.90 | | | | | | | | | | | | | (197) all_36_1 = all_22_2 % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | REDUCE: (81), (196) imply: % 187.99/29.90 | | | | | | | | | | | | | (198) ~ (all_40_2 = e1) % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | SIMP: (198) implies: % 187.99/29.90 | | | | | | | | | | | | | (199) ~ (all_40_2 = e1) % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | REDUCE: (164), (196) imply: % 187.99/29.90 | | | | | | | | | | | | | (200) ~ (all_28_1 = e1) % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | SIMP: (200) implies: % 187.99/29.90 | | | | | | | | | | | | | (201) ~ (all_28_1 = e1) % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | BETA: splitting (15) gives: % 187.99/29.90 | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | (202) ~ (all_62_2 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (21), (48), (54), (76), (108), % 187.99/29.90 | | | | | | | | | | | | | | (118), (120), (128), (136), (161), (202) are % 187.99/29.90 | | | | | | | | | | | | | | inconsistent by sub-proof #282. % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | Case 2: % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | (203) all_62_2 = e2 % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REDUCE: (75), (203) imply: % 187.99/29.90 | | | | | | | | | | | | | | (204) ~ (all_244_3 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REDUCE: (114), (203) imply: % 187.99/29.90 | | | | | | | | | | | | | | (205) ~ (all_84_2 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REDUCE: (163), (203) imply: % 187.99/29.90 | | | | | | | | | | | | | | (206) ~ (all_28_1 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REDUCE: (122), (203) imply: % 187.99/29.90 | | | | | | | | | | | | | | (207) ~ (all_22_2 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REDUCE: (70), (203) imply: % 187.99/29.90 | | | | | | | | | | | | | | (208) ~ (all_10_2 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | SIMP: (208) implies: % 187.99/29.90 | | | | | | | | | | | | | | (209) ~ (all_10_2 = e2) % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | REDUCE: (102), (203) imply: % 187.99/29.90 | | | | | | | | | | | | | | (210) op(e1, e2) = e3 % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | BETA: splitting (79) gives: % 187.99/29.90 | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | Case 1: % 187.99/29.90 | | | | | | | | | | | | | | | % 187.99/29.90 | | | | | | | | | | | | | | | (211) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 187.99/29.91 | | | | | | | | | | | | | | | e2 & op(e3, e3) = e2) % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | (212) all_252_1 = e2 & op(e4, e3) = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (27), (205), (212) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | | | | sub-proof #523. % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | (213) all_252_3 = e2 & op(e3, e3) = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (204), (213) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | | | | sub-proof #496. % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | (214) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 187.99/29.91 | | | | | | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 187.99/29.91 | | | | | | | | | | | | | | | op(e0, e3) = e2) % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | BETA: splitting (214) gives: % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | (215) all_252_7 = e2 & op(e2, e3) = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (24), (209), (215) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | | | | sub-proof #458. % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | (216) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 187.99/29.91 | | | | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_4_2, e3, e2, e1, % 187.99/29.91 | | | | | | | | | | | | | | | | | simplifying with (120), (210) gives: % 187.99/29.91 | | | | | | | | | | | | | | | | | (217) all_4_2 = e3 % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | REDUCE: (165), (217) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | (218) ~ (all_28_1 = e3) % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | BETA: splitting (64) gives: % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | (219) all_250_19 = e4 % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (219) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | (220) all_28_1 = e4 % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | SIMP: (220) implies: % 187.99/29.91 | | | | | | | | | | | | | | | | | | (221) all_28_1 = e4 % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | REDUCE: (183), (221) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | (222) $false % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | (223) all_250_19 = e3 | all_250_19 = e2 | all_250_19 = % 187.99/29.91 | | | | | | | | | | | | | | | | | | e1 | all_250_19 = e0 % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | (224) all_250_19 = e3 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (224) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | (225) all_28_1 = e3 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | SIMP: (225) implies: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | (226) all_28_1 = e3 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | REDUCE: (218), (226) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | (227) $false % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | CLOSE: (227) is inconsistent. % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | (228) all_250_19 = e2 | all_250_19 = e1 | all_250_19 = % 187.99/29.91 | | | | | | | | | | | | | | | | | | | e0 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | (229) all_250_19 = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (229) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | (230) all_28_1 = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | SIMP: (230) implies: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | (231) all_28_1 = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (231) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | (232) $false % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | CLOSE: (232) is inconsistent. % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | (233) all_250_19 = e1 | all_250_19 = e0 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | (234) all_250_19 = e1 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (234) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | (235) all_28_1 = e1 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (201), (235) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | (236) $false % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent. % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | (237) all_250_19 = e0 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (160), (237) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | (238) all_28_1 = e0 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (238) imply: % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | (239) op(e2, e0) = e1 % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (89), (199), (239) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | sub-proof #516. % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | (240) all_252_21 = e2 & op(e0, e3) = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 187.99/29.91 | | | | | | | | | | | | | | | | | (241) op(e0, e3) = e2 % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (55), (73), (241) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | | | | | sub-proof #543. % 187.99/29.91 | | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | (242) all_34_2 = e4 % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | COMBINE_EQS: (156), (242) imply: % 187.99/29.91 | | | | | | | | | | | (243) all_28_1 = e4 % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | COMBINE_EQS: (159), (243) imply: % 187.99/29.91 | | | | | | | | | | | (244) all_232_2 = e4 % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | REDUCE: (162), (243) imply: % 187.99/29.91 | | | | | | | | | | | (245) ~ (all_244_24 = e4) % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | REDUCE: (166), (243) imply: % 187.99/29.91 | | | | | | | | | | | (246) ~ (e4 = e2) % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | REDUCE: (168), (243) imply: % 187.99/29.91 | | | | | | | | | | | (247) op(e1, e4) = e0 % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | BETA: splitting (45) gives: % 187.99/29.91 | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | (248) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 % 187.99/29.91 | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | BETA: splitting (248) gives: % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | (249) all_252_20 = e4 & op(e0, e4) = e4 % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | ALPHA: (249) implies: % 187.99/29.91 | | | | | | | | | | | | | (250) op(e0, e4) = e4 % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | REF_CLOSE: (4), (13), (31), (62), (76), (82), (87), (244), % 187.99/29.91 | | | | | | | | | | | | | (247), (250) are inconsistent by sub-proof #19. % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | (251) all_252_21 = e4 & op(e0, e3) = e4 % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | REF_CLOSE: (4), (55), (151), (251) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | sub-proof #519. % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | End of split % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | (252) (all_252_22 = e4 & op(e0, e2) = e4) | (all_252_23 % 187.99/29.91 | | | | | | | | | | | | = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & % 187.99/29.91 | | | | | | | | | | | | op(e0, e0) = e4) % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | BETA: splitting (252) gives: % 187.99/29.91 | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | (253) all_252_22 = e4 & op(e0, e2) = e4 % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | ALPHA: (253) implies: % 187.99/29.91 | | | | | | | | | | | | | (254) op(e0, e2) = e4 % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | REF_CLOSE: (4), (125), (169), (254) are inconsistent by % 187.99/29.91 | | | | | | | | | | | | | sub-proof #256. % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | Case 2: % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | (255) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 % 187.99/29.91 | | | | | | | | | | | | | = e4 & op(e0, e0) = e4) % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | BETA: splitting (255) gives: % 187.99/29.91 | | | | | | | | | | | | | % 187.99/29.91 | | | | | | | | | | | | | Case 1: % 187.99/29.91 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | | (256) all_252_23 = e4 & op(e0, e1) = e4 % 187.99/29.93 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | | ALPHA: (256) implies: % 187.99/29.93 | | | | | | | | | | | | | | (257) op(e0, e1) = e4 % 187.99/29.93 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | | REF_CLOSE: (4), (149), (246), (257) are inconsistent by % 187.99/29.93 | | | | | | | | | | | | | | sub-proof #322. % 187.99/29.93 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | Case 2: % 187.99/29.93 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | | (258) all_252_24 = e4 & op(e0, e0) = e4 % 187.99/29.93 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | | REF_CLOSE: (4), (43), (245), (258) are inconsistent by % 187.99/29.93 | | | | | | | | | | | | | | sub-proof #18. % 187.99/29.93 | | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | | End of split % 187.99/29.93 | | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | | End of split % 187.99/29.93 | | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | | End of split % 187.99/29.93 | | | | | | | | | | | % 187.99/29.93 | | | | | | | | | | End of split % 187.99/29.93 | | | | | | | | | | % 187.99/29.93 | | | | | | | | | End of split % 187.99/29.93 | | | | | | | | | % 187.99/29.93 | | | | | | | | End of split % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | Case 2: % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | (259) all_90_2 = e4 % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | COMBINE_EQS: (2), (259) imply: % 187.99/29.93 | | | | | | | | (260) all_22_2 = e4 % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (57), (260) imply: % 187.99/29.93 | | | | | | | | (261) op(e0, e4) = e3 % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REF_CLOSE: (4), (101), (116), (261) are inconsistent by % 187.99/29.93 | | | | | | | | sub-proof #512. % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | End of split % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | Case 2: % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | (262) all_252_24 = e2 & op(e0, e0) = e2 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | ALPHA: (262) implies: % 187.99/29.93 | | | | | | | (263) op(e0, e0) = e2 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | REF_CLOSE: (4), (9), (43), (263) are inconsistent by sub-proof % 187.99/29.93 | | | | | | | #477. % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | End of split % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | End of split % 187.99/29.93 | | | | | % 187.99/29.93 | | | | End of split % 187.99/29.93 | | | | % 187.99/29.93 | | | End of split % 187.99/29.93 | | | % 187.99/29.93 | | End of split % 187.99/29.93 | | % 187.99/29.93 | Case 2: % 187.99/29.93 | | % 187.99/29.93 | | (264) all_24_2 = e2 % 187.99/29.93 | | % 187.99/29.93 | | COMBINE_EQS: (22), (264) imply: % 187.99/29.93 | | (265) all_16_2 = e2 % 187.99/29.93 | | % 187.99/29.93 | | REDUCE: (104), (265) imply: % 187.99/29.93 | | (266) ~ (all_244_0 = e2) % 187.99/29.93 | | % 187.99/29.93 | | REDUCE: (85), (265) imply: % 187.99/29.93 | | (267) ~ (all_100_2 = e2) % 187.99/29.93 | | % 187.99/29.93 | | REDUCE: (31), (265) imply: % 187.99/29.93 | | (268) ~ (all_64_2 = e2) % 187.99/29.93 | | % 187.99/29.93 | | REDUCE: (115), (265) imply: % 187.99/29.93 | | (269) ~ (all_6_1 = e2) % 187.99/29.93 | | % 187.99/29.93 | | REDUCE: (83), (265) imply: % 187.99/29.93 | | (270) ~ (all_4_2 = e2) % 187.99/29.93 | | % 187.99/29.93 | | SIMP: (270) implies: % 187.99/29.93 | | (271) ~ (all_4_2 = e2) % 187.99/29.93 | | % 187.99/29.93 | | REDUCE: (77), (265) imply: % 187.99/29.93 | | (272) op(e1, e2) = e4 % 187.99/29.93 | | % 187.99/29.93 | | BETA: splitting (88) gives: % 187.99/29.93 | | % 187.99/29.93 | | Case 1: % 187.99/29.93 | | | % 187.99/29.93 | | | (273) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) % 187.99/29.93 | | | = e2) % 187.99/29.93 | | | % 187.99/29.93 | | | REF_CLOSE: (4), (38), (58), (266), (267), (273) are inconsistent by % 187.99/29.93 | | | sub-proof #325. % 187.99/29.93 | | | % 187.99/29.93 | | Case 2: % 187.99/29.93 | | | % 187.99/29.93 | | | (274) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, % 187.99/29.93 | | | e4) = e2) | (all_252_20 = e2 & op(e0, e4) = e2) % 187.99/29.93 | | | % 187.99/29.93 | | | BETA: splitting (274) gives: % 187.99/29.93 | | | % 187.99/29.93 | | | Case 1: % 187.99/29.93 | | | | % 187.99/29.93 | | | | (275) all_252_6 = e2 & op(e2, e4) = e2 % 187.99/29.93 | | | | % 187.99/29.93 | | | | REF_CLOSE: (4), (87), (268), (275) are inconsistent by sub-proof #467. % 187.99/29.93 | | | | % 187.99/29.93 | | | Case 2: % 187.99/29.93 | | | | % 187.99/29.93 | | | | (276) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, % 187.99/29.93 | | | | e4) = e2) % 187.99/29.93 | | | | % 187.99/29.93 | | | | BETA: splitting (276) gives: % 187.99/29.93 | | | | % 187.99/29.93 | | | | Case 1: % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | (277) all_252_12 = e2 & op(e1, e4) = e2 % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | ALPHA: (277) implies: % 187.99/29.93 | | | | | (278) all_252_12 = e2 % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | GROUND_INST: instantiating (4) with all_4_2, e4, e2, e1, simplifying % 187.99/29.93 | | | | | with (120), (272) gives: % 187.99/29.93 | | | | | (279) all_4_2 = e4 % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | COMBINE_EQS: (117), (279) imply: % 187.99/29.93 | | | | | (280) all_180_2 = e4 % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | COMBINE_EQS: (61), (279) imply: % 187.99/29.93 | | | | | (281) all_192_2 = e4 % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | REDUCE: (123), (279) imply: % 187.99/29.93 | | | | | (282) ~ (all_244_15 = e4) % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | REDUCE: (60), (279) imply: % 187.99/29.93 | | | | | (283) ~ (all_28_2 = e4) % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | REDUCE: (271), (279) imply: % 187.99/29.93 | | | | | (284) ~ (e4 = e2) % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | REDUCE: (29), (279) imply: % 187.99/29.93 | | | | | (285) ~ (e4 = e0) % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | BETA: splitting (7) gives: % 187.99/29.93 | | | | | % 187.99/29.93 | | | | | Case 1: % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | (286) ~ (all_180_2 = e4) % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | REDUCE: (280), (286) imply: % 187.99/29.93 | | | | | | (287) $false % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | CLOSE: (287) is inconsistent. % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | Case 2: % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | (288) op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ (all_180_1 = % 187.99/29.93 | | | | | | e0) | ( ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 187.99/29.93 | | | | | | $i(all_180_0))) % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | ALPHA: (288) implies: % 187.99/29.93 | | | | | | (289) op(e4, e1) = all_180_1 % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | BETA: splitting (30) gives: % 187.99/29.93 | | | | | | % 187.99/29.93 | | | | | | Case 1: % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | (290) ~ (all_192_2 = e4) % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | REDUCE: (281), (290) imply: % 187.99/29.93 | | | | | | | (291) $false % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | CLOSE: (291) is inconsistent. % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | Case 2: % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | (292) op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ (all_192_1 = % 187.99/29.93 | | | | | | | e3) | ( ~ (all_192_0 = e0) & op(e1, e3) = all_192_0 & % 187.99/29.93 | | | | | | | $i(all_192_0))) % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | ALPHA: (292) implies: % 187.99/29.93 | | | | | | | (293) op(e4, e1) = all_192_1 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | GROUND_INST: instantiating (4) with all_26_2, all_192_1, e1, e4, % 187.99/29.93 | | | | | | | simplifying with (53), (293) gives: % 187.99/29.93 | | | | | | | (294) all_192_1 = all_26_2 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | GROUND_INST: instantiating (4) with all_180_1, all_192_1, e1, e4, % 187.99/29.93 | | | | | | | simplifying with (289), (293) gives: % 187.99/29.93 | | | | | | | (295) all_192_1 = all_180_1 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | COMBINE_EQS: (294), (295) imply: % 187.99/29.93 | | | | | | | (296) all_180_1 = all_26_2 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | SIMP: (296) implies: % 187.99/29.93 | | | | | | | (297) all_180_1 = all_26_2 % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | BETA: splitting (111) gives: % 187.99/29.93 | | | | | | | % 187.99/29.93 | | | | | | | Case 1: % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | (298) ~ (all_28_2 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REF_CLOSE: (4), (8), (9), (36), (43), (44), (46), (55), (56), % 187.99/29.93 | | | | | | | | (62), (67), (71), (73), (90), (109), (126), (298) are % 187.99/29.93 | | | | | | | | inconsistent by sub-proof #20. % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | Case 2: % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | (299) all_28_2 = e1 % 187.99/29.93 | | | | | | | | (300) op(e1, e0) = all_28_1 & $i(all_28_1) & ( ~ (all_28_1 = % 187.99/29.93 | | | | | | | | e3) | ( ~ (all_28_0 = e4) & op(e0, e3) = all_28_0 & % 187.99/29.93 | | | | | | | | $i(all_28_0))) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | ALPHA: (300) implies: % 187.99/29.93 | | | | | | | | (301) op(e1, e0) = all_28_1 % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | COMBINE_EQS: (99), (299) imply: % 187.99/29.93 | | | | | | | | (302) all_162_2 = e1 % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (84), (299) imply: % 187.99/29.93 | | | | | | | | (303) ~ (all_244_24 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (113), (299) imply: % 187.99/29.93 | | | | | | | | (304) ~ (all_22_2 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | SIMP: (304) implies: % 187.99/29.93 | | | | | | | | (305) ~ (all_22_2 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (37), (299) imply: % 187.99/29.93 | | | | | | | | (306) ~ (all_20_2 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | SIMP: (306) implies: % 187.99/29.93 | | | | | | | | (307) ~ (all_20_2 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (283), (299) imply: % 187.99/29.93 | | | | | | | | (308) ~ (e4 = e1) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (67), (299) imply: % 187.99/29.93 | | | | | | | | (309) ~ (e1 = e0) % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | REDUCE: (49), (299) imply: % 187.99/29.93 | | | | | | | | (310) op(all_40_2, e1) = e0 % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | BETA: splitting (5) gives: % 187.99/29.93 | | | | | | | | % 187.99/29.93 | | | | | | | | Case 1: % 187.99/29.93 | | | | | | | | | % 187.99/29.94 | | | | | | | | | (311) ~ (all_162_2 = e1) % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | | REDUCE: (302), (311) imply: % 187.99/29.94 | | | | | | | | | (312) $false % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | | CLOSE: (312) is inconsistent. % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | | (313) op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ % 187.99/29.94 | | | | | | | | | (all_162_1 = e4) | ( ~ (all_162_0 = e3) & op(e0, % 187.99/29.94 | | | | | | | | | e4) = all_162_0 & $i(all_162_0))) % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | | ALPHA: (313) implies: % 187.99/29.94 | | | | | | | | | (314) op(e1, e0) = all_162_1 % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | | BETA: splitting (109) gives: % 187.99/29.94 | | | | | | | | | % 187.99/29.94 | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | (315) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = % 187.99/29.94 | | | | | | | | | | e2 & op(e0, e3) = e2) % 187.99/29.94 | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | REF_CLOSE: (4), (55), (56), (62), (73), (315) are % 187.99/29.94 | | | | | | | | | | inconsistent by sub-proof #21. % 187.99/29.94 | | | | | | | | | | % 187.99/29.94 | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | (316) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = % 187.99/29.94 | | | | | | | | | | e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, % 187.99/29.94 | | | | | | | | | | e0) = e2) % 187.99/29.94 | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | BETA: splitting (316) gives: % 187.99/29.94 | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | (317) all_252_22 = e2 & op(e0, e2) = e2 % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | ALPHA: (317) implies: % 187.99/29.94 | | | | | | | | | | | (318) op(e0, e2) = e2 % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | REF_CLOSE: (4), (8), (67), (71), (90), (318) are inconsistent % 187.99/29.94 | | | | | | | | | | | by sub-proof #288. % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | (319) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 187.99/29.94 | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | BETA: splitting (319) gives: % 187.99/29.94 | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | (320) all_252_23 = e2 & op(e0, e1) = e2 % 187.99/29.94 | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | ALPHA: (320) implies: % 187.99/29.94 | | | | | | | | | | | | (321) all_252_23 = e2 % 187.99/29.94 | | | | | | | | | | | | (322) op(e0, e1) = e2 % 187.99/29.94 | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | BETA: splitting (42) gives: % 187.99/29.94 | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | (323) ~ (all_90_2 = e4) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | REDUCE: (2), (323) imply: % 187.99/29.94 | | | | | | | | | | | | | (324) ~ (all_22_2 = e4) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_20_2, e2, e1, e0, % 187.99/29.94 | | | | | | | | | | | | | simplifying with (44), (322) gives: % 187.99/29.94 | | | | | | | | | | | | | (325) all_20_2 = e2 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_34_2, all_162_1, e0, % 187.99/29.94 | | | | | | | | | | | | | e1, simplifying with (108), (314) gives: % 187.99/29.94 | | | | | | | | | | | | | (326) all_162_1 = all_34_2 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_28_1, all_162_1, e0, % 187.99/29.94 | | | | | | | | | | | | | e1, simplifying with (301), (314) gives: % 187.99/29.94 | | | | | | | | | | | | | (327) all_162_1 = all_28_1 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply: % 187.99/29.94 | | | | | | | | | | | | | (328) all_34_2 = all_28_1 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | SIMP: (328) implies: % 187.99/29.94 | | | | | | | | | | | | | (329) all_34_2 = all_28_1 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | COMBINE_EQS: (36), (325) imply: % 187.99/29.94 | | | | | | | | | | | | | (330) all_58_2 = e2 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | COMBINE_EQS: (26), (325) imply: % 187.99/29.94 | | | | | | | | | | | | | (331) all_60_2 = e2 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | REDUCE: (78), (325) imply: % 187.99/29.94 | | | | | | | | | | | | | (332) ~ (all_244_15 = e2) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | REDUCE: (41), (325) imply: % 187.99/29.94 | | | | | | | | | | | | | (333) ~ (all_36_2 = e2) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | REDUCE: (39), (325) imply: % 187.99/29.94 | | | | | | | | | | | | | (334) ~ (e3 = e2) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | SIMP: (334) implies: % 187.99/29.94 | | | | | | | | | | | | | (335) ~ (e3 = e2) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | REDUCE: (307), (325) imply: % 187.99/29.94 | | | | | | | | | | | | | (336) ~ (e2 = e1) % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | REDUCE: (86), (325), (329) imply: % 187.99/29.94 | | | | | | | | | | | | | (337) op(all_28_1, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | BETA: splitting (126) gives: % 187.99/29.94 | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | (338) ~ (all_58_2 = e2) % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | REDUCE: (330), (338) imply: % 187.99/29.94 | | | | | | | | | | | | | | (339) $false % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | CLOSE: (339) is inconsistent. % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | (340) op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 187.99/29.94 | | | | | | | | | | | | | | (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, % 187.99/29.94 | | | | | | | | | | | | | | e3) = all_58_0 & $i(all_58_0))) % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | ALPHA: (340) implies: % 187.99/29.94 | | | | | | | | | | | | | | (341) op(e2, e0) = all_58_1 % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | BETA: splitting (59) gives: % 187.99/29.94 | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | (342) ~ (all_60_2 = e2) % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | REDUCE: (331), (342) imply: % 187.99/29.94 | | | | | | | | | | | | | | | (343) $false % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | CLOSE: (343) is inconsistent. % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | (344) op(e2, e0) = all_60_1 & $i(all_60_1) & ( ~ % 187.99/29.94 | | | | | | | | | | | | | | | (all_60_1 = e4) | ( ~ (all_60_0 = e3) & op(e0, % 187.99/29.94 | | | | | | | | | | | | | | | e4) = all_60_0 & $i(all_60_0))) % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | ALPHA: (344) implies: % 187.99/29.94 | | | | | | | | | | | | | | | (345) op(e2, e0) = all_60_1 % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | BETA: splitting (97) gives: % 187.99/29.94 | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | (346) ~ (all_70_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | REDUCE: (96), (346) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | (347) ~ (all_62_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_40_2, all_60_1, e0, e2, % 187.99/29.94 | | | | | | | | | | | | | | | | simplifying with (89), (345) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | (348) all_60_1 = all_40_2 % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_58_1, all_60_1, e0, e2, % 187.99/29.94 | | | | | | | | | | | | | | | | simplifying with (341), (345) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | (349) all_60_1 = all_58_1 % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (348), (349) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | (350) all_58_1 = all_40_2 % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | BETA: splitting (3) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | (351) ~ (all_36_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (19), (20), (21), (34), (43), (50), % 187.99/29.94 | | | | | | | | | | | | | | | | | (53), (68), (80), (89), (98), (106), (112), (124), % 187.99/29.94 | | | | | | | | | | | | | | | | | (303), (310), (321), (351) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | sub-proof #284. % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | (352) all_36_2 = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (72), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (353) ~ (all_244_3 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (25), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (354) ~ (all_244_15 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (100), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (355) ~ (all_100_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (35), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (356) ~ (all_26_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (92), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (357) ~ (all_8_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | SIMP: (357) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | (358) ~ (all_8_2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (333), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (359) ~ (e2 = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | REDUCE: (103), (352) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | (360) op(e3, e0) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | (361) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 187.99/29.94 | | | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | BETA: splitting (361) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | (362) all_252_12 = e0 & op(e1, e4) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (278), (362) are inconsistent by sub-proof % 187.99/29.94 | | | | | | | | | | | | | | | | | | | #320. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | (363) all_252_13 = e0 & op(e1, e3) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (347), (363) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | sub-proof #319. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | (364) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 187.99/29.94 | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 187.99/29.94 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | BETA: splitting (364) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | (365) all_252_14 = e0 & op(e1, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | (366) op(e1, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (29), (120), (366) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | sub-proof #545. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | (367) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (367) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | (368) all_252_15 = e0 & op(e1, e1) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | ALPHA: (368) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | (369) op(e1, e1) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (354), (369) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | sub-proof #440. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | (370) all_252_19 = e0 & op(e1, e0) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | (371) op(e1, e0) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | (372) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (372) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | (373) all_252_9 = e0 & op(e4, e1) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (373) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | (374) op(e4, e1) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (53), (374) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | sub-proof #452. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_28_1, e0, e0, e1, % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | simplifying with (301), (371) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | (375) all_28_1 = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (337), (375) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | (376) op(e0, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (67), (376) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | sub-proof #24. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | (377) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (377) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | (378) all_252_11 = e0 & op(e2, e1) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (378) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | (379) all_252_11 = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | (380) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (380) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (381) all_252_9 = e4 & op(e4, e1) = e4 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (381) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (382) all_252_9 = e4 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (383) op(e4, e1) = e4 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (384) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (384) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (385) all_252_2 = e0 & op(e3, e4) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (355), (385) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (386) all_252_3 = e0 & op(e3, e3) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (353), (386) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #335. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (387) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (387) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (388) all_252_5 = e0 & op(e3, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (388) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (389) op(e3, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (66), (358), (389) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #547. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (390) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (390) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (391) all_252_10 = e0 & op(e3, e1) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (391) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (392) all_252_10 = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (393) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (394) all_252_9 = e3 & op(e4, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (394) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395) op(e4, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (28), (53), (383), (395) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #463. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396) all_252_10 = e3 & op(e3, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (392), (396) are inconsistent by sub-proof % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (397) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (397) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398) all_252_11 = e3 & op(e2, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (379), (398) are inconsistent by sub-proof % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (399) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (400) all_252_15 = e3 & op(e1, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (400) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (401) all_252_15 = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (402) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403) all_252_9 = e1 & op(e4, e1) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (403) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (404) all_252_9 = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (382), (404) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405) e4 = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (405) imply: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (406) $false % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (406) is inconsistent. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (407) all_252_10 = e1 & op(e3, e1) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (392), (407) are inconsistent by sub-proof % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #58. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (408) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (408) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409) all_252_11 = e1 & op(e2, e1) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (379), (409) are inconsistent by sub-proof % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (410) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (410) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (411) all_252_15 = e1 & op(e1, e1) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (401), (411) are inconsistent by sub-proof % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #143. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (412) all_252_23 = e1 & op(e0, e1) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (412) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (413) op(e0, e1) = e1 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (44), (322), (336), (413) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #475. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (414) all_252_23 = e3 & op(e0, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (414) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (415) op(e0, e1) = e3 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (322), (335), (415) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #446. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (416) all_252_17 = e0 & op(e3, e0) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (416) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (417) op(e3, e0) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (94), (309), (360), (417) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #362. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (418) all_252_10 = e4 & op(e3, e1) = e4 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (418) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (419) all_252_10 = e4 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (420) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (420) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (421) all_252_2 = e0 & op(e3, e4) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (355), (421) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (422) all_252_3 = e0 & op(e3, e3) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (353), (422) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #335. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (423) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0) % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (423) gives: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (424) all_252_5 = e0 & op(e3, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (424) implies: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (425) op(e3, e2) = e0 % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (66), (358), (425) are inconsistent by % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #547. % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 187.99/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (426) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (426) gives: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (427) all_252_10 = e0 & op(e3, e1) = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (427) implies: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (428) all_252_10 = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (419), (428) imply: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (429) e4 = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (285), (429) imply: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (430) $false % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (430) is inconsistent. % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (431) all_252_17 = e0 & op(e3, e0) = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (431) implies: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (432) op(e3, e0) = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (94), (309), (360), (432) are inconsistent by % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #362. % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | (433) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e4) % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (433) gives: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (434) all_252_11 = e4 & op(e2, e1) = e4 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (285), (379), (434) are inconsistent by sub-proof % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | #268. % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | (435) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e1) = e4) % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (435) gives: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (436) all_252_15 = e4 & op(e1, e1) = e4 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (436) implies: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (437) op(e1, e1) = e4 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (282), (437) are inconsistent by % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #460. % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (438) all_252_23 = e4 & op(e0, e1) = e4 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (438) implies: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | (439) op(e0, e1) = e4 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (107) gives: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (440) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (440) gives: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (441) all_252_2 = e0 & op(e3, e4) = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (38), (355), (441) are inconsistent by % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #251. % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (442) all_252_3 = e0 & op(e3, e3) = e0 % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (353), (442) are inconsistent by % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #335. % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (443) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e0) % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (443) gives: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (444) all_252_5 = e0 & op(e3, e2) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (444) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (445) op(e3, e2) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (66), (358), (445) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #547. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (446) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (446) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (447) all_252_10 = e0 & op(e3, e1) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (447) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448) all_252_10 = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (449) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (449) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (450) all_252_9 = e2 & op(e4, e1) = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (451) all_252_9 = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (452) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (452) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (453) all_252_9 = e3 & op(e4, e1) = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (453) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (454) all_252_9 = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (451), (454) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #367. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (455) all_252_10 = e3 & op(e3, e1) = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (448), (455) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e3) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (456) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (457) all_252_11 = e3 & op(e2, e1) = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (379), (457) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #273. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (458) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (458) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (459) all_252_15 = e3 & op(e1, e1) = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (459) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (460) all_252_15 = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (461) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (462) all_252_9 = e1 & op(e4, e1) = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_252_9 = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (451), (463) imply: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (464) e2 = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (464) imply: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) $false % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (465) is inconsistent. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) all_252_10 = e1 & op(e3, e1) = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (448), (466) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #94. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (467) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_252_11 = e1 & op(e2, e1) = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (309), (379), (468) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #276. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (469) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) all_252_15 = e1 & op(e1, e1) = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (105), (460), (470) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #143. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_252_23 = e1 & op(e0, e1) = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (471) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) op(e0, e1) = e1 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (44), (125), (439), (472) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #401. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) all_252_23 = e3 & op(e0, e1) = e3 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (28), (439), (473) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #316. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_252_10 = e2 & op(e3, e1) = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_252_10 = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (448), (475) imply: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) e2 = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (476) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) e2 = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (106), (477) imply: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) $false % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (479) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) all_252_11 = e2 & op(e2, e1) = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (379), (480) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #279. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (481) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) all_252_15 = e2 & op(e1, e1) = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (482) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) op(e1, e1) = e2 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (332), (483) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #515. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (284), (322), (439) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #322. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_252_17 = e0 & op(e3, e0) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) op(e3, e0) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (94), (309), (360), (485) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #362. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | (486) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e1) = e0) % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | (487) all_252_15 = e0 & op(e1, e1) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | (488) op(e1, e1) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (21), (354), (488) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #440. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | (489) all_252_23 = e0 & op(e0, e1) = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (489) implies: % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | (490) all_252_23 = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (321), (490) are inconsistent by sub-proof % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | #260. % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | (491) all_70_2 = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (96), (491) imply: % 188.37/29.95 | | | | | | | | | | | | | | | | (492) all_62_2 = e0 % 188.37/29.95 | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | REDUCE: (122), (492) imply: % 188.37/29.95 | | | | | | | | | | | | | | | | (493) ~ (all_22_2 = e0) % 188.37/29.95 | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (69), (73), (91), (110), (305), (324), % 188.37/29.95 | | | | | | | | | | | | | | | | (493) are inconsistent by sub-proof #317. % 188.37/29.95 | | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | (494) all_90_2 = e4 % 188.37/29.95 | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | COMBINE_EQS: (2), (494) imply: % 188.37/29.95 | | | | | | | | | | | | | (495) all_22_2 = e4 % 188.37/29.95 | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | REDUCE: (57), (495) imply: % 188.37/29.95 | | | | | | | | | | | | | (496) op(e0, e4) = e3 % 188.37/29.95 | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | | REF_CLOSE: (4), (101), (116), (496) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | | sub-proof #512. % 188.37/29.95 | | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | Case 2: % 188.37/29.95 | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | (497) all_252_24 = e2 & op(e0, e0) = e2 % 188.37/29.95 | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | ALPHA: (497) implies: % 188.37/29.95 | | | | | | | | | | | | (498) op(e0, e0) = e2 % 188.37/29.95 | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | | REF_CLOSE: (4), (9), (43), (498) are inconsistent by % 188.37/29.95 | | | | | | | | | | | | sub-proof #477. % 188.37/29.95 | | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | | % 188.37/29.95 | | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | | % 188.37/29.95 | | | | | | | | | End of split % 188.37/29.95 | | | | | | | | | % 188.37/29.95 | | | | | | | | End of split % 188.37/29.95 | | | | | | | | % 188.37/29.95 | | | | | | | End of split % 188.37/29.95 | | | | | | | % 188.37/29.95 | | | | | | End of split % 188.37/29.95 | | | | | | % 188.37/29.95 | | | | | End of split % 188.37/29.95 | | | | | % 188.37/29.95 | | | | Case 2: % 188.37/29.95 | | | | | % 188.37/29.95 | | | | | (499) all_252_20 = e2 & op(e0, e4) = e2 % 188.37/29.95 | | | | | % 188.37/29.95 | | | | | REF_CLOSE: (4), (56), (62), (499) are inconsistent by sub-proof #22. % 188.37/29.95 | | | | | % 188.37/29.95 | | | | End of split % 188.37/29.95 | | | | % 188.37/29.95 | | | End of split % 188.37/29.95 | | | % 188.37/29.95 | | End of split % 188.37/29.95 | | % 188.37/29.95 | End of split % 188.37/29.95 | % 188.37/29.95 End of proof % 188.37/29.95 % 188.37/29.95 Sub-proof #18 shows that the following formulas are inconsistent: % 188.37/29.95 ---------------------------------------------------------------- % 188.37/29.95 (1) all_252_24 = e4 & op(e0, e0) = e4 % 188.37/29.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.95 (3) op(e0, e0) = all_244_24 % 188.37/29.95 (4) ~ (all_244_24 = e4) % 188.37/29.95 % 188.37/29.95 Begin of proof % 188.37/29.95 | % 188.37/29.95 | ALPHA: (1) implies: % 188.37/29.95 | (5) op(e0, e0) = e4 % 188.37/29.95 | % 188.37/29.95 | GROUND_INST: instantiating (2) with all_244_24, e4, e0, e0, simplifying with % 188.37/29.95 | (3), (5) gives: % 188.37/29.95 | (6) all_244_24 = e4 % 188.37/29.95 | % 188.37/29.95 | REDUCE: (4), (6) imply: % 188.37/29.95 | (7) $false % 188.37/29.95 | % 188.37/29.95 | CLOSE: (7) is inconsistent. % 188.37/29.95 | % 188.37/29.95 End of proof % 188.37/29.95 % 188.37/29.95 Sub-proof #19 shows that the following formulas are inconsistent: % 188.37/29.95 ---------------------------------------------------------------- % 188.37/29.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.95 (2) op(e2, all_6_1) = e0 % 188.37/29.95 (3) ~ (all_64_2 = all_16_2) % 188.37/29.95 (4) op(e0, e4) = e4 % 188.37/29.95 (5) op(e1, e4) = e0 % 188.37/29.95 (6) op(e0, e4) = all_6_1 % 188.37/29.95 (7) all_232_2 = e4 % 188.37/29.95 (8) op(e1, e4) = all_16_2 % 188.37/29.95 (9) ~ (all_232_2 = e4) | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 188.37/29.95 (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 & % 188.37/29.95 $i(all_232_0)))) % 188.37/29.95 (10) op(e2, e4) = all_64_2 % 188.37/29.95 % 188.37/29.95 Begin of proof % 188.37/29.95 | % 188.37/29.95 | BETA: splitting (9) gives: % 188.37/29.95 | % 188.37/29.95 | Case 1: % 188.37/29.95 | | % 188.37/29.95 | | (11) ~ (all_232_2 = e4) % 188.37/29.95 | | % 188.37/29.95 | | REDUCE: (7), (11) imply: % 188.37/29.95 | | (12) $false % 188.37/29.95 | | % 188.37/29.95 | | CLOSE: (12) is inconsistent. % 188.37/29.95 | | % 188.37/29.95 | Case 2: % 188.37/29.95 | | % 188.37/29.95 | | % 188.37/29.95 | | GROUND_INST: instantiating (1) with all_6_1, e4, e4, e0, simplifying with % 188.37/29.95 | | (4), (6) gives: % 188.37/29.95 | | (13) all_6_1 = e4 % 188.37/29.95 | | % 188.37/29.95 | | GROUND_INST: instantiating (1) with all_16_2, e0, e4, e1, simplifying with % 188.37/29.95 | | (5), (8) gives: % 188.37/29.95 | | (14) all_16_2 = e0 % 188.37/29.95 | | % 188.37/29.95 | | REDUCE: (3), (14) imply: % 188.37/29.95 | | (15) ~ (all_64_2 = e0) % 188.37/29.95 | | % 188.37/29.95 | | REDUCE: (2), (13) imply: % 188.37/29.95 | | (16) op(e2, e4) = e0 % 188.37/29.95 | | % 188.37/29.95 | | REF_CLOSE: (1), (10), (15), (16) are inconsistent by sub-proof #382. % 188.37/29.95 | | % 188.37/29.95 | End of split % 188.37/29.95 | % 188.37/29.95 End of proof % 188.37/29.95 % 188.37/29.95 Sub-proof #20 shows that the following formulas are inconsistent: % 188.37/29.95 ---------------------------------------------------------------- % 188.37/29.95 (1) ~ (all_28_2 = e1) % 188.37/29.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.95 (3) op(e0, e2) = all_28_2 % 188.37/29.95 (4) ~ (all_244_24 = e2) % 188.37/29.95 (5) all_58_2 = all_20_2 % 188.37/29.95 (6) op(e0, e0) = all_244_24 % 188.37/29.95 (7) op(e0, e1) = all_20_2 % 188.37/29.95 (8) op(e0, all_20_2) = e1 % 188.37/29.95 (9) op(e0, e3) = all_22_2 % 188.37/29.95 (10) ~ (all_6_1 = e2) % 188.37/29.95 (11) op(e0, e4) = all_6_1 % 188.37/29.95 (12) ~ (all_28_2 = e0) % 188.37/29.95 (13) op(e2, all_40_2) = e0 % 188.37/29.95 (14) ~ (all_22_2 = e2) % 188.37/29.95 (15) op(all_28_2, all_40_2) = e2 % 188.37/29.95 (16) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 188.37/29.95 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 188.37/29.95 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.95 (17) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 188.37/29.95 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 188.37/29.95 $i(all_58_0)))) % 188.37/29.95 % 188.37/29.95 Begin of proof % 188.37/29.95 | % 188.37/29.95 | BETA: splitting (17) gives: % 188.37/29.95 | % 188.37/29.95 | Case 1: % 188.37/29.95 | | % 188.37/29.95 | | (18) ~ (all_58_2 = e2) % 188.37/29.95 | | % 188.37/29.95 | | REDUCE: (5), (18) imply: % 188.37/29.95 | | (19) ~ (all_20_2 = e2) % 188.37/29.95 | | % 188.37/29.95 | | BETA: splitting (16) gives: % 188.37/29.95 | | % 188.37/29.95 | | Case 1: % 188.37/29.95 | | | % 188.37/29.95 | | | (20) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, % 188.37/29.95 | | | e3) = e2) % 188.37/29.95 | | | % 188.37/29.95 | | | REF_CLOSE: (2), (9), (10), (11), (14), (20) are inconsistent by sub-proof % 188.37/29.95 | | | #21. % 188.37/29.95 | | | % 188.37/29.95 | | Case 2: % 188.37/29.95 | | | % 188.37/29.95 | | | (21) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 188.37/29.95 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.95 | | | % 188.37/29.95 | | | REF_CLOSE: (2), (3), (4), (6), (7), (12), (13), (15), (19), (21) are % 188.37/29.95 | | | inconsistent by sub-proof #287. % 188.37/29.95 | | | % 188.37/29.95 | | End of split % 188.37/29.95 | | % 188.37/29.95 | Case 2: % 188.37/29.95 | | % 188.37/29.95 | | (22) all_58_2 = e2 % 188.37/29.95 | | % 188.37/29.95 | | COMBINE_EQS: (5), (22) imply: % 188.37/29.95 | | (23) all_20_2 = e2 % 188.37/29.95 | | % 188.37/29.95 | | REDUCE: (8), (23) imply: % 188.37/29.95 | | (24) op(e0, e2) = e1 % 188.37/29.95 | | % 188.37/29.95 | | REF_CLOSE: (1), (2), (3), (24) are inconsistent by sub-proof #502. % 188.37/29.95 | | % 188.37/29.95 | End of split % 188.37/29.95 | % 188.37/29.95 End of proof % 188.37/29.95 % 188.37/29.95 Sub-proof #21 shows that the following formulas are inconsistent: % 188.37/29.95 ---------------------------------------------------------------- % 188.37/29.95 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.95 (2) op(e0, e3) = all_22_2 % 188.37/29.95 (3) ~ (all_6_1 = e2) % 188.37/29.95 (4) op(e0, e4) = all_6_1 % 188.37/29.95 (5) ~ (all_22_2 = e2) % 188.37/29.95 (6) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.37/29.95 % 188.37/29.95 Begin of proof % 188.37/29.95 | % 188.37/29.95 | BETA: splitting (6) gives: % 188.37/29.95 | % 188.37/29.95 | Case 1: % 188.37/29.95 | | % 188.37/29.95 | | (7) all_252_20 = e2 & op(e0, e4) = e2 % 188.37/29.95 | | % 188.37/29.95 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #22. % 188.37/29.95 | | % 188.37/29.95 | Case 2: % 188.37/29.95 | | % 188.37/29.95 | | (8) all_252_21 = e2 & op(e0, e3) = e2 % 188.37/29.95 | | % 188.37/29.95 | | ALPHA: (8) implies: % 188.37/29.95 | | (9) op(e0, e3) = e2 % 188.37/29.95 | | % 188.37/29.95 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #543. % 188.37/29.95 | | % 188.37/29.95 | End of split % 188.37/29.95 | % 188.37/29.95 End of proof % 188.37/29.95 % 188.37/29.95 Sub-proof #22 shows that the following formulas are inconsistent: % 188.37/29.95 ---------------------------------------------------------------- % 188.37/29.95 (1) all_252_20 = e2 & op(e0, e4) = e2 % 188.37/29.95 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.95 (3) op(e0, e4) = all_6_1 % 188.37/29.95 (4) ~ (all_6_1 = e2) % 188.37/29.95 % 188.37/29.95 Begin of proof % 188.37/29.95 | % 188.37/29.95 | ALPHA: (1) implies: % 188.37/29.95 | (5) op(e0, e4) = e2 % 188.37/29.95 | % 188.37/29.95 | GROUND_INST: instantiating (2) with all_6_1, e2, e4, e0, simplifying with (3), % 188.37/29.95 | (5) gives: % 188.37/29.95 | (6) all_6_1 = e2 % 188.37/29.95 | % 188.37/29.95 | REDUCE: (4), (6) imply: % 188.37/29.95 | (7) $false % 188.37/29.95 | % 188.37/29.95 | CLOSE: (7) is inconsistent. % 188.37/29.95 | % 188.37/29.95 End of proof % 188.37/29.95 % 188.37/29.95 Sub-proof #23 shows that the following formulas are inconsistent: % 188.37/29.95 ---------------------------------------------------------------- % 188.37/29.95 (1) ~ (all_244_8 = e0) % 188.37/29.95 (2) op(e2, e2) = all_244_8 % 188.37/29.95 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.95 (4) op(e0, e2) = all_28_2 % 188.37/29.95 (5) ~ (all_4_2 = e0) % 188.37/29.95 (6) ~ (all_28_2 = e0) % 188.37/29.95 (7) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = e0) % 188.37/29.95 | (all_252_22 = e0 & op(e0, e2) = e0) % 188.37/29.95 (8) op(e1, e2) = all_4_2 % 188.37/29.95 % 188.37/29.95 Begin of proof % 188.37/29.95 | % 188.37/29.95 | BETA: splitting (7) gives: % 188.37/29.95 | % 188.37/29.95 | Case 1: % 188.37/29.95 | | % 188.37/29.95 | | (9) all_252_8 = e0 & op(e2, e2) = e0 % 188.37/29.95 | | % 188.37/29.95 | | ALPHA: (9) implies: % 188.37/29.95 | | (10) op(e2, e2) = e0 % 188.37/29.95 | | % 188.37/29.95 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #448. % 188.37/29.95 | | % 188.37/29.95 | Case 2: % 188.37/29.95 | | % 188.37/29.95 | | (11) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) % 188.37/29.95 | | = e0) % 188.37/29.95 | | % 188.37/29.95 | | BETA: splitting (11) gives: % 188.37/29.95 | | % 188.37/29.95 | | Case 1: % 188.37/29.95 | | | % 188.37/29.95 | | | (12) all_252_14 = e0 & op(e1, e2) = e0 % 188.37/29.95 | | | % 188.37/29.95 | | | ALPHA: (12) implies: % 188.37/29.95 | | | (13) op(e1, e2) = e0 % 188.37/29.95 | | | % 188.37/29.95 | | | REF_CLOSE: (3), (5), (8), (13) are inconsistent by sub-proof #545. % 188.37/29.95 | | | % 188.37/29.95 | | Case 2: % 188.37/29.95 | | | % 188.37/29.95 | | | (14) all_252_22 = e0 & op(e0, e2) = e0 % 188.37/29.95 | | | % 188.37/29.95 | | | ALPHA: (14) implies: % 188.37/29.96 | | | (15) op(e0, e2) = e0 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (3), (4), (6), (15) are inconsistent by sub-proof #24. % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | End of split % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #24 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (2) op(e0, e2) = all_28_2 % 188.37/29.96 (3) op(e0, e2) = e0 % 188.37/29.96 (4) ~ (all_28_2 = e0) % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | GROUND_INST: instantiating (1) with all_28_2, e0, e2, e0, simplifying with % 188.37/29.96 | (2), (3) gives: % 188.37/29.96 | (5) all_28_2 = e0 % 188.37/29.96 | % 188.37/29.96 | REDUCE: (4), (5) imply: % 188.37/29.96 | (6) $false % 188.37/29.96 | % 188.37/29.96 | CLOSE: (6) is inconsistent. % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #25 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (2) ~ (all_244_24 = e2) % 188.37/29.96 (3) ~ (all_40_2 = e2) % 188.37/29.96 (4) op(e0, e0) = all_244_24 % 188.37/29.96 (5) (all_252_18 = e2 & op(e2, e0) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.37/29.96 | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.96 (6) op(e2, e0) = all_40_2 % 188.37/29.96 (7) op(e1, e0) = all_34_2 % 188.37/29.96 (8) ~ (all_34_2 = e2) % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | BETA: splitting (5) gives: % 188.37/29.96 | % 188.37/29.96 | Case 1: % 188.37/29.96 | | % 188.37/29.96 | | (9) all_252_18 = e2 & op(e2, e0) = e2 % 188.37/29.96 | | % 188.37/29.96 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #76. % 188.37/29.96 | | % 188.37/29.96 | Case 2: % 188.37/29.96 | | % 188.37/29.96 | | (10) (all_252_19 = e2 & op(e1, e0) = e2) | (all_252_24 = e2 & op(e0, e0) % 188.37/29.96 | | = e2) % 188.37/29.96 | | % 188.37/29.96 | | BETA: splitting (10) gives: % 188.37/29.96 | | % 188.37/29.96 | | Case 1: % 188.37/29.96 | | | % 188.37/29.96 | | | (11) all_252_19 = e2 & op(e1, e0) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (1), (7), (8), (11) are inconsistent by sub-proof #438. % 188.37/29.96 | | | % 188.37/29.96 | | Case 2: % 188.37/29.96 | | | % 188.37/29.96 | | | (12) all_252_24 = e2 & op(e0, e0) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | ALPHA: (12) implies: % 188.37/29.96 | | | (13) op(e0, e0) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (1), (2), (4), (13) are inconsistent by sub-proof #477. % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | End of split % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #26 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (2) op(e0, e2) = all_28_2 % 188.37/29.96 (3) ~ (all_244_24 = e2) % 188.37/29.96 (4) ~ (e2 = e1) % 188.37/29.96 (5) op(e0, e1) = e4 % 188.37/29.96 (6) op(e0, e0) = all_244_24 % 188.37/29.96 (7) ~ (all_28_2 = e0) % 188.37/29.96 (8) op(e2, all_40_2) = e0 % 188.37/29.96 (9) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) % 188.37/29.96 (10) ~ (e4 = e2) % 188.37/29.96 (11) op(all_28_2, all_40_2) = e2 % 188.37/29.96 (12) ~ (e1 = e0) % 188.37/29.96 (13) ~ (e2 = e0) % 188.37/29.96 (14) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 188.37/29.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 188.37/29.96 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.96 (15) all_252_20 = e1 % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | BETA: splitting (9) gives: % 188.37/29.96 | % 188.37/29.96 | Case 1: % 188.37/29.96 | | % 188.37/29.96 | | (16) all_252_20 = e0 & op(e0, e4) = e0 % 188.37/29.96 | | % 188.37/29.96 | | ALPHA: (16) implies: % 188.37/29.96 | | (17) all_252_20 = e0 % 188.37/29.96 | | % 188.37/29.96 | | COMBINE_EQS: (15), (17) imply: % 188.37/29.96 | | (18) e1 = e0 % 188.37/29.96 | | % 188.37/29.96 | | REDUCE: (12), (18) imply: % 188.37/29.96 | | (19) $false % 188.37/29.96 | | % 188.37/29.96 | | CLOSE: (19) is inconsistent. % 188.37/29.96 | | % 188.37/29.96 | Case 2: % 188.37/29.96 | | % 188.37/29.96 | | (20) all_252_21 = e0 & op(e0, e3) = e0 % 188.37/29.96 | | % 188.37/29.96 | | ALPHA: (20) implies: % 188.37/29.96 | | (21) all_252_21 = e0 % 188.37/29.96 | | % 188.37/29.96 | | BETA: splitting (14) gives: % 188.37/29.96 | | % 188.37/29.96 | | Case 1: % 188.37/29.96 | | | % 188.37/29.96 | | | (22) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, % 188.37/29.96 | | | e3) = e2) % 188.37/29.96 | | | % 188.37/29.96 | | | BETA: splitting (22) gives: % 188.37/29.96 | | | % 188.37/29.96 | | | Case 1: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (23) all_252_20 = e2 & op(e0, e4) = e2 % 188.37/29.96 | | | | % 188.37/29.96 | | | | ALPHA: (23) implies: % 188.37/29.96 | | | | (24) all_252_20 = e2 % 188.37/29.96 | | | | % 188.37/29.96 | | | | REF_CLOSE: (4), (15), (24) are inconsistent by sub-proof #228. % 188.37/29.96 | | | | % 188.37/29.96 | | | Case 2: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (25) all_252_21 = e2 & op(e0, e3) = e2 % 188.37/29.96 | | | | % 188.37/29.96 | | | | ALPHA: (25) implies: % 188.37/29.96 | | | | (26) all_252_21 = e2 % 188.37/29.96 | | | | % 188.37/29.96 | | | | REF_CLOSE: (13), (21), (26) are inconsistent by sub-proof #27. % 188.37/29.96 | | | | % 188.37/29.96 | | | End of split % 188.37/29.96 | | | % 188.37/29.96 | | Case 2: % 188.37/29.96 | | | % 188.37/29.96 | | | (27) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 188.37/29.96 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.96 | | | % 188.37/29.96 | | | BETA: splitting (27) gives: % 188.37/29.96 | | | % 188.37/29.96 | | | Case 1: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (28) all_252_22 = e2 & op(e0, e2) = e2 % 188.37/29.96 | | | | % 188.37/29.96 | | | | ALPHA: (28) implies: % 188.37/29.96 | | | | (29) op(e0, e2) = e2 % 188.37/29.96 | | | | % 188.37/29.96 | | | | REF_CLOSE: (1), (2), (7), (8), (11), (29) are inconsistent by sub-proof % 188.37/29.96 | | | | #288. % 188.37/29.96 | | | | % 188.37/29.96 | | | Case 2: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (30) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, % 188.37/29.96 | | | | e0) = e2) % 188.37/29.96 | | | | % 188.37/29.96 | | | | BETA: splitting (30) gives: % 188.37/29.96 | | | | % 188.37/29.96 | | | | Case 1: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | (31) all_252_23 = e2 & op(e0, e1) = e2 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | ALPHA: (31) implies: % 188.37/29.96 | | | | | (32) op(e0, e1) = e2 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | GROUND_INST: instantiating (1) with e4, e2, e1, e0, simplifying with % 188.37/29.96 | | | | | (5), (32) gives: % 188.37/29.96 | | | | | (33) e4 = e2 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | REDUCE: (10), (33) imply: % 188.37/29.96 | | | | | (34) $false % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | CLOSE: (34) is inconsistent. % 188.37/29.96 | | | | | % 188.37/29.96 | | | | Case 2: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | (35) all_252_24 = e2 & op(e0, e0) = e2 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | ALPHA: (35) implies: % 188.37/29.96 | | | | | (36) op(e0, e0) = e2 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | REF_CLOSE: (1), (3), (6), (36) are inconsistent by sub-proof #477. % 188.37/29.96 | | | | | % 188.37/29.96 | | | | End of split % 188.37/29.96 | | | | % 188.37/29.96 | | | End of split % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | End of split % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #27 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) all_252_21 = e2 % 188.37/29.96 (2) all_252_21 = e0 % 188.37/29.96 (3) ~ (e2 = e0) % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | COMBINE_EQS: (1), (2) imply: % 188.37/29.96 | (4) e2 = e0 % 188.37/29.96 | % 188.37/29.96 | SIMP: (4) implies: % 188.37/29.96 | (5) e2 = e0 % 188.37/29.96 | % 188.37/29.96 | REDUCE: (3), (5) imply: % 188.37/29.96 | (6) $false % 188.37/29.96 | % 188.37/29.96 | CLOSE: (6) is inconsistent. % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #28 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) all_252_21 = e3 % 188.37/29.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (3) op(e0, e2) = all_28_2 % 188.37/29.96 (4) ~ (all_244_24 = e2) % 188.37/29.96 (5) ~ (e2 = e1) % 188.37/29.96 (6) op(e0, e1) = e4 % 188.37/29.96 (7) op(e0, e0) = all_244_24 % 188.37/29.96 (8) ~ (all_28_2 = e0) % 188.37/29.96 (9) op(e2, all_40_2) = e0 % 188.37/29.96 (10) ~ (e3 = e2) % 188.37/29.96 (11) ~ (e4 = e2) % 188.37/29.96 (12) op(all_28_2, all_40_2) = e2 % 188.37/29.96 (13) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 188.37/29.96 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 188.37/29.96 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.96 (14) all_252_20 = e1 % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | BETA: splitting (13) gives: % 188.37/29.96 | % 188.37/29.96 | Case 1: % 188.37/29.96 | | % 188.37/29.96 | | (15) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) % 188.37/29.96 | | = e2) % 188.37/29.96 | | % 188.37/29.96 | | BETA: splitting (15) gives: % 188.37/29.96 | | % 188.37/29.96 | | Case 1: % 188.37/29.96 | | | % 188.37/29.96 | | | (16) all_252_20 = e2 & op(e0, e4) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | ALPHA: (16) implies: % 188.37/29.96 | | | (17) all_252_20 = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (5), (14), (17) are inconsistent by sub-proof #228. % 188.37/29.96 | | | % 188.37/29.96 | | Case 2: % 188.37/29.96 | | | % 188.37/29.96 | | | (18) all_252_21 = e2 & op(e0, e3) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | ALPHA: (18) implies: % 188.37/29.96 | | | (19) all_252_21 = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | COMBINE_EQS: (1), (19) imply: % 188.37/29.96 | | | (20) e3 = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | REDUCE: (10), (20) imply: % 188.37/29.96 | | | (21) $false % 188.37/29.96 | | | % 188.37/29.96 | | | CLOSE: (21) is inconsistent. % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | Case 2: % 188.37/29.96 | | % 188.37/29.96 | | (22) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) % 188.37/29.96 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.96 | | % 188.37/29.96 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), (22) are % 188.37/29.96 | | inconsistent by sub-proof #29. % 188.37/29.96 | | % 188.37/29.96 | End of split % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #29 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (2) op(e0, e2) = all_28_2 % 188.37/29.96 (3) ~ (all_244_24 = e2) % 188.37/29.96 (4) op(e0, e1) = e4 % 188.37/29.96 (5) op(e0, e0) = all_244_24 % 188.37/29.96 (6) ~ (all_28_2 = e0) % 188.37/29.96 (7) op(e2, all_40_2) = e0 % 188.37/29.96 (8) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.37/29.96 | (all_252_24 = e2 & op(e0, e0) = e2) % 188.37/29.96 (9) ~ (e4 = e2) % 188.37/29.96 (10) op(all_28_2, all_40_2) = e2 % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | BETA: splitting (8) gives: % 188.37/29.96 | % 188.37/29.96 | Case 1: % 188.37/29.96 | | % 188.37/29.96 | | (11) all_252_22 = e2 & op(e0, e2) = e2 % 188.37/29.96 | | % 188.37/29.96 | | ALPHA: (11) implies: % 188.37/29.96 | | (12) op(e0, e2) = e2 % 188.37/29.96 | | % 188.37/29.96 | | REF_CLOSE: (1), (2), (6), (7), (10), (12) are inconsistent by sub-proof % 188.37/29.96 | | #288. % 188.37/29.96 | | % 188.37/29.96 | Case 2: % 188.37/29.96 | | % 188.37/29.96 | | (13) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) % 188.37/29.96 | | = e2) % 188.37/29.96 | | % 188.37/29.96 | | BETA: splitting (13) gives: % 188.37/29.96 | | % 188.37/29.96 | | Case 1: % 188.37/29.96 | | | % 188.37/29.96 | | | (14) all_252_23 = e2 & op(e0, e1) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | ALPHA: (14) implies: % 188.37/29.96 | | | (15) op(e0, e1) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (1), (4), (9), (15) are inconsistent by sub-proof #322. % 188.37/29.96 | | | % 188.37/29.96 | | Case 2: % 188.37/29.96 | | | % 188.37/29.96 | | | (16) all_252_24 = e2 & op(e0, e0) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | ALPHA: (16) implies: % 188.37/29.96 | | | (17) op(e0, e0) = e2 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (1), (3), (5), (17) are inconsistent by sub-proof #477. % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | End of split % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #30 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (2) ~ (e2 = e1) % 188.37/29.96 (3) ~ (e4 = e0) % 188.37/29.96 (4) ~ (e4 = e3) % 188.37/29.96 (5) op(e3, e4) = all_100_2 % 188.37/29.96 (6) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 188.37/29.96 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.37/29.96 | (all_252_17 = e1 & op(e3, e0) = e1) % 188.37/29.96 (7) all_252_17 = e2 % 188.37/29.96 (8) ~ (all_100_2 = e3) % 188.37/29.96 (9) ~ (e3 = e0) % 188.37/29.96 (10) all_252_2 = e0 & op(e3, e4) = e0 % 188.37/29.96 (11) ~ (e3 = e2) % 188.37/29.96 (12) ~ (e4 = e2) % 188.37/29.96 (13) ~ (e1 = e0) % 188.37/29.96 (14) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.37/29.96 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.37/29.96 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.37/29.96 (15) ~ (e3 = e1) % 188.37/29.96 (16) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.37/29.96 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.37/29.96 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.37/29.96 (17) all_252_5 = e0 % 188.37/29.96 (18) ~ (e4 = e1) % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | ALPHA: (10) implies: % 188.37/29.96 | (19) all_252_2 = e0 % 188.37/29.96 | % 188.37/29.96 | BETA: splitting (14) gives: % 188.37/29.96 | % 188.37/29.96 | Case 1: % 188.37/29.96 | | % 188.37/29.96 | | (20) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = % 188.37/29.96 | | e3) % 188.37/29.96 | | % 188.37/29.96 | | BETA: splitting (20) gives: % 188.37/29.96 | | % 188.37/29.96 | | Case 1: % 188.37/29.96 | | | % 188.37/29.96 | | | (21) all_252_2 = e3 & op(e3, e4) = e3 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (1), (5), (8), (21) are inconsistent by sub-proof #560. % 188.37/29.96 | | | % 188.37/29.96 | | Case 2: % 188.37/29.96 | | | % 188.37/29.96 | | | (22) all_252_3 = e3 & op(e3, e3) = e3 % 188.37/29.96 | | | % 188.37/29.96 | | | ALPHA: (22) implies: % 188.37/29.96 | | | (23) all_252_3 = e3 % 188.37/29.96 | | | % 188.37/29.96 | | | BETA: splitting (16) gives: % 188.37/29.96 | | | % 188.37/29.96 | | | Case 1: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (24) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, % 188.37/29.96 | | | | e3) = e4) % 188.37/29.96 | | | | % 188.37/29.96 | | | | BETA: splitting (24) gives: % 188.37/29.96 | | | | % 188.37/29.96 | | | | Case 1: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | (25) all_252_2 = e4 & op(e3, e4) = e4 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | ALPHA: (25) implies: % 188.37/29.96 | | | | | (26) all_252_2 = e4 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | COMBINE_EQS: (19), (26) imply: % 188.37/29.96 | | | | | (27) e4 = e0 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | SIMP: (27) implies: % 188.37/29.96 | | | | | (28) e4 = e0 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | REDUCE: (3), (28) imply: % 188.37/29.96 | | | | | (29) $false % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | CLOSE: (29) is inconsistent. % 188.37/29.96 | | | | | % 188.37/29.96 | | | | Case 2: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | (30) all_252_3 = e4 & op(e3, e3) = e4 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | REF_CLOSE: (4), (23), (30) are inconsistent by sub-proof #92. % 188.37/29.96 | | | | | % 188.37/29.96 | | | | End of split % 188.37/29.96 | | | | % 188.37/29.96 | | | Case 2: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (31) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, % 188.37/29.96 | | | | e1) = e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.37/29.96 | | | | % 188.37/29.96 | | | | BETA: splitting (31) gives: % 188.37/29.96 | | | | % 188.37/29.96 | | | | Case 1: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | (32) all_252_5 = e4 & op(e3, e2) = e4 % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | REF_CLOSE: (3), (17), (32) are inconsistent by sub-proof #132. % 188.37/29.96 | | | | | % 188.37/29.96 | | | | Case 2: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | (33) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 = e4 & % 188.37/29.96 | | | | | op(e3, e0) = e4) % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | BETA: splitting (33) gives: % 188.37/29.96 | | | | | % 188.37/29.96 | | | | | Case 1: % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | (34) all_252_10 = e4 & op(e3, e1) = e4 % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | ALPHA: (34) implies: % 188.37/29.96 | | | | | | (35) all_252_10 = e4 % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | BETA: splitting (6) gives: % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | Case 1: % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | | (36) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & % 188.37/29.96 | | | | | | | op(e3, e3) = e1) % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | | BETA: splitting (36) gives: % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | | Case 1: % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | (37) all_252_2 = e1 & op(e3, e4) = e1 % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | REF_CLOSE: (13), (19), (37) are inconsistent by sub-proof #230. % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | Case 2: % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | (38) all_252_3 = e1 & op(e3, e3) = e1 % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | ALPHA: (38) implies: % 188.37/29.96 | | | | | | | | (39) all_252_3 = e1 % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | COMBINE_EQS: (23), (39) imply: % 188.37/29.96 | | | | | | | | (40) e3 = e1 % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | REDUCE: (15), (40) imply: % 188.37/29.96 | | | | | | | | (41) $false % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | CLOSE: (41) is inconsistent. % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | End of split % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | Case 2: % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | | (42) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & % 188.37/29.96 | | | | | | | op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | | BETA: splitting (42) gives: % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | | Case 1: % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | (43) all_252_5 = e1 & op(e3, e2) = e1 % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | REF_CLOSE: (13), (17), (43) are inconsistent by sub-proof #155. % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | Case 2: % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | (44) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 188.37/29.96 | | | | | | | | op(e3, e0) = e1) % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | BETA: splitting (44) gives: % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | | Case 1: % 188.37/29.96 | | | | | | | | | % 188.37/29.96 | | | | | | | | | (45) all_252_10 = e1 & op(e3, e1) = e1 % 188.37/29.96 | | | | | | | | | % 188.37/29.96 | | | | | | | | | REF_CLOSE: (18), (35), (45) are inconsistent by sub-proof % 188.37/29.96 | | | | | | | | | #277. % 188.37/29.96 | | | | | | | | | % 188.37/29.96 | | | | | | | | Case 2: % 188.37/29.96 | | | | | | | | | % 188.37/29.96 | | | | | | | | | (46) all_252_17 = e1 & op(e3, e0) = e1 % 188.37/29.96 | | | | | | | | | % 188.37/29.96 | | | | | | | | | REF_CLOSE: (2), (7), (46) are inconsistent by sub-proof #247. % 188.37/29.96 | | | | | | | | | % 188.37/29.96 | | | | | | | | End of split % 188.37/29.96 | | | | | | | | % 188.37/29.96 | | | | | | | End of split % 188.37/29.96 | | | | | | | % 188.37/29.96 | | | | | | End of split % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | Case 2: % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | (47) all_252_17 = e4 & op(e3, e0) = e4 % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | ALPHA: (47) implies: % 188.37/29.96 | | | | | | (48) all_252_17 = e4 % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | COMBINE_EQS: (7), (48) imply: % 188.37/29.96 | | | | | | (49) e4 = e2 % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | SIMP: (49) implies: % 188.37/29.96 | | | | | | (50) e4 = e2 % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | REDUCE: (12), (50) imply: % 188.37/29.96 | | | | | | (51) $false % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | | CLOSE: (51) is inconsistent. % 188.37/29.96 | | | | | | % 188.37/29.96 | | | | | End of split % 188.37/29.96 | | | | | % 188.37/29.96 | | | | End of split % 188.37/29.96 | | | | % 188.37/29.96 | | | End of split % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | Case 2: % 188.37/29.96 | | % 188.37/29.96 | | (52) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.37/29.96 | | e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.37/29.96 | | % 188.37/29.96 | | BETA: splitting (52) gives: % 188.37/29.96 | | % 188.37/29.96 | | Case 1: % 188.37/29.96 | | | % 188.37/29.96 | | | (53) all_252_5 = e3 & op(e3, e2) = e3 % 188.37/29.96 | | | % 188.37/29.96 | | | REF_CLOSE: (9), (17), (53) are inconsistent by sub-proof #134. % 188.37/29.96 | | | % 188.37/29.96 | | Case 2: % 188.37/29.96 | | | % 188.37/29.96 | | | (54) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, % 188.37/29.96 | | | e0) = e3) % 188.37/29.96 | | | % 188.37/29.96 | | | BETA: splitting (54) gives: % 188.37/29.96 | | | % 188.37/29.96 | | | Case 1: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (55) all_252_10 = e3 & op(e3, e1) = e3 % 188.37/29.96 | | | | % 188.37/29.96 | | | | ALPHA: (55) implies: % 188.37/29.96 | | | | (56) all_252_10 = e3 % 188.37/29.96 | | | | % 188.37/29.96 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (12), (13), (15), (16), (17), (18), % 188.37/29.96 | | | | (19), (56) are inconsistent by sub-proof #86. % 188.37/29.96 | | | | % 188.37/29.96 | | | Case 2: % 188.37/29.96 | | | | % 188.37/29.96 | | | | (57) all_252_17 = e3 & op(e3, e0) = e3 % 188.37/29.96 | | | | % 188.37/29.96 | | | | REF_CLOSE: (7), (11), (57) are inconsistent by sub-proof #249. % 188.37/29.96 | | | | % 188.37/29.96 | | | End of split % 188.37/29.96 | | | % 188.37/29.96 | | End of split % 188.37/29.96 | | % 188.37/29.96 | End of split % 188.37/29.96 | % 188.37/29.96 End of proof % 188.37/29.96 % 188.37/29.96 Sub-proof #31 shows that the following formulas are inconsistent: % 188.37/29.96 ---------------------------------------------------------------- % 188.37/29.96 (1) op(e2, e2) = all_244_8 % 188.37/29.96 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.96 (3) ~ (e3 = e0) % 188.37/29.96 (4) op(all_8_1, e2) = e3 % 188.37/29.96 (5) all_22_2 = e2 % 188.37/29.96 (6) op(e2, all_8_1) = e0 % 188.37/29.96 (7) all_22_2 = all_8_1 % 188.37/29.96 % 188.37/29.96 Begin of proof % 188.37/29.96 | % 188.37/29.96 | COMBINE_EQS: (5), (7) imply: % 188.37/29.96 | (8) all_8_1 = e2 % 188.37/29.96 | % 188.37/29.96 | SIMP: (8) implies: % 188.37/29.96 | (9) all_8_1 = e2 % 188.37/29.96 | % 188.37/29.96 | REDUCE: (4), (9) imply: % 188.37/29.97 | (10) op(e2, e2) = e3 % 188.37/29.97 | % 188.37/29.97 | REDUCE: (6), (9) imply: % 188.37/29.97 | (11) op(e2, e2) = e0 % 188.37/29.97 | % 188.37/29.97 | REF_CLOSE: (1), (2), (3), (10), (11) are inconsistent by sub-proof #468. % 188.37/29.97 | % 188.37/29.97 End of proof % 188.37/29.97 % 188.37/29.97 Sub-proof #32 shows that the following formulas are inconsistent: % 188.37/29.97 ---------------------------------------------------------------- % 188.37/29.97 (1) all_252_24 = e3 & op(e0, e0) = e3 % 188.37/29.97 (2) all_252_24 = e4 % 188.37/29.97 (3) ~ (e4 = e3) % 188.37/29.97 % 188.37/29.97 Begin of proof % 188.37/29.97 | % 188.37/29.97 | ALPHA: (1) implies: % 188.37/29.97 | (4) all_252_24 = e3 % 188.37/29.97 | % 188.37/29.97 | COMBINE_EQS: (2), (4) imply: % 188.37/29.97 | (5) e4 = e3 % 188.37/29.97 | % 188.37/29.97 | REDUCE: (3), (5) imply: % 188.37/29.97 | (6) $false % 188.37/29.97 | % 188.37/29.97 | CLOSE: (6) is inconsistent. % 188.37/29.97 | % 188.37/29.97 End of proof % 188.37/29.97 % 188.37/29.97 Sub-proof #33 shows that the following formulas are inconsistent: % 188.37/29.97 ---------------------------------------------------------------- % 188.37/29.97 (1) all_252_24 = e1 & op(e0, e0) = e1 % 188.37/29.97 (2) all_252_24 = e4 % 188.37/29.97 (3) ~ (e4 = e1) % 188.37/29.97 % 188.37/29.97 Begin of proof % 188.37/29.97 | % 188.37/29.97 | ALPHA: (1) implies: % 188.37/29.97 | (4) all_252_24 = e1 % 188.37/29.97 | % 188.37/29.97 | COMBINE_EQS: (2), (4) imply: % 188.37/29.97 | (5) e4 = e1 % 188.37/29.97 | % 188.37/29.97 | REDUCE: (3), (5) imply: % 188.37/29.97 | (6) $false % 188.37/29.97 | % 188.37/29.97 | CLOSE: (6) is inconsistent. % 188.37/29.97 | % 188.37/29.97 End of proof % 188.37/29.97 % 188.37/29.97 Sub-proof #34 shows that the following formulas are inconsistent: % 188.37/29.97 ---------------------------------------------------------------- % 188.37/29.97 (1) all_252_24 = e0 & op(e0, e0) = e0 % 188.37/29.97 (2) all_252_24 = e4 % 188.37/29.97 (3) ~ (e4 = e0) % 188.37/29.97 % 188.37/29.97 Begin of proof % 188.37/29.97 | % 188.37/29.97 | ALPHA: (1) implies: % 188.37/29.97 | (4) all_252_24 = e0 % 188.37/29.97 | % 188.37/29.97 | COMBINE_EQS: (2), (4) imply: % 188.37/29.97 | (5) e4 = e0 % 188.37/29.97 | % 188.37/29.97 | REDUCE: (3), (5) imply: % 188.37/29.97 | (6) $false % 188.37/29.97 | % 188.37/29.97 | CLOSE: (6) is inconsistent. % 188.37/29.97 | % 188.37/29.97 End of proof % 188.37/29.97 % 188.37/29.97 Sub-proof #35 shows that the following formulas are inconsistent: % 188.37/29.97 ---------------------------------------------------------------- % 188.37/29.97 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.37/29.97 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.37/29.97 (all_252_16 = e1 & op(e4, e0) = e1) % 188.37/29.97 (2) all_252_20 = e2 % 188.37/29.97 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.37/29.97 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.37/29.97 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.37/29.97 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.37/29.97 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.37/29.97 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.37/29.97 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.37/29.97 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.37/29.97 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.37/29.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.97 (7) ~ (all_20_2 = e4) % 188.37/29.97 (8) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) | % 188.37/29.97 (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 188.37/29.97 | (all_252_21 = e0 & op(e0, e3) = e0) % 188.37/29.97 (9) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.37/29.97 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.37/29.97 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.37/29.97 (10) op(e0, e2) = e4 % 188.37/29.97 (11) op(e0, e2) = all_28_2 % 188.37/29.97 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) % 188.37/29.97 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = % 188.37/29.97 e0) | (all_252_18 = e0 & op(e2, e0) = e0) % 188.37/29.97 (13) op(e3, e1) = all_36_2 % 188.37/29.97 (14) ~ (all_40_2 = e2) % 188.37/29.97 (15) ~ (e2 = e1) % 188.37/29.97 (16) ~ (all_62_2 = e0) % 188.37/29.97 (17) all_252_12 = e0 % 188.37/29.97 (18) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.37/29.97 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.37/29.97 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.37/29.97 (19) op(e1, e3) = all_62_2 % 188.37/29.97 (20) op(e3, e0) = e2 % 188.37/29.97 (21) op(e2, e1) = e0 % 188.37/29.97 (22) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 188.37/29.97 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = % 188.37/29.97 e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 188.37/29.97 (23) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.37/29.97 all_250_23 = e0 % 188.37/29.97 (24) ~ (e4 = e0) % 188.37/29.97 (25) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.37/29.97 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.37/29.97 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.37/29.97 (26) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.37/29.97 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.37/29.97 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.37/29.97 (27) ~ (e4 = e3) % 188.37/29.97 (28) ~ (all_36_2 = e2) % 188.37/29.97 (29) ~ (all_40_2 = all_34_2) % 188.37/29.97 (30) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.37/29.97 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.37/29.97 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.37/29.97 (31) ~ (all_244_24 = all_20_2) % 188.37/29.97 (32) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.37/29.97 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.37/29.97 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.37/29.97 (33) op(e1, e4) = e0 % 188.37/29.97 (34) ~ (all_6_2 = e4) % 188.37/29.97 (35) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.37/29.97 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.37/29.97 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.37/29.97 (36) ~ (all_20_2 = e3) % 188.37/29.97 (37) op(all_20_2, e4) = e1 % 188.37/29.97 (38) op(e0, e0) = all_244_24 % 188.37/29.97 (39) op(e0, e1) = all_20_2 % 188.37/29.97 (40) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.37/29.97 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.37/29.97 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.37/29.97 (41) all_252_19 = e4 % 188.37/29.97 (42) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.37/29.97 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.37/29.97 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.37/29.97 (43) ~ (all_8_1 = e2) % 188.37/29.97 (44) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.37/29.97 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.37/29.97 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.37/29.97 (45) ~ (all_20_2 = e0) % 188.37/29.97 (46) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.37/29.97 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.37/29.97 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.37/29.97 (47) all_252_17 = e2 % 188.37/29.97 (48) ~ (all_20_2 = e2) % 188.37/29.97 (49) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.37/29.97 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.37/29.97 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.37/29.97 (50) op(e4, e4) = all_244_0 % 188.37/29.97 (51) op(e0, e4) = e2 % 188.37/29.97 (52) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) % 188.37/29.97 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.37/29.97 e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.37/29.97 (53) ~ (e3 = e0) % 188.37/29.97 (54) ~ (all_20_2 = all_8_1) % 188.37/29.97 (55) ~ (all_28_2 = e0) % 188.37/29.97 (56) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.37/29.97 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.37/29.97 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.37/29.97 (57) ~ (all_244_0 = e2) % 188.37/29.97 (58) all_252_10 = e0 % 188.37/29.97 (59) op(e2, all_40_2) = e0 % 188.37/29.97 (60) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.37/29.97 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.37/29.97 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.37/29.97 (61) all_252_12 = e2 & op(e1, e4) = e2 % 188.37/29.97 (62) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.37/29.97 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.37/29.97 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.37/29.97 (63) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.37/29.97 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.37/29.97 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.37/29.97 (64) ~ (e3 = e2) % 188.37/29.97 (65) all_252_22 = e4 % 188.37/29.97 (66) op(e4, all_20_2) = e0 % 188.37/29.97 (67) op(e0, e3) = all_8_1 % 188.37/29.97 (68) op(e2, e4) = all_64_2 % 188.37/29.97 (69) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.37/29.97 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.37/29.97 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.37/29.97 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.37/29.97 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.37/29.97 op(e0, e1) = e0))) % 188.37/29.97 (70) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.37/29.97 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.37/29.97 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.37/29.97 (71) ~ (e4 = e2) % 188.37/29.97 (72) op(e2, e0) = all_40_2 % 188.37/29.97 (73) op(all_28_2, all_40_2) = e2 % 188.37/29.97 (74) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.37/29.97 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.37/29.97 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.37/29.97 (75) ~ (e1 = e0) % 188.37/29.97 (76) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.37/29.97 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.37/29.97 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.37/29.97 (77) ~ (all_64_2 = e0) % 188.37/29.97 (78) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.37/29.97 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.37/29.97 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.37/29.97 (79) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.37/29.97 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.37/29.97 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.37/29.97 (80) op(e0, e4) = all_12_2 % 188.37/29.97 (81) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.37/29.97 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.37/29.97 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.37/29.97 (82) all_250_23 = all_20_2 % 188.37/29.97 (83) ~ (e3 = e1) % 188.37/29.97 (84) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.37/29.97 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.37/29.97 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.37/29.97 (85) ~ (e2 = e0) % 188.37/29.97 (86) op(e1, e0) = all_34_2 % 188.37/29.97 (87) all_252_7 = e2 % 188.37/29.97 (88) ~ (all_12_2 = e3) % 188.37/29.97 (89) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.37/29.97 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.37/29.97 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.37/29.97 (90) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.37/29.97 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.37/29.97 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.37/29.97 (91) ~ (all_34_2 = e2) % 188.37/29.97 (92) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.37/29.97 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.37/29.97 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.37/29.97 (93) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.37/29.97 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.37/29.97 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.37/29.97 (94) op(e4, e2) = all_6_2 % 188.37/29.97 (95) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.37/29.97 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.37/29.97 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.37/29.97 (96) all_252_5 = e0 % 188.37/29.97 (97) ~ (e4 = e1) % 188.37/29.97 (98) op(e2, e0) = e1 % 188.37/29.97 % 188.37/29.97 Begin of proof % 188.37/29.97 | % 188.37/29.97 | ALPHA: (61) implies: % 188.37/29.97 | (99) all_252_12 = e2 % 188.37/29.97 | % 188.37/29.97 | COMBINE_EQS: (17), (99) imply: % 188.37/29.97 | (100) e2 = e0 % 188.37/29.97 | % 188.37/29.97 | COMBINE_EQS: (87), (100) imply: % 188.37/29.97 | (101) all_252_7 = e0 % 188.37/29.97 | % 188.37/29.97 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.37/29.97 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 188.37/29.97 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 188.37/29.97 | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 188.37/29.97 | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 188.37/29.97 | (57), (58), (59), (60), (62), (63), (64), (65), (66), (67), (68), % 188.37/29.97 | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 188.37/29.97 | (80), (81), (82), (83), (84), (85), (86), (88), (89), (90), (91), % 188.37/29.97 | (92), (93), (94), (95), (96), (97), (98), (101) are inconsistent by % 188.37/29.97 | sub-proof #36. % 188.37/29.97 | % 188.37/29.97 End of proof % 188.37/29.97 % 188.37/29.97 Sub-proof #36 shows that the following formulas are inconsistent: % 188.37/29.97 ---------------------------------------------------------------- % 188.37/29.97 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.37/29.97 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.37/29.97 (all_252_16 = e1 & op(e4, e0) = e1) % 188.37/29.97 (2) all_252_20 = e2 % 188.37/29.97 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.37/29.97 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.37/29.97 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.37/29.97 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.37/29.97 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.37/29.97 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.37/29.97 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.37/29.97 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.37/29.97 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.37/29.97 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.37/29.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.37/29.97 (7) ~ (all_20_2 = e4) % 188.37/29.97 (8) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) | % 188.37/29.97 (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 188.37/29.97 | (all_252_21 = e0 & op(e0, e3) = e0) % 188.37/29.97 (9) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.37/29.97 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.37/29.97 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.37/29.97 (10) op(e0, e2) = e4 % 188.37/29.97 (11) op(e0, e2) = all_28_2 % 188.37/29.97 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) % 188.37/29.97 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = % 188.37/29.97 e0) | (all_252_18 = e0 & op(e2, e0) = e0) % 188.37/29.97 (13) op(e3, e1) = all_36_2 % 188.37/29.97 (14) ~ (all_40_2 = e2) % 188.37/29.97 (15) ~ (e2 = e1) % 188.37/29.97 (16) ~ (all_62_2 = e0) % 188.37/29.97 (17) all_252_12 = e0 % 188.37/29.97 (18) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.37/29.97 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.37/29.97 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.37/29.97 (19) op(e1, e3) = all_62_2 % 188.37/29.97 (20) op(e3, e0) = e2 % 188.37/29.97 (21) op(e2, e1) = e0 % 188.37/29.97 (22) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 188.37/29.97 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = % 188.37/29.97 e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 188.37/29.97 (23) all_252_7 = e0 % 188.37/29.97 (24) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.37/29.97 all_250_23 = e0 % 188.37/29.97 (25) ~ (e4 = e0) % 188.37/29.97 (26) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.37/29.97 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.37/29.97 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.37/29.97 (27) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.37/29.97 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.37/29.97 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.37/29.97 (28) ~ (e4 = e3) % 188.37/29.97 (29) ~ (all_36_2 = e2) % 188.37/29.97 (30) ~ (all_40_2 = all_34_2) % 188.37/29.97 (31) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.37/29.97 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.37/29.97 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.37/29.98 (32) ~ (all_244_24 = all_20_2) % 188.37/29.98 (33) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.37/29.98 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.37/29.98 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.37/29.98 (34) op(e1, e4) = e0 % 188.37/29.98 (35) ~ (all_6_2 = e4) % 188.37/29.98 (36) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.37/29.98 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.37/29.98 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.37/29.98 (37) ~ (all_20_2 = e3) % 188.37/29.98 (38) op(all_20_2, e4) = e1 % 188.37/29.98 (39) op(e0, e0) = all_244_24 % 188.37/29.98 (40) op(e0, e1) = all_20_2 % 188.37/29.98 (41) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.37/29.98 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.37/29.98 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.37/29.98 (42) all_252_19 = e4 % 188.37/29.98 (43) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.37/29.98 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.37/29.98 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.37/29.98 (44) ~ (all_8_1 = e2) % 188.37/29.98 (45) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.37/29.98 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.37/29.98 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.37/29.98 (46) ~ (all_20_2 = e0) % 188.37/29.98 (47) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.37/29.98 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.37/29.98 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.37/29.98 (48) all_252_17 = e2 % 188.37/29.98 (49) ~ (all_20_2 = e2) % 188.37/29.98 (50) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.37/29.98 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.37/29.98 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.37/29.98 (51) op(e4, e4) = all_244_0 % 188.37/29.98 (52) op(e0, e4) = e2 % 188.37/29.98 (53) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) % 188.37/29.98 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.37/29.98 e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.37/29.98 (54) ~ (e3 = e0) % 188.37/29.98 (55) ~ (all_20_2 = all_8_1) % 188.37/29.98 (56) ~ (all_28_2 = e0) % 188.37/29.98 (57) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.37/29.98 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.37/29.98 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.37/29.98 (58) ~ (all_244_0 = e2) % 188.37/29.98 (59) all_252_10 = e0 % 188.37/29.98 (60) op(e2, all_40_2) = e0 % 188.37/29.98 (61) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.37/29.98 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.37/29.98 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.37/29.98 (62) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.37/29.98 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.37/29.98 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.37/29.98 (63) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.37/29.98 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.37/29.98 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.37/29.98 (64) ~ (e3 = e2) % 188.37/29.98 (65) all_252_22 = e4 % 188.37/29.98 (66) op(e4, all_20_2) = e0 % 188.37/29.98 (67) op(e0, e3) = all_8_1 % 188.37/29.98 (68) op(e2, e4) = all_64_2 % 188.37/29.98 (69) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.37/29.98 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.37/29.98 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.37/29.98 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.37/29.98 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.37/29.98 op(e0, e1) = e0))) % 188.37/29.98 (70) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.37/29.98 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.37/29.98 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.37/29.98 (71) ~ (e4 = e2) % 188.37/29.98 (72) op(e2, e0) = all_40_2 % 188.37/29.98 (73) op(all_28_2, all_40_2) = e2 % 188.37/29.98 (74) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.37/29.98 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.37/29.98 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.37/29.98 (75) ~ (e1 = e0) % 188.37/29.98 (76) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.37/29.98 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.37/29.98 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.37/29.98 (77) ~ (all_64_2 = e0) % 188.37/29.98 (78) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.37/29.98 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.37/29.98 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.37/29.98 (79) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.37/29.98 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.37/29.98 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.37/29.98 (80) op(e0, e4) = all_12_2 % 188.37/29.98 (81) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.37/29.98 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.37/29.98 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.37/29.98 (82) all_250_23 = all_20_2 % 188.37/29.98 (83) ~ (e3 = e1) % 188.37/29.98 (84) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.37/29.98 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.37/29.98 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.37/29.98 (85) ~ (e2 = e0) % 188.37/29.98 (86) op(e1, e0) = all_34_2 % 188.37/29.98 (87) ~ (all_12_2 = e3) % 188.37/29.98 (88) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.37/29.98 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.37/29.98 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.37/29.98 (89) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.37/29.98 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.37/29.98 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.37/29.98 (90) ~ (all_34_2 = e2) % 188.37/29.98 (91) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.37/29.98 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.37/29.98 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.37/29.98 (92) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.37/29.98 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.37/29.98 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.37/29.98 (93) op(e4, e2) = all_6_2 % 188.37/29.98 (94) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.37/29.98 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.37/29.98 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.37/29.98 (95) all_252_5 = e0 % 188.37/29.98 (96) ~ (e4 = e1) % 188.37/29.98 (97) op(e2, e0) = e1 % 188.37/29.98 % 188.37/29.98 Begin of proof % 188.37/29.98 | % 188.37/29.98 | BETA: splitting (53) gives: % 188.37/29.98 | % 188.37/29.98 | Case 1: % 188.37/29.98 | | % 188.37/29.98 | | (98) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = % 188.37/29.98 | | e2) % 188.37/29.98 | | % 188.37/29.98 | | REF_CLOSE: (2), (3), (4), (6), (15), (17), (23), (25), (28), (52), (54), % 188.37/29.98 | | (64), (70), (71), (75), (80), (83), (85), (87), (89), (96), (98) % 188.37/29.98 | | are inconsistent by sub-proof #221. % 188.37/29.98 | | % 188.37/29.98 | Case 2: % 188.37/29.98 | | % 188.37/29.98 | | (99) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.37/29.98 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.37/29.98 | | % 188.37/29.98 | | BETA: splitting (99) gives: % 188.37/29.98 | | % 188.37/29.98 | | Case 1: % 188.37/29.98 | | | % 188.37/29.98 | | | (100) all_252_8 = e2 & op(e2, e2) = e2 % 188.37/29.98 | | | % 188.37/29.98 | | | ALPHA: (100) implies: % 188.37/29.98 | | | (101) all_252_8 = e2 % 188.37/29.98 | | | % 188.37/29.98 | | | BETA: splitting (24) gives: % 188.37/29.98 | | | % 188.37/29.98 | | | Case 1: % 188.37/29.98 | | | | % 188.37/29.98 | | | | (102) all_250_23 = e4 % 188.37/29.98 | | | | % 188.37/29.98 | | | | REF_CLOSE: (7), (82), (102) are inconsistent by sub-proof #489. % 188.37/29.98 | | | | % 188.37/29.98 | | | Case 2: % 188.37/29.98 | | | | % 188.37/29.98 | | | | (103) ~ (all_250_23 = e4) % 188.37/29.98 | | | | (104) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.37/29.98 | | | | all_250_23 = e0 % 188.37/29.98 | | | | % 188.37/29.98 | | | | BETA: splitting (104) gives: % 188.37/29.98 | | | | % 188.37/29.98 | | | | Case 1: % 188.37/29.98 | | | | | % 188.37/29.98 | | | | | (105) all_250_23 = e3 % 188.37/29.98 | | | | | % 188.37/29.98 | | | | | REF_CLOSE: (37), (82), (105) are inconsistent by sub-proof #488. % 188.37/29.98 | | | | | % 188.37/29.98 | | | | Case 2: % 188.37/29.98 | | | | | % 188.37/29.98 | | | | | (106) ~ (all_250_23 = e3) % 188.37/29.98 | | | | | (107) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.37/29.98 | | | | | % 188.37/29.98 | | | | | BETA: splitting (107) gives: % 188.37/29.98 | | | | | % 188.37/29.98 | | | | | Case 1: % 188.37/29.98 | | | | | | % 188.37/29.98 | | | | | | (108) all_250_23 = e2 % 188.37/29.98 | | | | | | % 188.37/29.98 | | | | | | REF_CLOSE: (49), (82), (108) are inconsistent by sub-proof #487. % 188.37/29.98 | | | | | | % 188.37/29.98 | | | | | Case 2: % 188.37/29.98 | | | | | | % 188.37/29.98 | | | | | | (109) ~ (all_250_23 = e2) % 188.37/29.98 | | | | | | (110) all_250_23 = e1 | all_250_23 = e0 % 188.37/29.98 | | | | | | % 188.37/29.98 | | | | | | BETA: splitting (110) gives: % 188.37/29.98 | | | | | | % 188.37/29.98 | | | | | | Case 1: % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | (111) all_250_23 = e1 % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | COMBINE_EQS: (82), (111) imply: % 188.37/29.98 | | | | | | | (112) all_20_2 = e1 % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | SIMP: (112) implies: % 188.37/29.98 | | | | | | | (113) all_20_2 = e1 % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (32), (113) imply: % 188.37/29.98 | | | | | | | (114) ~ (all_244_24 = e1) % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (55), (113) imply: % 188.37/29.98 | | | | | | | (115) ~ (all_8_1 = e1) % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | SIMP: (115) implies: % 188.37/29.98 | | | | | | | (116) ~ (all_8_1 = e1) % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (7), (113) imply: % 188.37/29.98 | | | | | | | (117) ~ (e4 = e1) % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (37), (113) imply: % 188.37/29.98 | | | | | | | (118) ~ (e3 = e1) % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (49), (113) imply: % 188.37/29.98 | | | | | | | (119) ~ (e2 = e1) % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (38), (113) imply: % 188.37/29.98 | | | | | | | (120) op(e1, e4) = e1 % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (66), (113) imply: % 188.37/29.98 | | | | | | | (121) op(e4, e1) = e0 % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | REDUCE: (40), (113) imply: % 188.37/29.98 | | | | | | | (122) op(e0, e1) = e1 % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | BETA: splitting (50) gives: % 188.37/29.98 | | | | | | | % 188.37/29.98 | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | % 188.37/29.98 | | | | | | | | (123) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & % 188.37/29.98 | | | | | | | | op(e3, e1) = e4) % 188.37/29.98 | | | | | | | | % 188.37/29.98 | | | | | | | | BETA: splitting (123) gives: % 188.37/29.98 | | | | | | | | % 188.37/29.98 | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | % 188.37/29.98 | | | | | | | | | (124) all_252_9 = e4 & op(e4, e1) = e4 % 188.37/29.98 | | | | | | | | | % 188.37/29.98 | | | | | | | | | ALPHA: (124) implies: % 188.37/29.98 | | | | | | | | | (125) all_252_9 = e4 % 188.37/29.98 | | | | | | | | | % 188.37/29.98 | | | | | | | | | BETA: splitting (63) gives: % 188.37/29.98 | | | | | | | | | % 188.37/29.98 | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | (126) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 188.37/29.98 | | | | | | | | | | e2 & op(e3, e3) = e2) % 188.37/29.98 | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | BETA: splitting (126) gives: % 188.37/29.98 | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | (127) all_252_1 = e2 & op(e4, e3) = e2 % 188.37/29.98 | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | ALPHA: (127) implies: % 188.37/29.98 | | | | | | | | | | | (128) all_252_1 = e2 % 188.37/29.98 | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | BETA: splitting (18) gives: % 188.37/29.98 | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | (129) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 188.37/29.98 | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | BETA: splitting (129) gives: % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | (130) all_252_9 = e3 & op(e4, e1) = e3 % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | REF_CLOSE: (6), (54), (121), (130) are inconsistent by % 188.37/29.98 | | | | | | | | | | | | | sub-proof #275. % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | (131) all_252_10 = e3 & op(e3, e1) = e3 % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | REF_CLOSE: (54), (59), (131) are inconsistent by sub-proof % 188.37/29.98 | | | | | | | | | | | | | #59. % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | End of split % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | (132) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 188.37/29.98 | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 188.37/29.98 | | | | | | | | | | | | op(e0, e1) = e3) % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | BETA: splitting (132) gives: % 188.37/29.98 | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | (133) all_252_11 = e3 & op(e2, e1) = e3 % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | ALPHA: (133) implies: % 188.37/29.98 | | | | | | | | | | | | | (134) all_252_11 = e3 % 188.37/29.98 | | | | | | | | | | | | | (135) op(e2, e1) = e3 % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | BETA: splitting (78) gives: % 188.37/29.98 | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | (136) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.37/29.98 | | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.37/29.98 | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | BETA: splitting (136) gives: % 188.37/29.98 | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | (137) all_252_6 = e4 & op(e2, e4) = e4 % 188.37/29.98 | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | ALPHA: (137) implies: % 188.37/29.98 | | | | | | | | | | | | | | | (138) all_252_6 = e4 % 188.37/29.98 | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | BETA: splitting (62) gives: % 188.37/29.98 | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | (139) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 188.37/29.98 | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 188.37/29.98 | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | REF_CLOSE: (59), (75), (96), (125), (139) are inconsistent by % 188.37/29.98 | | | | | | | | | | | | | | | | sub-proof #57. % 188.37/29.98 | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | (140) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 188.37/29.98 | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 188.37/29.98 | | | | | | | | | | | | | | | | op(e0, e1) = e1) % 188.37/29.98 | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | (141) all_252_11 = e1 & op(e2, e1) = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | ALPHA: (141) implies: % 188.37/29.98 | | | | | | | | | | | | | | | | | (142) all_252_11 = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (142) imply: % 188.37/29.98 | | | | | | | | | | | | | | | | | (143) e3 = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | REDUCE: (83), (143) imply: % 188.37/29.98 | | | | | | | | | | | | | | | | | (144) $false % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | CLOSE: (144) is inconsistent. % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | (145) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 188.37/29.98 | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | BETA: splitting (145) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | (146) all_252_15 = e1 & op(e1, e1) = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (13), (15), % 188.37/29.98 | | | | | | | | | | | | | | | | | | (17), (18), (21), (24), (25), (28), (29), (30), % 188.37/29.98 | | | | | | | | | | | | | | | | | | (32), (34), (37), (38), (39), (40), (42), (43), % 188.37/29.98 | | | | | | | | | | | | | | | | | | (46), (47), (49), (50), (52), (54), (55), (57), % 188.37/29.98 | | | | | | | | | | | | | | | | | | (59), (62), (64), (66), (67), (70), (71), (72), % 188.37/29.98 | | | | | | | | | | | | | | | | | | (74), (75), (80), (82), (83), (85), (86), (87), % 188.37/29.98 | | | | | | | | | | | | | | | | | | (89), (90), (96), (97), (125), (138), (146) are % 188.37/29.98 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #55. % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | (147) all_252_23 = e1 & op(e0, e1) = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies: % 188.37/29.98 | | | | | | | | | | | | | | | | | | (148) all_252_23 = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | (149) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 188.37/29.98 | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (150) all_252_1 = e4 & op(e4, e3) = e4 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (15), (17), (25), (28), (52), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (54), (64), (70), (71), (75), (80), (83), (85), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (87), (89), (96), (128), (138), (150) are % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212. % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (151) all_252_3 = e4 & op(e3, e3) = e4 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (54), (59), (64), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (71), (75), (76), (83), (92), (95), (96), (151) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #54. % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | (152) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 188.37/29.98 | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 188.37/29.98 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (153) all_252_7 = e4 & op(e2, e3) = e4 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (11), (13), (17), (18), (19), (21), (23), (24), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (48), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (56), (57), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (58), (60), (61), (62), (63), (64), (65), (66), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (67), (69), (70), (71), (72), (73), (74), (76), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (84), (85), (86), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (95), (97), (101), (125), (153) are inconsistent % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | by sub-proof #53. % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | (154) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | (155) all_252_13 = e4 & op(e1, e3) = e4 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | (156) op(e1, e3) = e4 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | (157) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_12 = e1 & op(e1, e4) = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (17), (32), (39), (43), (46), % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | (49), (55), (67), (82), (110), (148), (158) are % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_13 = e1 & op(e1, e3) = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (96), (156), (159) are inconsistent by % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #423. % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | (160) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | (161) all_252_14 = e1 & op(e1, e2) = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | (162) all_252_14 = e1 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | (163) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_4 = e3 & op(e4, e2) = e3 % 188.37/29.98 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_252_4 = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (166) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (19), (25), (28), (31), (42), (47), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (54), (64), (71), (74), (75), (83), (85), (86), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (90), (96), (156), (166) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #83. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (167) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_14 = e3 & op(e1, e2) = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (28), (33), (54), (64), (83), (95), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (101), (162), (165), (168) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #96. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_15 = e3 & op(e1, e1) = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_252_15 = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (13), (15), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (17), (18), (21), (24), (25), (28), (29), (30), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (34), (37), (38), (39), (40), (42), (43), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (46), (47), (49), (50), (52), (54), (55), (57), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (59), (62), (64), (66), (67), (70), (71), (72), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (74), (75), (80), (82), (83), (85), (86), (87), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (96), (97), (110), (125), (138), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (148), (156), (171) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #49. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_19 = e3 & op(e1, e0) = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (42), (172) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #243. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_252_5 = e3 & op(e3, e2) = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_5 = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (95), (174) imply: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (175) e3 = e0 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (18), (25), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (28), (29), (32), (34), (37), (39), (40), (43), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (46), (49), (50), (54), (55), (62), (64), (67), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (71), (75), (82), (83), (85), (96), (110), (120), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (121), (122), (134), (175) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #110. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | (176) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_252_8 = e3 & op(e2, e2) = e3 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (101), (177) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | #48. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (178) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (28), (83), (162), (178) are % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #98. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (179) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (13), (15), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (17), (18), (21), (24), (25), (28), (29), (30), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (32), (34), (37), (38), (39), (40), (42), (43), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (46), (47), (49), (50), (52), (54), (55), (57), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (59), (62), (64), (66), (67), (70), (71), (72), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (74), (75), (80), (82), (83), (85), (86), (87), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (89), (90), (96), (97), (125), (138), (179) are % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #50. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (180) all_252_21 = e4 & op(e0, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (25), (28), (32), (37), (39), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (40), (43), (46), (49), (52), (54), (55), (67), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (69), (80), (82), (85), (87), (91), (107), (180) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #47. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | (181) all_252_7 = e4 & op(e2, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.37/29.99 | | | | | | | | | | | | | | | (11), (13), (17), (18), (19), (21), (23), (24), % 188.37/29.99 | | | | | | | | | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), % 188.37/29.99 | | | | | | | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), % 188.37/29.99 | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (48), % 188.37/29.99 | | | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (56), (57), % 188.37/29.99 | | | | | | | | | | | | | | | (58), (60), (61), (62), (63), (64), (65), (66), % 188.37/29.99 | | | | | | | | | | | | | | | (67), (69), (70), (71), (72), (73), (74), (76), % 188.37/29.99 | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (84), (85), (86), % 188.37/29.99 | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), % 188.37/29.99 | | | | | | | | | | | | | | | (95), (97), (101), (125), (181) are inconsistent % 188.37/29.99 | | | | | | | | | | | | | | | by sub-proof #46. % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | (182) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.37/29.99 | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.37/29.99 | | | | | | | | | | | | | | op(e2, e0) = e4) % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (18), (21), % 188.37/29.99 | | | | | | | | | | | | | | (25), (27), (28), (29), (32), (34), (37), (39), % 188.37/29.99 | | | | | | | | | | | | | | (40), (42), (43), (45), (46), (48), (49), (50), % 188.37/29.99 | | | | | | | | | | | | | | (52), (54), (55), (62), (64), (67), (69), (71), % 188.37/29.99 | | | | | | | | | | | | | | (75), (82), (83), (85), (96), (101), (110), (114), % 188.37/29.99 | | | | | | | | | | | | | | (116), (120), (121), (122), (134), (135), (182) % 188.37/29.99 | | | | | | | | | | | | | | are inconsistent by sub-proof #42. % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | (183) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 188.37/29.99 | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 188.37/29.99 | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | BETA: splitting (183) gives: % 188.37/29.99 | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | (184) all_252_15 = e3 & op(e1, e1) = e3 % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | ALPHA: (184) implies: % 188.37/29.99 | | | | | | | | | | | | | | (185) all_252_15 = e3 % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | BETA: splitting (78) gives: % 188.37/29.99 | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | (186) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.37/29.99 | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | (187) all_252_6 = e4 & op(e2, e4) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | ALPHA: (187) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | (188) all_252_6 = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | (189) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 188.37/29.99 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (52), (67), (116), (189) are % 188.37/29.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | (190) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 188.37/29.99 | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 188.37/29.99 | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | BETA: splitting (190) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | (191) all_252_22 = e1 & op(e0, e2) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | ALPHA: (191) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | (192) op(e0, e2) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (96), (192) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | sub-proof #256. % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | (193) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.37/29.99 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (194) all_252_23 = e1 & op(e0, e1) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (195) all_252_23 = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | (196) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (197) all_252_1 = e4 & op(e4, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (15), (17), (25), (28), (52), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (54), (64), (70), (71), (75), (80), (83), (85), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (87), (89), (96), (128), (188), (197) are % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #212. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (198) all_252_3 = e4 & op(e3, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (54), (59), (64), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (71), (75), (76), (83), (92), (95), (96), (198) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #54. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | (199) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (200) all_252_7 = e4 & op(e2, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (11), (13), (17), (18), (19), (21), (23), (24), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (48), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (56), (57), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (58), (60), (61), (62), (63), (64), (65), (66), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (67), (69), (70), (71), (72), (73), (74), (76), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (84), (85), (86), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (95), (97), (101), (125), (200) are inconsistent % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | by sub-proof #53. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (201) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (202) all_252_13 = e4 & op(e1, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (203) op(e1, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (13), (15), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (17), (18), (21), (24), (25), (28), (29), (30), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (32), (34), (37), (38), (39), (40), (42), (43), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (46), (47), (49), (50), (52), (54), (55), (57), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (59), (62), (64), (66), (67), (70), (71), (72), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (74), (75), (80), (82), (83), (85), (86), (87), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (89), (90), (96), (97), (110), (125), (185), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (188), (195), (203) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | #49. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (204) all_252_21 = e4 & op(e0, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (25), (28), (32), (37), (39), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (40), (43), (46), (49), (52), (54), (55), (67), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (69), (80), (82), (85), (87), (91), (107), (204) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #47. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (205) all_252_24 = e1 & op(e0, e0) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (206) op(e0, e0) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (114), (206) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | sub-proof #474. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | (207) all_252_7 = e4 & op(e2, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.37/29.99 | | | | | | | | | | | | | | | | (11), (13), (17), (18), (19), (21), (23), (24), % 188.37/29.99 | | | | | | | | | | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), % 188.37/29.99 | | | | | | | | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), % 188.37/29.99 | | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (48), % 188.37/29.99 | | | | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (56), (57), % 188.37/29.99 | | | | | | | | | | | | | | | | (58), (60), (61), (62), (63), (64), (65), (66), % 188.37/29.99 | | | | | | | | | | | | | | | | (67), (69), (70), (71), (72), (73), (74), (76), % 188.37/29.99 | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (84), (85), (86), % 188.37/29.99 | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), % 188.37/29.99 | | | | | | | | | | | | | | | | (95), (97), (101), (125), (207) are inconsistent % 188.37/29.99 | | | | | | | | | | | | | | | | by sub-proof #46. % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | (208) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.37/29.99 | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.37/29.99 | | | | | | | | | | | | | | | op(e2, e0) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 188.37/29.99 | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | (209) all_252_8 = e4 & op(e2, e2) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | (210) all_252_8 = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | REF_CLOSE: (71), (101), (210) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | #163. % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | (211) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 188.37/29.99 | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | BETA: splitting (211) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | (212) all_252_11 = e4 & op(e2, e1) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (18), (21), % 188.37/29.99 | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (34), (37), (39), (40), % 188.37/29.99 | | | | | | | | | | | | | | | | | (43), (46), (49), (50), (52), (54), (55), (62), % 188.37/29.99 | | | | | | | | | | | | | | | | | (64), (67), (71), (75), (82), (83), (85), (96), % 188.37/29.99 | | | | | | | | | | | | | | | | | (110), (114), (116), (120), (121), (212) are % 188.37/29.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #67. % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | (213) all_252_18 = e4 & op(e2, e0) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | ALPHA: (213) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | (214) all_252_18 = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | (215) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 188.37/29.99 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (52), (67), (116), (215) are % 188.37/29.99 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | (216) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 188.37/29.99 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (217) all_252_22 = e1 & op(e0, e2) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (218) op(e0, e2) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (96), (218) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | sub-proof #256. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | (219) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | (220) all_252_23 = e1 & op(e0, e1) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | (221) all_252_23 = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (79) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (222) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (223) all_252_1 = e4 & op(e4, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (128), (223) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | #152. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (224) all_252_3 = e4 & op(e3, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (54), (59), (64), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (71), (75), (76), (83), (92), (95), (96), (224) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #54. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | (225) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (226) all_252_7 = e4 & op(e2, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (227) all_252_7 = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (227) imply: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (228) e4 = e0 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (228) imply: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (229) all_252_9 = e0 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (17), (18), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (21), (24), (25), (27), (28), (29), (30), (32), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (34), (37), (38), (39), (40), (42), (43), (45), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (46), (47), (48), (49), (50), (52), (54), (55), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (57), (62), (64), (65), (66), (67), (69), (71), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (72), (74), (75), (82), (83), (85), (86), (90), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (96), (97), (214), (229) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | sub-proof #158. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | (230) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (231) all_252_13 = e4 & op(e1, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | (232) op(e1, e3) = e4 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | (233) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_12 = e2 & op(e1, e4) = e2 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_12 = e2 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (85), (235) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | #81. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_252_13 = e2 & op(e1, e3) = e2 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_13 = e2 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (13), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (15), (17), (18), (21), (23), (24), (25), (28), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (29), (30), (32), (34), (37), (38), (39), (40), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (42), (43), (46), (47), (49), (50), (52), (54), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (59), (62), (64), (66), (67), (70), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (71), (72), (74), (75), (80), (82), (83), (85), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (86), (87), (89), (90), (96), (97), (101), (110), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (125), (185), (214), (221), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (237) are inconsistent by sub-proof #38. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | (238) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_252_14 = e2 & op(e1, e2) = e2 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_252_14 = e2 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (241) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_252_12 = e1 & op(e1, e4) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (17), (32), (39), (43), (46), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (55), (67), (82), (110), (221), (242) are % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_252_13 = e1 & op(e1, e3) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (96), (232), (243) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #423. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (244) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_252_14 = e1 & op(e1, e2) = e1 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (240), (245) are inconsistent by sub-proof % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | #395. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (17), (18), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (21), (24), (25), (28), (29), (30), (32), (34), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (46), (47), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (50), (52), (54), (55), (57), (59), (62), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (66), (67), (71), (72), (74), (82), (85), % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (86), (90), (97), (125), (246) are inconsistent by % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #40. % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/29.99 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | (247) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_252_15 = e2 & op(e1, e1) = e2 % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (185), (248) are inconsistent by sub-proof % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | #114. % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_252_19 = e2 & op(e1, e0) = e2 % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (86), (90), (249) are inconsistent by % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #438. % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | (250) all_252_21 = e4 & op(e0, e3) = e4 % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (25), (28), (32), (37), (39), % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | (40), (43), (46), (49), (52), (54), (55), (67), % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | (69), (80), (82), (85), (87), (91), (107), (250) % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #47. % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | (251) all_252_24 = e1 & op(e0, e0) = e1 % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies: % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | (252) op(e0, e0) = e1 % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (114), (252) are inconsistent by % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | sub-proof #474. % 188.37/30.00 | | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | (253) all_252_23 = e3 & op(e0, e1) = e3 % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | ALPHA: (253) implies: % 188.37/30.00 | | | | | | | | | | | | | | (254) op(e0, e1) = e3 % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | REF_CLOSE: (6), (37), (40), (254) are inconsistent by % 188.37/30.00 | | | | | | | | | | | | | | sub-proof #508. % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | (255) all_252_3 = e2 & op(e3, e3) = e2 % 188.37/30.00 | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | ALPHA: (255) implies: % 188.37/30.00 | | | | | | | | | | | (256) all_252_3 = e2 % 188.37/30.00 | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | BETA: splitting (76) gives: % 188.37/30.00 | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | (257) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = % 188.37/30.00 | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 188.37/30.00 | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | BETA: splitting (257) gives: % 188.37/30.00 | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | (258) all_252_2 = e3 & op(e3, e4) = e3 % 188.37/30.00 | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | ALPHA: (258) implies: % 188.37/30.00 | | | | | | | | | | | | | (259) all_252_2 = e3 % 188.37/30.00 | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | BETA: splitting (92) gives: % 188.37/30.00 | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | (260) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = % 188.37/30.00 | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | BETA: splitting (260) gives: % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | (261) all_252_2 = e4 & op(e3, e4) = e4 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | ALPHA: (261) implies: % 188.37/30.00 | | | | | | | | | | | | | | | (262) all_252_2 = e4 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | COMBINE_EQS: (259), (262) imply: % 188.37/30.00 | | | | | | | | | | | | | | | (263) e4 = e3 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | SIMP: (263) implies: % 188.37/30.00 | | | | | | | | | | | | | | | (264) e4 = e3 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | REDUCE: (28), (264) imply: % 188.37/30.00 | | | | | | | | | | | | | | | (265) $false % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent. % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | (266) all_252_3 = e4 & op(e3, e3) = e4 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (54), (59), (64), % 188.37/30.00 | | | | | | | | | | | | | | | (71), (75), (76), (83), (92), (95), (96), (266) % 188.37/30.00 | | | | | | | | | | | | | | | are inconsistent by sub-proof #54. % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | End of split % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | (267) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = % 188.37/30.00 | | | | | | | | | | | | | | e4 & op(e3, e1) = e4) | (all_252_17 = e4 & % 188.37/30.00 | | | | | | | | | | | | | | op(e3, e0) = e4) % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | BETA: splitting (267) gives: % 188.37/30.00 | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | (268) all_252_5 = e4 & op(e3, e2) = e4 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | ALPHA: (268) implies: % 188.37/30.00 | | | | | | | | | | | | | | | (269) all_252_5 = e4 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | COMBINE_EQS: (95), (269) imply: % 188.37/30.00 | | | | | | | | | | | | | | | (270) e4 = e0 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | COMBINE_EQS: (125), (270) imply: % 188.37/30.00 | | | | | | | | | | | | | | | (271) all_252_9 = e0 % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.37/30.00 | | | | | | | | | | | | | | | (11), (12), (13), (14), (15), (16), (17), (18), % 188.37/30.00 | | | | | | | | | | | | | | | (19), (21), (22), (24), (25), (26), (27), (28), % 188.37/30.00 | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), % 188.37/30.00 | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), % 188.37/30.00 | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), % 188.37/30.00 | | | | | | | | | | | | | | | (53), (54), (55), (56), (57), (58), (60), (61), % 188.37/30.00 | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), % 188.37/30.00 | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), % 188.37/30.00 | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85), % 188.37/30.00 | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), % 188.37/30.00 | | | | | | | | | | | | | | | (94), (95), (96), (97), (121), (271) are % 188.37/30.00 | | | | | | | | | | | | | | | inconsistent by sub-proof #60. % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | Case 2: % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | (272) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 % 188.37/30.00 | | | | | | | | | | | | | | | = e4 & op(e3, e0) = e4) % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | BETA: splitting (272) gives: % 188.37/30.00 | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | Case 1: % 188.37/30.00 | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | (273) all_252_10 = e4 & op(e3, e1) = e4 % 188.37/30.00 | | | | | | | | | | | | | | | | % 188.37/30.00 | | | | | | | | | | | | | | | | ALPHA: (273) implies: % 188.37/30.00 | | | | | | | | | | | | | | | | (274) all_252_10 = e4 % 188.37/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (54), (64), (71), % 188.54/30.00 | | | | | | | | | | | | | | | | (75), (76), (83), (92), (95), (96), (256), (274) % 188.54/30.00 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #127. % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | (275) all_252_17 = e4 & op(e3, e0) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | ALPHA: (275) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | (276) op(e3, e0) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (20), (71), (276) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | sub-proof #250. % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | (277) all_252_3 = e3 & op(e3, e3) = e3 % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (59), (71), (75), % 188.54/30.00 | | | | | | | | | | | | | (83), (92), (95), (96), (277) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | sub-proof #90. % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | (278) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = % 188.54/30.00 | | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 188.54/30.00 | | | | | | | | | | | | op(e3, e0) = e3) % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | BETA: splitting (278) gives: % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | (279) all_252_5 = e3 & op(e3, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | REF_CLOSE: (54), (95), (279) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | #217. % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | (280) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 % 188.54/30.00 | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | BETA: splitting (280) gives: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | (281) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | REF_CLOSE: (15), (25), (28), (41), (48), (71), (75), (83), % 188.54/30.00 | | | | | | | | | | | | | | (92), (95), (96), (256), (281) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | sub-proof #130. % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | (282) all_252_17 = e3 & op(e3, e0) = e3 % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | REF_CLOSE: (48), (64), (282) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | | #159. % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | % 188.54/30.00 | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | (283) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 188.54/30.00 | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, % 188.54/30.00 | | | | | | | | | | e3) = e2) % 188.54/30.00 | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | BETA: splitting (283) gives: % 188.54/30.00 | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | (284) all_252_7 = e2 & op(e2, e3) = e2 % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | REF_CLOSE: (23), (85), (284) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | #222. % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | (285) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 188.54/30.00 | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | BETA: splitting (285) gives: % 188.54/30.00 | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | (286) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | ALPHA: (286) implies: % 188.54/30.00 | | | | | | | | | | | | (287) all_252_13 = e2 % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | BETA: splitting (18) gives: % 188.54/30.00 | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | (288) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 188.54/30.00 | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | BETA: splitting (288) gives: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | (289) all_252_9 = e3 & op(e4, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | REF_CLOSE: (6), (54), (121), (289) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | sub-proof #275. % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | (290) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | REF_CLOSE: (54), (59), (290) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | | #59. % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | (291) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 188.54/30.00 | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 188.54/30.00 | | | | | | | | | | | | | op(e0, e1) = e3) % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | BETA: splitting (291) gives: % 188.54/30.00 | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | (292) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | ALPHA: (292) implies: % 188.54/30.00 | | | | | | | | | | | | | | (293) all_252_11 = e3 % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | BETA: splitting (43) gives: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | (294) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 188.54/30.00 | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (52), (67), (116), (294) are % 188.54/30.00 | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | (295) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 188.54/30.00 | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 188.54/30.00 | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | (296) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | ALPHA: (296) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | (297) op(e0, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (96), (297) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | sub-proof #256. % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | (298) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.54/30.00 | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | BETA: splitting (298) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | (299) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | (300) all_252_23 = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (17), (18), % 188.54/30.00 | | | | | | | | | | | | | | | | | (21), (24), (25), (28), (29), (30), (32), (34), % 188.54/30.00 | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (42), (43), (46), (47), % 188.54/30.00 | | | | | | | | | | | | | | | | | (49), (50), (52), (54), (55), (57), (59), (62), % 188.54/30.00 | | | | | | | | | | | | | | | | | (64), (66), (67), (71), (72), (74), (75), (82), % 188.54/30.00 | | | | | | | | | | | | | | | | | (83), (85), (86), (90), (96), (97), (110), (120), % 188.54/30.00 | | | | | | | | | | | | | | | | | (121), (122), (125), (287), (293), (300) are % 188.54/30.00 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #39. % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | (301) all_252_24 = e1 & op(e0, e0) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | ALPHA: (301) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | (302) op(e0, e0) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (114), (302) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | | sub-proof #474. % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | (303) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 188.54/30.00 | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | BETA: splitting (303) gives: % 188.54/30.00 | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | (304) all_252_15 = e3 & op(e1, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | ALPHA: (304) implies: % 188.54/30.00 | | | | | | | | | | | | | | | (305) all_252_15 = e3 % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | BETA: splitting (78) gives: % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | (306) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.54/30.00 | | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | BETA: splitting (306) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | (307) all_252_6 = e4 & op(e2, e4) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | ALPHA: (307) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | (308) all_252_6 = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (13), (15), % 188.54/30.00 | | | | | | | | | | | | | | | | | (17), (18), (21), (25), (28), (29), (30), (32), % 188.54/30.00 | | | | | | | | | | | | | | | | | (34), (37), (38), (39), (40), (43), (46), (49), % 188.54/30.00 | | | | | | | | | | | | | | | | | (50), (52), (54), (55), (62), (64), (66), (67), % 188.54/30.00 | | | | | | | | | | | | | | | | | (70), (71), (72), (74), (75), (80), (82), (83), % 188.54/30.00 | | | | | | | | | | | | | | | | | (85), (86), (87), (89), (96), (97), (110), (125), % 188.54/30.00 | | | | | | | | | | | | | | | | | (287), (305), (308) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | | | | | #51. % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | (309) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.54/30.00 | | | | | | | | | | | | | | | | | (11), (13), (17), (18), (19), (21), (23), (24), % 188.54/30.00 | | | | | | | | | | | | | | | | | (25), (26), (27), (28), (29), (30), (31), (32), % 188.54/30.00 | | | | | | | | | | | | | | | | | (33), (34), (35), (36), (37), (38), (39), (40), % 188.54/30.00 | | | | | | | | | | | | | | | | | (41), (42), (43), (44), (45), (46), (47), (48), % 188.54/30.00 | | | | | | | | | | | | | | | | | (49), (50), (51), (52), (54), (55), (56), (57), % 188.54/30.00 | | | | | | | | | | | | | | | | | (58), (60), (61), (62), (63), (64), (65), (66), % 188.54/30.00 | | | | | | | | | | | | | | | | | (67), (69), (70), (71), (72), (73), (74), (76), % 188.54/30.00 | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (84), (85), (86), % 188.54/30.00 | | | | | | | | | | | | | | | | | (87), (88), (89), (90), (91), (92), (93), (94), % 188.54/30.00 | | | | | | | | | | | | | | | | | (95), (97), (101), (125), (309) are inconsistent % 188.54/30.00 | | | | | | | | | | | | | | | | | by sub-proof #53. % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | (310) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.54/30.00 | | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.54/30.00 | | | | | | | | | | | | | | | | op(e2, e0) = e4) % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | BETA: splitting (310) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | (311) all_252_8 = e4 & op(e2, e2) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | ALPHA: (311) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | (312) all_252_8 = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | (313) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 188.54/30.00 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (52), (67), (116), (313) are % 188.54/30.00 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | (314) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 188.54/30.00 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 188.54/30.00 | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | (315) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | (316) op(e0, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (96), (316) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | | | | sub-proof #256. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | (317) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | BETA: splitting (317) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (318) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | ALPHA: (318) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (319) all_252_23 = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (320) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (15), (17), (32), (39), (43), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (46), (49), (55), (67), (82), (110), (287), (319), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (320) are inconsistent by sub-proof #124. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (321) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (321) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | (322) all_252_14 = e1 & op(e1, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | (323) all_252_14 = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | (324) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e2) = e3) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (324) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | (325) all_252_4 = e3 & op(e4, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (325) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | (326) all_252_4 = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (15), (36), (56), (60), (64), (71), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | (73), (85), (95), (312), (323), (326) are % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #154. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | (327) all_252_5 = e3 & op(e3, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (95), (327) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | #217. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | (328) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e2) = e3) | (all_252_22 = e3 & % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e3) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (328) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | (329) all_252_8 = e3 & op(e2, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (312), (329) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | #140. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | (330) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e2) = e3) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (330) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | (331) all_252_14 = e3 & op(e1, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (331) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | (332) all_252_14 = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (323), (332) are inconsistent by sub-proof % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | #179. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | (333) all_252_22 = e3 & op(e0, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | (334) op(e0, e2) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (28), (334) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #328. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | (335) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (30), (72), (83), (86), (97), (305), (335) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #122. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (336) all_252_24 = e1 & op(e0, e0) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | ALPHA: (336) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (337) op(e0, e0) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (114), (337) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | sub-proof #474. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | (338) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 188.54/30.00 | | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | BETA: splitting (338) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | (339) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (18), (21), % 188.54/30.00 | | | | | | | | | | | | | | | | | | (25), (28), (29), (32), (34), (37), (39), (40), % 188.54/30.00 | | | | | | | | | | | | | | | | | | (43), (46), (49), (50), (52), (54), (55), (62), % 188.54/30.00 | | | | | | | | | | | | | | | | | | (64), (67), (71), (75), (82), (83), (85), (96), % 188.54/30.00 | | | | | | | | | | | | | | | | | | (110), (114), (116), (120), (121), (339) are % 188.54/30.00 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #67. % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | (340) all_252_18 = e4 & op(e2, e0) = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | ALPHA: (340) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | (341) all_252_18 = e4 % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | (342) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (52), (67), (116), (342) are % 188.54/30.00 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | (343) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 188.54/30.00 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (344) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (345) op(e0, e2) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (96), (345) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | sub-proof #256. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | (346) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (347) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (348) all_252_23 = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (13), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (15), (17), (18), (21), (23), (24), (25), (28), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (29), (30), (32), (34), (37), (38), (39), (40), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (42), (43), (46), (47), (49), (50), (52), (54), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (55), (57), (59), (62), (64), (66), (67), (70), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (71), (72), (74), (75), (80), (82), (83), (85), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (86), (87), (89), (90), (96), (97), (101), (110), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (120), (121), (122), (125), (287), (305), (341), % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (348) are inconsistent by sub-proof #38. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (349) all_252_24 = e1 & op(e0, e0) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies: % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | (350) op(e0, e0) = e1 % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (114), (350) are inconsistent by % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | sub-proof #474. % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | End of split % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | Case 2: % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | (351) all_252_23 = e3 & op(e0, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.00 | | | | | | | | | | | | | | | ALPHA: (351) implies: % 188.54/30.00 | | | | | | | | | | | | | | | (352) op(e0, e1) = e3 % 188.54/30.00 | | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | | REF_CLOSE: (6), (37), (40), (352) are inconsistent by % 188.54/30.01 | | | | | | | | | | | | | | | sub-proof #508. % 188.54/30.01 | | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | (353) all_252_21 = e2 & op(e0, e3) = e2 % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | REF_CLOSE: (6), (44), (67), (353) are inconsistent by % 188.54/30.01 | | | | | | | | | | | | sub-proof #289. % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | (354) all_252_10 = e4 & op(e3, e1) = e4 % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | REF_CLOSE: (25), (59), (354) are inconsistent by sub-proof % 188.54/30.01 | | | | | | | | | #37. % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | End of split % 188.54/30.01 | | | | | | | | % 188.54/30.01 | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | % 188.54/30.01 | | | | | | | | (355) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 % 188.54/30.01 | | | | | | | | & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = % 188.54/30.01 | | | | | | | | e4) % 188.54/30.01 | | | | | | | | % 188.54/30.01 | | | | | | | | BETA: splitting (355) gives: % 188.54/30.01 | | | | | | | | % 188.54/30.01 | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | (356) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (18), (21), % 188.54/30.01 | | | | | | | | | (25), (28), (29), (32), (34), (37), (39), (40), % 188.54/30.01 | | | | | | | | | (43), (46), (49), (50), (52), (54), (55), (62), % 188.54/30.01 | | | | | | | | | (64), (67), (71), (75), (82), (83), (85), (96), % 188.54/30.01 | | | | | | | | | (110), (114), (116), (120), (121), (356) are % 188.54/30.01 | | | | | | | | | inconsistent by sub-proof #67. % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | (357) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = % 188.54/30.01 | | | | | | | | | e4 & op(e0, e1) = e4) % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | BETA: splitting (357) gives: % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | (358) all_252_15 = e4 & op(e1, e1) = e4 % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | ALPHA: (358) implies: % 188.54/30.01 | | | | | | | | | | (359) all_252_15 = e4 % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | BETA: splitting (18) gives: % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | (360) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 188.54/30.01 | | | | | | | | | | | e3 & op(e3, e1) = e3) % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | BETA: splitting (360) gives: % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | (361) all_252_9 = e3 & op(e4, e1) = e3 % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | REF_CLOSE: (6), (54), (121), (361) are inconsistent by % 188.54/30.01 | | | | | | | | | | | | sub-proof #275. % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | (362) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | REF_CLOSE: (54), (59), (362) are inconsistent by sub-proof % 188.54/30.01 | | | | | | | | | | | | #59. % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | (363) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 188.54/30.01 | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 188.54/30.01 | | | | | | | | | | | op(e0, e1) = e3) % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | BETA: splitting (363) gives: % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | (364) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | ALPHA: (364) implies: % 188.54/30.01 | | | | | | | | | | | | (365) all_252_11 = e3 % 188.54/30.01 | | | | | | | | | | | | (366) op(e2, e1) = e3 % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | BETA: splitting (78) gives: % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | (367) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.54/30.01 | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | BETA: splitting (367) gives: % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | Case 1: % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | (368) all_252_6 = e4 & op(e2, e4) = e4 % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | ALPHA: (368) implies: % 188.54/30.01 | | | | | | | | | | | | | | (369) all_252_6 = e4 % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (15), (17), (25), % 188.54/30.01 | | | | | | | | | | | | | | (28), (30), (32), (39), (42), (43), (46), (47), % 188.54/30.01 | | | | | | | | | | | | | | (49), (52), (54), (55), (57), (64), (67), (70), % 188.54/30.01 | | | | | | | | | | | | | | (71), (72), (74), (75), (80), (82), (83), (85), % 188.54/30.01 | | | | | | | | | | | | | | (86), (87), (89), (90), (96), (97), (110), (114), % 188.54/30.01 | | | | | | | | | | | | | | (116), (359), (369) are inconsistent by sub-proof % 188.54/30.01 | | | | | | | | | | | | | | #79. % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | (370) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | | REF_CLOSE: (23), (25), (370) are inconsistent by sub-proof % 188.54/30.01 | | | | | | | | | | | | | | #165. % 188.54/30.01 | | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | (371) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.54/30.01 | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.54/30.01 | | | | | | | | | | | | | op(e2, e0) = e4) % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (15), (18), (21), % 188.54/30.01 | | | | | | | | | | | | | (25), (27), (28), (29), (32), (34), (37), (39), % 188.54/30.01 | | | | | | | | | | | | | (40), (42), (43), (45), (46), (48), (49), (50), % 188.54/30.01 | | | | | | | | | | | | | (52), (54), (55), (62), (64), (67), (69), (71), % 188.54/30.01 | | | | | | | | | | | | | (75), (82), (83), (85), (96), (101), (110), (114), % 188.54/30.01 | | | | | | | | | | | | | (116), (120), (121), (122), (365), (366), (371) % 188.54/30.01 | | | | | | | | | | | | | are inconsistent by sub-proof #42. % 188.54/30.01 | | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | (372) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 188.54/30.01 | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | | REF_CLOSE: (6), (28), (37), (40), (359), (372) are % 188.54/30.01 | | | | | | | | | | | | inconsistent by sub-proof #264. % 188.54/30.01 | | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | Case 2: % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | (373) all_252_23 = e4 & op(e0, e1) = e4 % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | ALPHA: (373) implies: % 188.54/30.01 | | | | | | | | | | (374) op(e0, e1) = e4 % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | | REF_CLOSE: (6), (40), (96), (122), (374) are inconsistent by % 188.54/30.01 | | | | | | | | | | sub-proof #401. % 188.54/30.01 | | | | | | | | | | % 188.54/30.01 | | | | | | | | | End of split % 188.54/30.01 | | | | | | | | | % 188.54/30.01 | | | | | | | | End of split % 188.54/30.01 | | | | | | | | % 188.54/30.01 | | | | | | | End of split % 188.54/30.01 | | | | | | | % 188.54/30.01 | | | | | | Case 2: % 188.54/30.01 | | | | | | | % 188.54/30.01 | | | | | | | (375) all_250_23 = e0 % 188.54/30.01 | | | | | | | % 188.54/30.01 | | | | | | | REF_CLOSE: (46), (82), (375) are inconsistent by sub-proof #486. % 188.54/30.01 | | | | | | | % 188.54/30.01 | | | | | | End of split % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | End of split % 188.54/30.01 | | | | | % 188.54/30.01 | | | | End of split % 188.54/30.01 | | | | % 188.54/30.01 | | | End of split % 188.54/30.01 | | | % 188.54/30.01 | | Case 2: % 188.54/30.01 | | | % 188.54/30.01 | | | (376) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, % 188.54/30.01 | | | e0) = e2) % 188.54/30.01 | | | % 188.54/30.01 | | | BETA: splitting (376) gives: % 188.54/30.01 | | | % 188.54/30.01 | | | Case 1: % 188.54/30.01 | | | | % 188.54/30.01 | | | | (377) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.01 | | | | % 188.54/30.01 | | | | ALPHA: (377) implies: % 188.54/30.01 | | | | (378) all_252_11 = e2 % 188.54/30.01 | | | | (379) op(e2, e1) = e2 % 188.54/30.01 | | | | % 188.54/30.01 | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (17), (18), (21), (24), (25), % 188.54/30.01 | | | | (28), (29), (30), (32), (34), (37), (38), (39), (40), (42), % 188.54/30.01 | | | | (43), (46), (47), (49), (50), (52), (54), (55), (57), (59), % 188.54/30.01 | | | | (62), (64), (66), (67), (71), (72), (74), (82), (85), (86), % 188.54/30.01 | | | | (90), (97), (378), (379) are inconsistent by sub-proof #56. % 188.54/30.01 | | | | % 188.54/30.01 | | | Case 2: % 188.54/30.01 | | | | % 188.54/30.01 | | | | (380) all_252_18 = e2 & op(e2, e0) = e2 % 188.54/30.01 | | | | % 188.54/30.01 | | | | REF_CLOSE: (6), (14), (72), (380) are inconsistent by sub-proof #76. % 188.54/30.01 | | | | % 188.54/30.01 | | | End of split % 188.54/30.01 | | | % 188.54/30.01 | | End of split % 188.54/30.01 | | % 188.54/30.01 | End of split % 188.54/30.01 | % 188.54/30.01 End of proof % 188.54/30.01 % 188.54/30.01 Sub-proof #37 shows that the following formulas are inconsistent: % 188.54/30.01 ---------------------------------------------------------------- % 188.54/30.01 (1) all_252_10 = e4 & op(e3, e1) = e4 % 188.54/30.01 (2) all_252_10 = e0 % 188.54/30.01 (3) ~ (e4 = e0) % 188.54/30.01 % 188.54/30.01 Begin of proof % 188.54/30.01 | % 188.54/30.01 | ALPHA: (1) implies: % 188.54/30.01 | (4) all_252_10 = e4 % 188.54/30.01 | % 188.54/30.01 | COMBINE_EQS: (2), (4) imply: % 188.54/30.01 | (5) e4 = e0 % 188.54/30.01 | % 188.54/30.01 | SIMP: (5) implies: % 188.54/30.01 | (6) e4 = e0 % 188.54/30.01 | % 188.54/30.01 | REDUCE: (3), (6) imply: % 188.54/30.01 | (7) $false % 188.54/30.01 | % 188.54/30.01 | CLOSE: (7) is inconsistent. % 188.54/30.01 | % 188.54/30.01 End of proof % 188.54/30.01 % 188.54/30.01 Sub-proof #38 shows that the following formulas are inconsistent: % 188.54/30.01 ---------------------------------------------------------------- % 188.54/30.01 (1) all_252_13 = e2 % 188.54/30.01 (2) all_252_20 = e2 % 188.54/30.01 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.01 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.01 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.01 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.01 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.01 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.01 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.01 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.01 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.01 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.01 (7) ~ (all_20_2 = e4) % 188.54/30.01 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.01 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.01 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.01 (9) op(e0, e2) = e4 % 188.54/30.01 (10) op(e3, e1) = all_36_2 % 188.54/30.01 (11) ~ (e2 = e1) % 188.54/30.01 (12) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.01 (13) all_252_12 = e0 % 188.54/30.01 (14) op(e4, e1) = e0 % 188.54/30.01 (15) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.01 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.01 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.01 (16) op(e2, e1) = e0 % 188.54/30.01 (17) all_252_15 = e3 % 188.54/30.01 (18) all_252_7 = e0 % 188.54/30.01 (19) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.01 all_250_23 = e0 % 188.54/30.01 (20) ~ (e4 = e0) % 188.54/30.01 (21) ~ (e4 = e3) % 188.54/30.01 (22) ~ (all_36_2 = e2) % 188.54/30.01 (23) ~ (all_40_2 = all_34_2) % 188.54/30.01 (24) ~ (all_244_24 = all_20_2) % 188.54/30.01 (25) all_252_8 = e2 % 188.54/30.01 (26) op(e1, e4) = e0 % 188.54/30.01 (27) all_252_23 = e1 % 188.54/30.01 (28) ~ (all_20_2 = e3) % 188.54/30.01 (29) op(all_20_2, e4) = e1 % 188.54/30.01 (30) op(e0, e0) = all_244_24 % 188.54/30.01 (31) op(e0, e1) = all_20_2 % 188.54/30.01 (32) all_252_19 = e4 % 188.54/30.01 (33) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.01 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.01 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.01 (34) ~ (all_20_2 = e0) % 188.54/30.01 (35) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.01 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.01 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.01 (36) ~ (all_20_2 = e2) % 188.54/30.01 (37) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.01 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.01 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.01 (38) op(e0, e4) = e2 % 188.54/30.01 (39) ~ (e3 = e0) % 188.54/30.01 (40) ~ (all_20_2 = all_8_1) % 188.54/30.01 (41) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.01 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.01 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.01 (42) all_252_10 = e0 % 188.54/30.01 (43) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.01 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.01 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.01 (44) ~ (e3 = e2) % 188.54/30.01 (45) op(e4, all_20_2) = e0 % 188.54/30.01 (46) op(e0, e3) = all_8_1 % 188.54/30.01 (47) op(e1, e4) = e1 % 188.54/30.01 (48) all_252_18 = e4 % 188.54/30.01 (49) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.01 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.01 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.01 (50) ~ (e4 = e2) % 188.54/30.01 (51) op(e2, e0) = all_40_2 % 188.54/30.01 (52) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.01 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.01 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.01 (53) ~ (e1 = e0) % 188.54/30.01 (54) op(e0, e4) = all_12_2 % 188.54/30.01 (55) all_250_23 = all_20_2 % 188.54/30.01 (56) ~ (e3 = e1) % 188.54/30.01 (57) ~ (e2 = e0) % 188.54/30.01 (58) op(e0, e1) = e1 % 188.54/30.01 (59) op(e1, e0) = all_34_2 % 188.54/30.01 (60) ~ (all_12_2 = e3) % 188.54/30.01 (61) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.01 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.01 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.01 (62) ~ (all_34_2 = e2) % 188.54/30.01 (63) all_252_9 = e4 % 188.54/30.01 (64) ~ (e4 = e1) % 188.54/30.01 (65) op(e2, e0) = e1 % 188.54/30.01 % 188.54/30.01 Begin of proof % 188.54/30.01 | % 188.54/30.01 | BETA: splitting (5) gives: % 188.54/30.01 | % 188.54/30.01 | Case 1: % 188.54/30.01 | | % 188.54/30.01 | | (66) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = % 188.54/30.01 | | e3) % 188.54/30.01 | | % 188.54/30.01 | | BETA: splitting (66) gives: % 188.54/30.01 | | % 188.54/30.01 | | Case 1: % 188.54/30.01 | | | % 188.54/30.01 | | | (67) all_252_6 = e3 & op(e2, e4) = e3 % 188.54/30.01 | | | % 188.54/30.01 | | | ALPHA: (67) implies: % 188.54/30.01 | | | (68) all_252_6 = e3 % 188.54/30.01 | | | % 188.54/30.01 | | | BETA: splitting (8) gives: % 188.54/30.01 | | | % 188.54/30.01 | | | Case 1: % 188.54/30.01 | | | | % 188.54/30.01 | | | | (69) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, % 188.54/30.01 | | | | e1) = e2) % 188.54/30.01 | | | | % 188.54/30.01 | | | | REF_CLOSE: (6), (10), (22), (50), (63), (69) are inconsistent by % 188.54/30.01 | | | | sub-proof #41. % 188.54/30.01 | | | | % 188.54/30.01 | | | Case 2: % 188.54/30.01 | | | | % 188.54/30.01 | | | | (70) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.01 | | | | e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.01 | | | | % 188.54/30.01 | | | | BETA: splitting (70) gives: % 188.54/30.01 | | | | % 188.54/30.01 | | | | Case 1: % 188.54/30.01 | | | | | % 188.54/30.01 | | | | | (71) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.01 | | | | | % 188.54/30.01 | | | | | ALPHA: (71) implies: % 188.54/30.01 | | | | | (72) all_252_11 = e2 % 188.54/30.01 | | | | | (73) op(e2, e1) = e2 % 188.54/30.01 | | | | | % 188.54/30.01 | | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (12), (13), (15), (16), % 188.54/30.01 | | | | | (17), (20), (21), (22), (23), (24), (26), (28), (29), (30), % 188.54/30.01 | | | | | (31), (33), (34), (36), (37), (38), (39), (40), (43), (44), % 188.54/30.01 | | | | | (45), (46), (50), (51), (52), (55), (57), (59), (65), (72), % 188.54/30.01 | | | | | (73) are inconsistent by sub-proof #119. % 188.54/30.01 | | | | | % 188.54/30.01 | | | | Case 2: % 188.54/30.01 | | | | | % 188.54/30.01 | | | | | (74) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.01 | | | | | op(e0, e1) = e2) % 188.54/30.01 | | | | | % 188.54/30.01 | | | | | BETA: splitting (74) gives: % 188.54/30.01 | | | | | % 188.54/30.01 | | | | | Case 1: % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | (75) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | ALPHA: (75) implies: % 188.54/30.01 | | | | | | (76) all_252_15 = e2 % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | COMBINE_EQS: (17), (76) imply: % 188.54/30.01 | | | | | | (77) e3 = e2 % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | SIMP: (77) implies: % 188.54/30.01 | | | | | | (78) e3 = e2 % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | COMBINE_EQS: (68), (78) imply: % 188.54/30.01 | | | | | | (79) all_252_6 = e2 % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | REF_CLOSE: (2), (3), (4), (6), (11), (13), (20), (21), (38), (39), % 188.54/30.01 | | | | | | (44), (49), (50), (53), (54), (56), (57), (60), (61), % 188.54/30.01 | | | | | | (64), (79) are inconsistent by sub-proof #223. % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | Case 2: % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | (80) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | | REF_CLOSE: (6), (31), (36), (80) are inconsistent by sub-proof #540. % 188.54/30.01 | | | | | | % 188.54/30.01 | | | | | End of split % 188.54/30.01 | | | | | % 188.54/30.01 | | | | End of split % 188.54/30.01 | | | | % 188.54/30.01 | | | End of split % 188.54/30.01 | | | % 188.54/30.01 | | Case 2: % 188.54/30.01 | | | % 188.54/30.01 | | | (81) all_252_7 = e3 & op(e2, e3) = e3 % 188.54/30.01 | | | % 188.54/30.01 | | | REF_CLOSE: (18), (39), (81) are inconsistent by sub-proof #358. % 188.54/30.01 | | | % 188.54/30.01 | | End of split % 188.54/30.01 | | % 188.54/30.01 | Case 2: % 188.54/30.01 | | % 188.54/30.01 | | (82) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = % 188.54/30.01 | | e3) | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.01 | | % 188.54/30.01 | | BETA: splitting (82) gives: % 188.54/30.01 | | % 188.54/30.01 | | Case 1: % 188.54/30.01 | | | % 188.54/30.01 | | | (83) all_252_8 = e3 & op(e2, e2) = e3 % 188.54/30.01 | | | % 188.54/30.01 | | | REF_CLOSE: (25), (44), (83) are inconsistent by sub-proof #48. % 188.54/30.01 | | | % 188.54/30.01 | | Case 2: % 188.54/30.01 | | | % 188.54/30.01 | | | (84) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, % 188.54/30.01 | | | e0) = e3) % 188.54/30.01 | | | % 188.54/30.01 | | | BETA: splitting (84) gives: % 188.54/30.01 | | | % 188.54/30.01 | | | Case 1: % 188.54/30.01 | | | | % 188.54/30.01 | | | | (85) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.01 | | | | % 188.54/30.01 | | | | ALPHA: (85) implies: % 188.54/30.01 | | | | (86) all_252_11 = e3 % 188.54/30.01 | | | | % 188.54/30.01 | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 188.54/30.01 | | | | (15), (16), (19), (20), (21), (22), (23), (24), (26), (27), % 188.54/30.01 | | | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 188.54/30.01 | | | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), % 188.54/30.01 | | | | (50), (51), (52), (53), (55), (56), (57), (58), (59), (62), % 188.54/30.01 | | | | (63), (64), (65), (86) are inconsistent by sub-proof #39. % 188.54/30.01 | | | | % 188.54/30.01 | | | Case 2: % 188.54/30.01 | | | | % 188.54/30.01 | | | | (87) all_252_18 = e3 & op(e2, e0) = e3 % 188.54/30.01 | | | | % 188.54/30.01 | | | | REF_CLOSE: (21), (48), (87) are inconsistent by sub-proof #355. % 188.54/30.01 | | | | % 188.54/30.01 | | | End of split % 188.54/30.01 | | | % 188.54/30.01 | | End of split % 188.54/30.01 | | % 188.54/30.01 | End of split % 188.54/30.01 | % 188.54/30.01 End of proof % 188.54/30.01 % 188.54/30.01 Sub-proof #39 shows that the following formulas are inconsistent: % 188.54/30.01 ---------------------------------------------------------------- % 188.54/30.01 (1) all_252_13 = e2 % 188.54/30.01 (2) all_252_20 = e2 % 188.54/30.01 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.01 (4) ~ (all_20_2 = e4) % 188.54/30.01 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.01 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.01 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.01 (6) op(e0, e2) = e4 % 188.54/30.01 (7) op(e3, e1) = all_36_2 % 188.54/30.01 (8) ~ (e2 = e1) % 188.54/30.01 (9) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.01 (10) all_252_12 = e0 % 188.54/30.01 (11) op(e4, e1) = e0 % 188.54/30.01 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.01 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.01 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.01 (13) op(e2, e1) = e0 % 188.54/30.01 (14) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.01 all_250_23 = e0 % 188.54/30.01 (15) ~ (e4 = e0) % 188.54/30.01 (16) ~ (e4 = e3) % 188.54/30.01 (17) ~ (all_36_2 = e2) % 188.54/30.01 (18) ~ (all_40_2 = all_34_2) % 188.54/30.01 (19) ~ (all_244_24 = all_20_2) % 188.54/30.01 (20) op(e1, e4) = e0 % 188.54/30.01 (21) all_252_23 = e1 % 188.54/30.01 (22) ~ (all_20_2 = e3) % 188.54/30.01 (23) op(all_20_2, e4) = e1 % 188.54/30.01 (24) op(e0, e0) = all_244_24 % 188.54/30.01 (25) op(e0, e1) = all_20_2 % 188.54/30.01 (26) all_252_19 = e4 % 188.54/30.01 (27) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.01 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.01 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.01 (28) ~ (all_20_2 = e0) % 188.54/30.01 (29) all_252_11 = e3 % 188.54/30.01 (30) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.01 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.01 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.01 (31) ~ (all_20_2 = e2) % 188.54/30.01 (32) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.01 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.01 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.02 (33) op(e0, e4) = e2 % 188.54/30.02 (34) ~ (e3 = e0) % 188.54/30.02 (35) ~ (all_20_2 = all_8_1) % 188.54/30.02 (36) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.02 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.02 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.02 (37) all_252_10 = e0 % 188.54/30.02 (38) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.02 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.02 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.02 (39) ~ (e3 = e2) % 188.54/30.02 (40) op(e4, all_20_2) = e0 % 188.54/30.02 (41) op(e0, e3) = all_8_1 % 188.54/30.02 (42) op(e1, e4) = e1 % 188.54/30.02 (43) ~ (e4 = e2) % 188.54/30.02 (44) op(e2, e0) = all_40_2 % 188.54/30.02 (45) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.02 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.02 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.02 (46) ~ (e1 = e0) % 188.54/30.02 (47) all_250_23 = all_20_2 % 188.54/30.02 (48) ~ (e3 = e1) % 188.54/30.02 (49) ~ (e2 = e0) % 188.54/30.02 (50) op(e0, e1) = e1 % 188.54/30.02 (51) op(e1, e0) = all_34_2 % 188.54/30.02 (52) ~ (all_34_2 = e2) % 188.54/30.02 (53) all_252_9 = e4 % 188.54/30.02 (54) ~ (e4 = e1) % 188.54/30.02 (55) op(e2, e0) = e1 % 188.54/30.02 % 188.54/30.02 Begin of proof % 188.54/30.02 | % 188.54/30.02 | BETA: splitting (45) gives: % 188.54/30.02 | % 188.54/30.02 | Case 1: % 188.54/30.02 | | % 188.54/30.02 | | (56) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 188.54/30.02 | | = e1) % 188.54/30.02 | | % 188.54/30.02 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (19), (21), (24), (27), % 188.54/30.02 | | (28), (31), (35), (41), (47), (56) are inconsistent by sub-proof % 188.54/30.02 | | #124. % 188.54/30.02 | | % 188.54/30.02 | Case 2: % 188.54/30.02 | | % 188.54/30.02 | | (57) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) % 188.54/30.02 | | = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.02 | | % 188.54/30.02 | | BETA: splitting (57) gives: % 188.54/30.02 | | % 188.54/30.02 | | Case 1: % 188.54/30.02 | | | % 188.54/30.02 | | | (58) all_252_14 = e1 & op(e1, e2) = e1 % 188.54/30.02 | | | % 188.54/30.02 | | | ALPHA: (58) implies: % 188.54/30.02 | | | (59) all_252_14 = e1 % 188.54/30.02 | | | % 188.54/30.02 | | | BETA: splitting (36) gives: % 188.54/30.02 | | | % 188.54/30.02 | | | Case 1: % 188.54/30.02 | | | | % 188.54/30.02 | | | | (60) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, % 188.54/30.02 | | | | e3) = e3) % 188.54/30.02 | | | | % 188.54/30.02 | | | | BETA: splitting (60) gives: % 188.54/30.02 | | | | % 188.54/30.02 | | | | Case 1: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | (61) all_252_12 = e3 & op(e1, e4) = e3 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.02 | | | | | (15), (16), (17), (19), (20), (22), (24), (25), (27), (28), % 188.54/30.02 | | | | | (29), (31), (32), (34), (35), (38), (39), (41), (42), (43), % 188.54/30.02 | | | | | (46), (47), (48), (49), (50), (54), (61) are inconsistent % 188.54/30.02 | | | | | by sub-proof #70. % 188.54/30.02 | | | | | % 188.54/30.02 | | | | Case 2: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | (62) all_252_13 = e3 & op(e1, e3) = e3 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | REF_CLOSE: (1), (39), (62) are inconsistent by sub-proof #109. % 188.54/30.02 | | | | | % 188.54/30.02 | | | | End of split % 188.54/30.02 | | | | % 188.54/30.02 | | | Case 2: % 188.54/30.02 | | | | % 188.54/30.02 | | | | (63) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.02 | | | | e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.02 | | | | % 188.54/30.02 | | | | BETA: splitting (63) gives: % 188.54/30.02 | | | | % 188.54/30.02 | | | | Case 1: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | (64) all_252_14 = e3 & op(e1, e2) = e3 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | ALPHA: (64) implies: % 188.54/30.02 | | | | | (65) all_252_14 = e3 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | REF_CLOSE: (48), (59), (65) are inconsistent by sub-proof #179. % 188.54/30.02 | | | | | % 188.54/30.02 | | | | Case 2: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | (66) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 188.54/30.02 | | | | | op(e1, e0) = e3) % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | BETA: splitting (66) gives: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | Case 1: % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | | (67) all_252_15 = e3 & op(e1, e1) = e3 % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | | ALPHA: (67) implies: % 188.54/30.02 | | | | | | (68) all_252_15 = e3 % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | | BETA: splitting (5) gives: % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | | Case 1: % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | | (69) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & % 188.54/30.02 | | | | | | | op(e3, e1) = e2) % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | | REF_CLOSE: (3), (7), (17), (43), (53), (69) are inconsistent by % 188.54/30.02 | | | | | | | sub-proof #41. % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | Case 2: % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | | (70) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & % 188.54/30.02 | | | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | | BETA: splitting (70) gives: % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | | Case 1: % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | | (71) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | | ALPHA: (71) implies: % 188.54/30.02 | | | | | | | | (72) all_252_11 = e2 % 188.54/30.02 | | | | | | | | (73) op(e2, e1) = e2 % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), % 188.54/30.02 | | | | | | | | (13), (15), (16), (17), (18), (19), (20), (22), (23), % 188.54/30.02 | | | | | | | | (24), (25), (27), (28), (31), (32), (33), (34), (35), % 188.54/30.02 | | | | | | | | (38), (39), (40), (41), (43), (44), (45), (47), (49), % 188.54/30.02 | | | | | | | | (51), (55), (68), (72), (73) are inconsistent by % 188.54/30.02 | | | | | | | | sub-proof #119. % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | Case 2: % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | | (74) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.02 | | | | | | | | op(e0, e1) = e2) % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | | BETA: splitting (74) gives: % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | | Case 1: % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | | (75) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | | ALPHA: (75) implies: % 188.54/30.02 | | | | | | | | | (76) all_252_15 = e2 % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | | BETA: splitting (36) gives: % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | | Case 1: % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | (77) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = % 188.54/30.02 | | | | | | | | | | e3 & op(e1, e3) = e3) % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.02 | | | | | | | | | | (11), (12), (15), (16), (17), (19), (20), (22), % 188.54/30.02 | | | | | | | | | | (24), (25), (27), (28), (29), (31), (32), (34), % 188.54/30.02 | | | | | | | | | | (35), (38), (39), (41), (42), (43), (46), (47), % 188.54/30.02 | | | | | | | | | | (48), (49), (50), (54), (77) are inconsistent by % 188.54/30.02 | | | | | | | | | | sub-proof #108. % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | Case 2: % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | BETA: splitting (63) gives: % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | Case 1: % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | (78) all_252_14 = e3 & op(e1, e2) = e3 % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | REF_CLOSE: (48), (59), (78) are inconsistent by sub-proof % 188.54/30.02 | | | | | | | | | | | #99. % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | Case 2: % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | BETA: splitting (66) gives: % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | Case 1: % 188.54/30.02 | | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | | REF_CLOSE: (39), (67), (76) are inconsistent by sub-proof % 188.54/30.02 | | | | | | | | | | | | #188. % 188.54/30.02 | | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | Case 2: % 188.54/30.02 | | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | | (79) all_252_19 = e3 & op(e1, e0) = e3 % 188.54/30.02 | | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | | REF_CLOSE: (16), (26), (79) are inconsistent by sub-proof % 188.54/30.02 | | | | | | | | | | | | #243. % 188.54/30.02 | | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | | End of split % 188.54/30.02 | | | | | | | | | | | % 188.54/30.02 | | | | | | | | | | End of split % 188.54/30.02 | | | | | | | | | | % 188.54/30.02 | | | | | | | | | End of split % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | Case 2: % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | | (80) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | | REF_CLOSE: (3), (25), (31), (80) are inconsistent by sub-proof % 188.54/30.02 | | | | | | | | | #540. % 188.54/30.02 | | | | | | | | | % 188.54/30.02 | | | | | | | | End of split % 188.54/30.02 | | | | | | | | % 188.54/30.02 | | | | | | | End of split % 188.54/30.02 | | | | | | | % 188.54/30.02 | | | | | | End of split % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | Case 2: % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | | (81) all_252_19 = e3 & op(e1, e0) = e3 % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | | REF_CLOSE: (16), (26), (81) are inconsistent by sub-proof #177. % 188.54/30.02 | | | | | | % 188.54/30.02 | | | | | End of split % 188.54/30.02 | | | | | % 188.54/30.02 | | | | End of split % 188.54/30.02 | | | | % 188.54/30.02 | | | End of split % 188.54/30.02 | | | % 188.54/30.02 | | Case 2: % 188.54/30.02 | | | % 188.54/30.02 | | | (82) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.02 | | | e0) = e1) % 188.54/30.02 | | | % 188.54/30.02 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14), % 188.54/30.02 | | | (15), (16), (17), (18), (19), (20), (22), (23), (24), (25), % 188.54/30.02 | | | (26), (27), (28), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.02 | | | (37), (38), (39), (40), (41), (43), (44), (45), (47), (49), % 188.54/30.02 | | | (51), (52), (53), (55), (82) are inconsistent by sub-proof #40. % 188.54/30.02 | | | % 188.54/30.02 | | End of split % 188.54/30.02 | | % 188.54/30.02 | End of split % 188.54/30.02 | % 188.54/30.02 End of proof % 188.54/30.02 % 188.54/30.02 Sub-proof #40 shows that the following formulas are inconsistent: % 188.54/30.02 ---------------------------------------------------------------- % 188.54/30.02 (1) all_252_20 = e2 % 188.54/30.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.02 (3) ~ (all_20_2 = e4) % 188.54/30.02 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.02 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.02 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.02 (5) op(e0, e2) = e4 % 188.54/30.02 (6) op(e3, e1) = all_36_2 % 188.54/30.02 (7) ~ (e2 = e1) % 188.54/30.02 (8) all_252_12 = e0 % 188.54/30.02 (9) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.02 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.02 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.02 (10) op(e2, e1) = e0 % 188.54/30.02 (11) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.02 all_250_23 = e0 % 188.54/30.02 (12) ~ (e4 = e0) % 188.54/30.02 (13) ~ (e4 = e3) % 188.54/30.02 (14) ~ (all_36_2 = e2) % 188.54/30.02 (15) ~ (all_40_2 = all_34_2) % 188.54/30.02 (16) ~ (all_244_24 = all_20_2) % 188.54/30.02 (17) op(e1, e4) = e0 % 188.54/30.02 (18) ~ (all_20_2 = e3) % 188.54/30.02 (19) op(all_20_2, e4) = e1 % 188.54/30.02 (20) op(e0, e0) = all_244_24 % 188.54/30.02 (21) op(e0, e1) = all_20_2 % 188.54/30.02 (22) all_252_19 = e4 % 188.54/30.02 (23) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.02 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.02 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.02 (24) ~ (all_20_2 = e0) % 188.54/30.02 (25) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.02 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.02 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.02 (26) ~ (all_20_2 = e2) % 188.54/30.02 (27) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.02 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.02 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.02 (28) op(e0, e4) = e2 % 188.54/30.02 (29) ~ (e3 = e0) % 188.54/30.02 (30) ~ (all_20_2 = all_8_1) % 188.54/30.02 (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.02 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.02 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.02 (32) all_252_10 = e0 % 188.54/30.02 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.02 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.02 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.02 (34) ~ (e3 = e2) % 188.54/30.02 (35) op(e4, all_20_2) = e0 % 188.54/30.02 (36) op(e0, e3) = all_8_1 % 188.54/30.02 (37) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = % 188.54/30.02 e1) % 188.54/30.02 (38) ~ (e4 = e2) % 188.54/30.02 (39) op(e2, e0) = all_40_2 % 188.54/30.02 (40) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.02 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.02 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.02 (41) all_250_23 = all_20_2 % 188.54/30.02 (42) ~ (e2 = e0) % 188.54/30.02 (43) op(e1, e0) = all_34_2 % 188.54/30.02 (44) ~ (all_34_2 = e2) % 188.54/30.02 (45) all_252_9 = e4 % 188.54/30.02 (46) op(e2, e0) = e1 % 188.54/30.02 % 188.54/30.02 Begin of proof % 188.54/30.02 | % 188.54/30.02 | BETA: splitting (37) gives: % 188.54/30.02 | % 188.54/30.02 | Case 1: % 188.54/30.02 | | % 188.54/30.02 | | (47) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.02 | | % 188.54/30.02 | | ALPHA: (47) implies: % 188.54/30.02 | | (48) all_252_15 = e1 % 188.54/30.02 | | % 188.54/30.02 | | BETA: splitting (4) gives: % 188.54/30.02 | | % 188.54/30.02 | | Case 1: % 188.54/30.02 | | | % 188.54/30.02 | | | (49) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) % 188.54/30.02 | | | = e2) % 188.54/30.02 | | | % 188.54/30.02 | | | REF_CLOSE: (2), (6), (14), (38), (45), (49) are inconsistent by sub-proof % 188.54/30.02 | | | #198. % 188.54/30.02 | | | % 188.54/30.02 | | Case 2: % 188.54/30.02 | | | % 188.54/30.02 | | | (50) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.02 | | | e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.02 | | | % 188.54/30.02 | | | BETA: splitting (50) gives: % 188.54/30.02 | | | % 188.54/30.02 | | | Case 1: % 188.54/30.02 | | | | % 188.54/30.02 | | | | (51) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.02 | | | | % 188.54/30.02 | | | | ALPHA: (51) implies: % 188.54/30.02 | | | | (52) all_252_11 = e2 % 188.54/30.02 | | | | (53) op(e2, e1) = e2 % 188.54/30.02 | | | | % 188.54/30.02 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), % 188.54/30.02 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), % 188.54/30.02 | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), % 188.54/30.02 | | | | (33), (34), (35), (36), (38), (39), (40), (41), (42), (43), % 188.54/30.02 | | | | (44), (46), (52), (53) are inconsistent by sub-proof #56. % 188.54/30.02 | | | | % 188.54/30.02 | | | Case 2: % 188.54/30.02 | | | | % 188.54/30.02 | | | | (54) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, % 188.54/30.02 | | | | e1) = e2) % 188.54/30.02 | | | | % 188.54/30.02 | | | | BETA: splitting (54) gives: % 188.54/30.02 | | | | % 188.54/30.02 | | | | Case 1: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | (55) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | ALPHA: (55) implies: % 188.54/30.02 | | | | | (56) all_252_15 = e2 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | COMBINE_EQS: (48), (56) imply: % 188.54/30.02 | | | | | (57) e2 = e1 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | REDUCE: (7), (57) imply: % 188.54/30.02 | | | | | (58) $false % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | CLOSE: (58) is inconsistent. % 188.54/30.02 | | | | | % 188.54/30.02 | | | | Case 2: % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | (59) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.02 | | | | | % 188.54/30.02 | | | | | REF_CLOSE: (2), (21), (26), (59) are inconsistent by sub-proof #540. % 188.54/30.02 | | | | | % 188.54/30.02 | | | | End of split % 188.54/30.02 | | | | % 188.54/30.02 | | | End of split % 188.54/30.02 | | | % 188.54/30.02 | | End of split % 188.54/30.02 | | % 188.54/30.02 | Case 2: % 188.54/30.02 | | % 188.54/30.02 | | (60) all_252_19 = e1 & op(e1, e0) = e1 % 188.54/30.02 | | % 188.54/30.02 | | ALPHA: (60) implies: % 188.54/30.02 | | (61) op(e1, e0) = e1 % 188.54/30.02 | | % 188.54/30.02 | | REF_CLOSE: (2), (15), (39), (43), (46), (61) are inconsistent by sub-proof % 188.54/30.02 | | #352. % 188.54/30.02 | | % 188.54/30.02 | End of split % 188.54/30.02 | % 188.54/30.02 End of proof % 188.54/30.02 % 188.54/30.02 Sub-proof #41 shows that the following formulas are inconsistent: % 188.54/30.02 ---------------------------------------------------------------- % 188.54/30.02 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.02 (2) op(e3, e1) = all_36_2 % 188.54/30.02 (3) ~ (all_36_2 = e2) % 188.54/30.02 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.02 (5) ~ (e4 = e2) % 188.54/30.02 (6) all_252_9 = e4 % 188.54/30.02 % 188.54/30.02 Begin of proof % 188.54/30.02 | % 188.54/30.02 | BETA: splitting (4) gives: % 188.54/30.02 | % 188.54/30.02 | Case 1: % 188.54/30.02 | | % 188.54/30.02 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 188.54/30.02 | | % 188.54/30.02 | | ALPHA: (7) implies: % 188.54/30.02 | | (8) all_252_9 = e2 % 188.54/30.02 | | % 188.54/30.02 | | REF_CLOSE: (5), (6), (8) are inconsistent by sub-proof #196. % 188.54/30.02 | | % 188.54/30.02 | Case 2: % 188.54/30.02 | | % 188.54/30.02 | | (9) all_252_10 = e2 & op(e3, e1) = e2 % 188.54/30.02 | | % 188.54/30.02 | | ALPHA: (9) implies: % 188.54/30.02 | | (10) op(e3, e1) = e2 % 188.54/30.02 | | % 188.54/30.02 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #557. % 188.54/30.02 | | % 188.54/30.02 | End of split % 188.54/30.02 | % 188.54/30.02 End of proof % 188.54/30.02 % 188.54/30.02 Sub-proof #42 shows that the following formulas are inconsistent: % 188.54/30.02 ---------------------------------------------------------------- % 188.54/30.02 (1) all_252_20 = e2 % 188.54/30.02 (2) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = e4) % 188.54/30.02 | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.02 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.02 (4) ~ (all_20_2 = e4) % 188.54/30.02 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.02 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.02 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.02 (6) op(e0, e2) = e4 % 188.54/30.02 (7) op(e3, e1) = all_36_2 % 188.54/30.02 (8) ~ (e2 = e1) % 188.54/30.02 (9) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.02 (10) op(e4, e1) = e0 % 188.54/30.02 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.02 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.02 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.02 (12) op(e2, e1) = e0 % 188.54/30.02 (13) ~ (e4 = e0) % 188.54/30.02 (14) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.02 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.02 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.02 (15) ~ (e4 = e3) % 188.54/30.02 (16) ~ (all_36_2 = e2) % 188.54/30.02 (17) ~ (all_244_24 = all_20_2) % 188.54/30.02 (18) all_252_8 = e2 % 188.54/30.02 (19) op(e1, e4) = e0 % 188.54/30.02 (20) ~ (all_20_2 = e3) % 188.54/30.02 (21) op(e0, e0) = all_244_24 % 188.54/30.02 (22) op(e0, e1) = all_20_2 % 188.54/30.02 (23) all_252_19 = e4 % 188.54/30.02 (24) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.02 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.02 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.02 (25) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.02 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.02 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.02 (26) ~ (all_20_2 = e0) % 188.54/30.02 (27) all_252_11 = e3 % 188.54/30.02 (28) all_252_17 = e2 % 188.54/30.02 (29) ~ (all_20_2 = e2) % 188.54/30.02 (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.02 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.02 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.02 (31) op(e2, e1) = e3 % 188.54/30.02 (32) op(e0, e4) = e2 % 188.54/30.02 (33) ~ (e3 = e0) % 188.54/30.02 (34) ~ (all_20_2 = all_8_1) % 188.54/30.02 (35) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.02 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.02 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.02 (36) ~ (e3 = e2) % 188.54/30.02 (37) op(e0, e3) = all_8_1 % 188.54/30.02 (38) op(e1, e4) = e1 % 188.54/30.02 (39) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.02 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.02 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.02 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.02 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.02 op(e0, e1) = e0))) % 188.54/30.02 (40) ~ (e4 = e2) % 188.54/30.02 (41) ~ (e1 = e0) % 188.54/30.02 (42) all_250_23 = all_20_2 % 188.54/30.02 (43) ~ (e3 = e1) % 188.54/30.02 (44) ~ (e2 = e0) % 188.54/30.02 (45) op(e0, e1) = e1 % 188.54/30.02 (46) ~ (all_244_24 = e1) % 188.54/30.02 (47) ~ (all_8_1 = e1) % 188.54/30.02 (48) ~ (e4 = e1) % 188.54/30.02 % 188.54/30.02 Begin of proof % 188.54/30.02 | % 188.54/30.02 | BETA: splitting (2) gives: % 188.54/30.02 | % 188.54/30.02 | Case 1: % 188.54/30.02 | | % 188.54/30.02 | | (49) all_252_8 = e4 & op(e2, e2) = e4 % 188.54/30.02 | | % 188.54/30.02 | | ALPHA: (49) implies: % 188.54/30.02 | | (50) all_252_8 = e4 % 188.54/30.02 | | % 188.54/30.02 | | REF_CLOSE: (18), (40), (50) are inconsistent by sub-proof #163. % 188.54/30.02 | | % 188.54/30.02 | Case 2: % 188.54/30.02 | | % 188.54/30.02 | | (51) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) % 188.54/30.02 | | = e4) % 188.54/30.02 | | % 188.54/30.02 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 188.54/30.02 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), (25), % 188.54/30.02 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.02 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), % 188.54/30.02 | | (48), (51) are inconsistent by sub-proof #43. % 188.54/30.02 | | % 188.54/30.02 | End of split % 188.54/30.02 | % 188.54/30.02 End of proof % 188.54/30.02 % 188.54/30.02 Sub-proof #43 shows that the following formulas are inconsistent: % 188.54/30.02 ---------------------------------------------------------------- % 188.54/30.02 (1) all_252_20 = e2 % 188.54/30.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.02 (3) ~ (all_20_2 = e4) % 188.54/30.02 (4) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.02 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.02 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.02 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.02 (6) op(e0, e2) = e4 % 188.54/30.02 (7) op(e3, e1) = all_36_2 % 188.54/30.02 (8) ~ (e2 = e1) % 188.54/30.03 (9) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.03 (10) op(e4, e1) = e0 % 188.54/30.03 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.03 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.03 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.03 (12) op(e2, e1) = e0 % 188.54/30.03 (13) ~ (e4 = e0) % 188.54/30.03 (14) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.03 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.03 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.03 (15) ~ (e4 = e3) % 188.54/30.03 (16) ~ (all_36_2 = e2) % 188.54/30.03 (17) ~ (all_244_24 = all_20_2) % 188.54/30.03 (18) op(e1, e4) = e0 % 188.54/30.03 (19) ~ (all_20_2 = e3) % 188.54/30.03 (20) op(e0, e0) = all_244_24 % 188.54/30.03 (21) op(e0, e1) = all_20_2 % 188.54/30.03 (22) all_252_19 = e4 % 188.54/30.03 (23) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.03 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.03 (24) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.03 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.03 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.03 (25) ~ (all_20_2 = e0) % 188.54/30.03 (26) all_252_11 = e3 % 188.54/30.03 (27) all_252_17 = e2 % 188.54/30.03 (28) ~ (all_20_2 = e2) % 188.54/30.03 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.03 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.03 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.03 (30) op(e2, e1) = e3 % 188.54/30.03 (31) op(e0, e4) = e2 % 188.54/30.03 (32) ~ (e3 = e0) % 188.54/30.03 (33) ~ (all_20_2 = all_8_1) % 188.54/30.03 (34) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.03 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.03 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.03 (35) ~ (e3 = e2) % 188.54/30.03 (36) op(e0, e3) = all_8_1 % 188.54/30.03 (37) op(e1, e4) = e1 % 188.54/30.03 (38) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.03 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.03 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.03 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.03 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.03 op(e0, e1) = e0))) % 188.54/30.03 (39) ~ (e4 = e2) % 188.54/30.03 (40) ~ (e1 = e0) % 188.54/30.03 (41) all_250_23 = all_20_2 % 188.54/30.03 (42) ~ (e3 = e1) % 188.54/30.03 (43) ~ (e2 = e0) % 188.54/30.03 (44) op(e0, e1) = e1 % 188.54/30.03 (45) ~ (all_244_24 = e1) % 188.54/30.03 (46) ~ (all_8_1 = e1) % 188.54/30.03 (47) ~ (e4 = e1) % 188.54/30.03 % 188.54/30.03 Begin of proof % 188.54/30.03 | % 188.54/30.03 | BETA: splitting (4) gives: % 188.54/30.03 | % 188.54/30.03 | Case 1: % 188.54/30.03 | | % 188.54/30.03 | | (48) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.03 | | % 188.54/30.03 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 188.54/30.03 | | (15), (16), (17), (18), (19), (20), (21), (23), (25), (28), (29), % 188.54/30.03 | | (31), (32), (33), (34), (35), (36), (37), (39), (40), (41), (42), % 188.54/30.03 | | (43), (45), (46), (47), (48) are inconsistent by sub-proof #67. % 188.54/30.03 | | % 188.54/30.03 | Case 2: % 188.54/30.03 | | % 188.54/30.03 | | (49) all_252_18 = e4 & op(e2, e0) = e4 % 188.54/30.03 | | % 188.54/30.03 | | ALPHA: (49) implies: % 188.54/30.03 | | (50) all_252_18 = e4 % 188.54/30.03 | | % 188.54/30.03 | | BETA: splitting (24) gives: % 188.54/30.03 | | % 188.54/30.03 | | Case 1: % 188.54/30.03 | | | % 188.54/30.03 | | | (51) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, % 188.54/30.03 | | | e0) = e3) % 188.54/30.03 | | | % 188.54/30.03 | | | BETA: splitting (51) gives: % 188.54/30.03 | | | % 188.54/30.03 | | | Case 1: % 188.54/30.03 | | | | % 188.54/30.03 | | | | (52) all_252_16 = e3 & op(e4, e0) = e3 % 188.54/30.03 | | | | % 188.54/30.03 | | | | REF_CLOSE: (2), (8), (13), (14), (22), (27), (32), (38), (40), (42), % 188.54/30.03 | | | | (43), (47), (50), (52) are inconsistent by sub-proof #160. % 188.54/30.03 | | | | % 188.54/30.03 | | | Case 2: % 188.54/30.03 | | | | % 188.54/30.03 | | | | (53) all_252_17 = e3 & op(e3, e0) = e3 % 188.54/30.03 | | | | % 188.54/30.03 | | | | REF_CLOSE: (27), (35), (53) are inconsistent by sub-proof #249. % 188.54/30.03 | | | | % 188.54/30.03 | | | End of split % 188.54/30.03 | | | % 188.54/30.03 | | Case 2: % 188.54/30.03 | | | % 188.54/30.03 | | | (54) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.03 | | | e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.03 | | | % 188.54/30.03 | | | BETA: splitting (54) gives: % 188.54/30.03 | | | % 188.54/30.03 | | | Case 1: % 188.54/30.03 | | | | % 188.54/30.03 | | | | (55) all_252_18 = e3 & op(e2, e0) = e3 % 188.54/30.03 | | | | % 188.54/30.03 | | | | REF_CLOSE: (15), (50), (55) are inconsistent by sub-proof #355. % 188.54/30.03 | | | | % 188.54/30.03 | | | Case 2: % 188.54/30.03 | | | | % 188.54/30.03 | | | | (56) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, % 188.54/30.03 | | | | e0) = e3) % 188.54/30.03 | | | | % 188.54/30.03 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.03 | | | | (13), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 188.54/30.03 | | | | (25), (26), (28), (29), (30), (31), (32), (33), (34), (35), % 188.54/30.03 | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 188.54/30.03 | | | | (47), (56) are inconsistent by sub-proof #44. % 188.54/30.03 | | | | % 188.54/30.03 | | | End of split % 188.54/30.03 | | | % 188.54/30.03 | | End of split % 188.54/30.03 | | % 188.54/30.03 | End of split % 188.54/30.03 | % 188.54/30.03 End of proof % 188.54/30.03 % 188.54/30.03 Sub-proof #44 shows that the following formulas are inconsistent: % 188.54/30.03 ---------------------------------------------------------------- % 188.54/30.03 (1) all_252_20 = e2 % 188.54/30.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.03 (3) ~ (all_20_2 = e4) % 188.54/30.03 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.03 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.03 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.03 (5) op(e0, e2) = e4 % 188.54/30.03 (6) op(e3, e1) = all_36_2 % 188.54/30.03 (7) ~ (e2 = e1) % 188.54/30.03 (8) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.03 (9) op(e4, e1) = e0 % 188.54/30.03 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.03 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.03 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.03 (11) op(e2, e1) = e0 % 188.54/30.03 (12) ~ (e4 = e0) % 188.54/30.03 (13) ~ (e4 = e3) % 188.54/30.03 (14) ~ (all_36_2 = e2) % 188.54/30.03 (15) ~ (all_244_24 = all_20_2) % 188.54/30.03 (16) op(e1, e4) = e0 % 188.54/30.03 (17) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = % 188.54/30.03 e3) % 188.54/30.03 (18) ~ (all_20_2 = e3) % 188.54/30.03 (19) op(e0, e0) = all_244_24 % 188.54/30.03 (20) op(e0, e1) = all_20_2 % 188.54/30.03 (21) all_252_19 = e4 % 188.54/30.03 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.03 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.03 (23) ~ (all_20_2 = e0) % 188.54/30.03 (24) all_252_11 = e3 % 188.54/30.03 (25) ~ (all_20_2 = e2) % 188.54/30.03 (26) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.03 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.03 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.03 (27) op(e2, e1) = e3 % 188.54/30.03 (28) op(e0, e4) = e2 % 188.54/30.03 (29) ~ (e3 = e0) % 188.54/30.03 (30) ~ (all_20_2 = all_8_1) % 188.54/30.03 (31) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.03 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.03 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.03 (32) ~ (e3 = e2) % 188.54/30.03 (33) op(e0, e3) = all_8_1 % 188.54/30.03 (34) op(e1, e4) = e1 % 188.54/30.03 (35) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.03 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.03 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.03 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.03 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.03 op(e0, e1) = e0))) % 188.54/30.03 (36) ~ (e4 = e2) % 188.54/30.03 (37) ~ (e1 = e0) % 188.54/30.03 (38) all_250_23 = all_20_2 % 188.54/30.03 (39) ~ (e3 = e1) % 188.54/30.03 (40) ~ (e2 = e0) % 188.54/30.03 (41) op(e0, e1) = e1 % 188.54/30.03 (42) ~ (all_244_24 = e1) % 188.54/30.03 (43) ~ (e4 = e1) % 188.54/30.03 % 188.54/30.03 Begin of proof % 188.54/30.03 | % 188.54/30.03 | BETA: splitting (17) gives: % 188.54/30.03 | % 188.54/30.03 | Case 1: % 188.54/30.03 | | % 188.54/30.03 | | (44) all_252_19 = e3 & op(e1, e0) = e3 % 188.54/30.03 | | % 188.54/30.03 | | REF_CLOSE: (13), (21), (44) are inconsistent by sub-proof #177. % 188.54/30.03 | | % 188.54/30.03 | Case 2: % 188.54/30.03 | | % 188.54/30.03 | | (45) all_252_24 = e3 & op(e0, e0) = e3 % 188.54/30.03 | | % 188.54/30.03 | | ALPHA: (45) implies: % 188.54/30.03 | | (46) all_252_24 = e3 % 188.54/30.03 | | % 188.54/30.03 | | BETA: splitting (35) gives: % 188.54/30.03 | | % 188.54/30.03 | | Case 1: % 188.54/30.03 | | | % 188.54/30.03 | | | (47) all_252_24 = e0 & op(e0, e0) = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | ALPHA: (47) implies: % 188.54/30.03 | | | (48) all_252_24 = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | COMBINE_EQS: (46), (48) imply: % 188.54/30.03 | | | (49) e3 = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | COMBINE_EQS: (24), (49) imply: % 188.54/30.03 | | | (50) all_252_11 = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), % 188.54/30.03 | | | (14), (15), (16), (18), (19), (20), (22), (23), (25), (26), % 188.54/30.03 | | | (29), (30), (31), (32), (33), (34), (36), (37), (38), (39), % 188.54/30.03 | | | (40), (41), (43), (50) are inconsistent by sub-proof #191. % 188.54/30.03 | | | % 188.54/30.03 | | Case 2: % 188.54/30.03 | | | % 188.54/30.03 | | | (51) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, % 188.54/30.03 | | | e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | % 188.54/30.03 | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 & % 188.54/30.03 | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 188.54/30.03 | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, % 188.54/30.03 | | | e1) = e0)) % 188.54/30.03 | | | % 188.54/30.03 | | | ALPHA: (51) implies: % 188.54/30.03 | | | (52) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, % 188.54/30.03 | | | e3) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 % 188.54/30.03 | | | = e0 & op(e0, e1) = e0) % 188.54/30.03 | | | % 188.54/30.03 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.03 | | | (13), (14), (15), (16), (18), (19), (20), (22), (23), (24), % 188.54/30.03 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 188.54/30.03 | | | (36), (37), (38), (39), (40), (42), (43), (52) are inconsistent % 188.54/30.03 | | | by sub-proof #45. % 188.54/30.03 | | | % 188.54/30.03 | | End of split % 188.54/30.03 | | % 188.54/30.03 | End of split % 188.54/30.03 | % 188.54/30.03 End of proof % 188.54/30.03 % 188.54/30.03 Sub-proof #45 shows that the following formulas are inconsistent: % 188.54/30.03 ---------------------------------------------------------------- % 188.54/30.03 (1) all_252_20 = e2 % 188.54/30.03 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.03 (3) ~ (all_20_2 = e4) % 188.54/30.03 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.03 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.03 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.03 (5) op(e0, e2) = e4 % 188.54/30.03 (6) op(e3, e1) = all_36_2 % 188.54/30.03 (7) ~ (e2 = e1) % 188.54/30.03 (8) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.03 (9) op(e4, e1) = e0 % 188.54/30.03 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.03 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.03 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.03 (11) op(e2, e1) = e0 % 188.54/30.03 (12) ~ (e4 = e0) % 188.54/30.03 (13) ~ (e4 = e3) % 188.54/30.03 (14) ~ (all_36_2 = e2) % 188.54/30.03 (15) ~ (all_244_24 = all_20_2) % 188.54/30.03 (16) op(e1, e4) = e0 % 188.54/30.03 (17) ~ (all_20_2 = e3) % 188.54/30.03 (18) op(e0, e0) = all_244_24 % 188.54/30.03 (19) op(e0, e1) = all_20_2 % 188.54/30.03 (20) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.03 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, % 188.54/30.03 e1) = e0) % 188.54/30.03 (21) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.03 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.03 (22) ~ (all_20_2 = e0) % 188.54/30.03 (23) all_252_11 = e3 % 188.54/30.03 (24) ~ (all_20_2 = e2) % 188.54/30.03 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.03 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.03 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.03 (26) op(e2, e1) = e3 % 188.54/30.03 (27) op(e0, e4) = e2 % 188.54/30.03 (28) ~ (e3 = e0) % 188.54/30.03 (29) ~ (all_20_2 = all_8_1) % 188.54/30.03 (30) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.03 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.03 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.03 (31) ~ (e3 = e2) % 188.54/30.03 (32) op(e0, e3) = all_8_1 % 188.54/30.03 (33) op(e1, e4) = e1 % 188.54/30.03 (34) ~ (e4 = e2) % 188.54/30.03 (35) ~ (e1 = e0) % 188.54/30.03 (36) all_250_23 = all_20_2 % 188.54/30.03 (37) ~ (e3 = e1) % 188.54/30.03 (38) ~ (e2 = e0) % 188.54/30.03 (39) ~ (all_244_24 = e1) % 188.54/30.03 (40) ~ (e4 = e1) % 188.54/30.03 % 188.54/30.03 Begin of proof % 188.54/30.03 | % 188.54/30.03 | BETA: splitting (20) gives: % 188.54/30.03 | % 188.54/30.03 | Case 1: % 188.54/30.03 | | % 188.54/30.03 | | (41) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 188.54/30.03 | | = e0) % 188.54/30.03 | | % 188.54/30.03 | | BETA: splitting (41) gives: % 188.54/30.03 | | % 188.54/30.03 | | Case 1: % 188.54/30.03 | | | % 188.54/30.03 | | | (42) all_252_20 = e0 & op(e0, e4) = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | REF_CLOSE: (2), (27), (38), (42) are inconsistent by sub-proof #255. % 188.54/30.03 | | | % 188.54/30.03 | | Case 2: % 188.54/30.03 | | | % 188.54/30.03 | | | (43) all_252_21 = e0 & op(e0, e3) = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | ALPHA: (43) implies: % 188.54/30.03 | | | (44) op(e0, e3) = e0 % 188.54/30.03 | | | % 188.54/30.03 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.03 | | | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), % 188.54/30.03 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 188.54/30.03 | | | (34), (35), (36), (37), (38), (39), (40), (44) are inconsistent % 188.54/30.03 | | | by sub-proof #189. % 188.54/30.03 | | | % 188.54/30.03 | | End of split % 188.54/30.03 | | % 188.54/30.03 | Case 2: % 188.54/30.03 | | % 188.54/30.03 | | (45) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 188.54/30.03 | | = e0) % 188.54/30.03 | | % 188.54/30.03 | | REF_CLOSE: (1), (2), (3), (5), (8), (12), (15), (18), (21), (22), (24), % 188.54/30.03 | | (29), (32), (36), (45) are inconsistent by sub-proof #136. % 188.54/30.03 | | % 188.54/30.03 | End of split % 188.54/30.03 | % 188.54/30.03 End of proof % 188.54/30.03 % 188.54/30.03 Sub-proof #46 shows that the following formulas are inconsistent: % 188.54/30.03 ---------------------------------------------------------------- % 188.54/30.03 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.54/30.03 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.54/30.03 (all_252_16 = e1 & op(e4, e0) = e1) % 188.54/30.03 (2) all_252_20 = e2 % 188.54/30.03 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.03 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.03 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.03 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.03 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.03 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.03 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.03 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.03 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.03 (7) ~ (all_20_2 = e4) % 188.54/30.03 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.03 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.03 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.03 (9) op(e0, e2) = e4 % 188.54/30.03 (10) op(e0, e2) = all_28_2 % 188.54/30.03 (11) op(e3, e1) = all_36_2 % 188.54/30.03 (12) all_252_12 = e0 % 188.54/30.03 (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.03 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.03 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.03 (14) op(e1, e3) = all_62_2 % 188.54/30.03 (15) op(e2, e1) = e0 % 188.54/30.03 (16) all_252_7 = e0 % 188.54/30.03 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.03 all_250_23 = e0 % 188.54/30.03 (18) ~ (e4 = e0) % 188.54/30.03 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.54/30.03 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.54/30.03 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.54/30.03 (20) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.03 (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.03 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.03 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.03 (22) ~ (e4 = e3) % 188.54/30.03 (23) ~ (all_36_2 = e2) % 188.54/30.03 (24) ~ (all_40_2 = all_34_2) % 188.54/30.03 (25) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.54/30.03 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.54/30.03 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.54/30.03 (26) ~ (all_244_24 = all_20_2) % 188.54/30.03 (27) all_252_8 = e2 % 188.54/30.03 (28) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.54/30.03 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.54/30.03 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.54/30.03 (29) op(e1, e4) = e0 % 188.54/30.03 (30) ~ (all_6_2 = e4) % 188.54/30.03 (31) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.54/30.03 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.54/30.03 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.54/30.03 (32) ~ (all_20_2 = e3) % 188.54/30.03 (33) op(all_20_2, e4) = e1 % 188.54/30.03 (34) op(e0, e0) = all_244_24 % 188.54/30.03 (35) op(e0, e1) = all_20_2 % 188.54/30.03 (36) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.03 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.03 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.03 (37) all_252_19 = e4 % 188.54/30.03 (38) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.03 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.03 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.03 (39) ~ (all_8_1 = e2) % 188.54/30.03 (40) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.03 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.03 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.03 (41) ~ (all_20_2 = e0) % 188.54/30.03 (42) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.03 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.03 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.03 (43) all_252_17 = e2 % 188.54/30.03 (44) ~ (all_20_2 = e2) % 188.54/30.03 (45) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.03 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.03 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.03 (46) op(e4, e4) = all_244_0 % 188.54/30.03 (47) op(e0, e4) = e2 % 188.54/30.03 (48) ~ (e3 = e0) % 188.54/30.03 (49) ~ (all_20_2 = all_8_1) % 188.54/30.03 (50) ~ (all_28_2 = e0) % 188.54/30.03 (51) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.03 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.03 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.03 (52) ~ (all_244_0 = e2) % 188.54/30.03 (53) op(e2, all_40_2) = e0 % 188.54/30.04 (54) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.04 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.04 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.54/30.04 (55) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.04 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.04 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.04 (56) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.54/30.04 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.04 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.54/30.04 (57) ~ (e3 = e2) % 188.54/30.04 (58) all_252_22 = e4 % 188.54/30.04 (59) op(e4, all_20_2) = e0 % 188.54/30.04 (60) op(e0, e3) = all_8_1 % 188.54/30.04 (61) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.04 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.04 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.04 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.04 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.04 op(e0, e1) = e0))) % 188.54/30.04 (62) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.04 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.04 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.04 (63) ~ (e4 = e2) % 188.54/30.04 (64) op(e2, e0) = all_40_2 % 188.54/30.04 (65) op(all_28_2, all_40_2) = e2 % 188.54/30.04 (66) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.04 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.04 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.04 (67) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.04 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.04 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.04 (68) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.54/30.04 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.54/30.04 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.04 (69) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.04 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.54/30.04 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.54/30.04 (70) op(e0, e4) = all_12_2 % 188.54/30.04 (71) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.54/30.04 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.54/30.04 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.54/30.04 (72) all_250_23 = all_20_2 % 188.54/30.04 (73) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.54/30.04 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.54/30.04 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.54/30.04 (74) ~ (e2 = e0) % 188.54/30.04 (75) op(e1, e0) = all_34_2 % 188.54/30.04 (76) ~ (all_12_2 = e3) % 188.54/30.04 (77) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.04 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.04 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.54/30.04 (78) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.04 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.04 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.04 (79) ~ (all_34_2 = e2) % 188.54/30.04 (80) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.04 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.04 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.04 (81) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.04 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.04 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.04 (82) op(e4, e2) = all_6_2 % 188.54/30.04 (83) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.54/30.04 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.54/30.04 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.54/30.04 (84) all_252_5 = e0 % 188.54/30.04 (85) all_252_9 = e4 % 188.54/30.04 (86) op(e2, e0) = e1 % 188.54/30.04 % 188.54/30.04 Begin of proof % 188.54/30.04 | % 188.54/30.04 | ALPHA: (20) implies: % 188.54/30.04 | (87) all_252_7 = e4 % 188.54/30.04 | % 188.54/30.04 | COMBINE_EQS: (16), (87) imply: % 188.54/30.04 | (88) e4 = e0 % 188.54/30.04 | % 188.54/30.04 | COMBINE_EQS: (85), (88) imply: % 188.54/30.04 | (89) all_252_9 = e0 % 188.54/30.04 | % 188.54/30.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.04 | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), % 188.54/30.04 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 188.54/30.04 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.04 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 188.54/30.04 | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 188.54/30.04 | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 188.54/30.04 | (80), (81), (82), (83), (84), (86), (89) are inconsistent by % 188.54/30.04 | sub-proof #77. % 188.54/30.04 | % 188.54/30.04 End of proof % 188.54/30.04 % 188.54/30.04 Sub-proof #47 shows that the following formulas are inconsistent: % 188.54/30.04 ---------------------------------------------------------------- % 188.54/30.04 (1) all_252_20 = e2 % 188.54/30.04 (2) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.04 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.04 (4) ~ (all_20_2 = e4) % 188.54/30.04 (5) op(e0, e2) = e4 % 188.54/30.04 (6) ~ (e4 = e0) % 188.54/30.04 (7) ~ (e4 = e3) % 188.54/30.04 (8) ~ (all_244_24 = all_20_2) % 188.54/30.04 (9) all_252_21 = e4 & op(e0, e3) = e4 % 188.54/30.04 (10) ~ (all_20_2 = e3) % 188.54/30.04 (11) op(e0, e0) = all_244_24 % 188.54/30.04 (12) op(e0, e1) = all_20_2 % 188.54/30.04 (13) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.04 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.04 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.04 (14) ~ (all_20_2 = e0) % 188.54/30.04 (15) ~ (all_20_2 = e2) % 188.54/30.04 (16) op(e0, e4) = e2 % 188.54/30.04 (17) ~ (e3 = e0) % 188.54/30.04 (18) ~ (all_20_2 = all_8_1) % 188.54/30.04 (19) op(e0, e3) = all_8_1 % 188.54/30.04 (20) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.04 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.04 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.04 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.04 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.04 op(e0, e1) = e0))) % 188.54/30.04 (21) op(e0, e4) = all_12_2 % 188.54/30.04 (22) all_250_23 = all_20_2 % 188.54/30.04 (23) ~ (e2 = e0) % 188.54/30.04 (24) ~ (all_12_2 = e3) % 188.54/30.04 (25) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.04 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.04 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.04 % 188.54/30.04 Begin of proof % 188.54/30.04 | % 188.54/30.04 | ALPHA: (9) implies: % 188.54/30.04 | (26) all_252_21 = e4 % 188.54/30.04 | % 188.54/30.04 | BETA: splitting (20) gives: % 188.54/30.04 | % 188.54/30.04 | Case 1: % 188.54/30.04 | | % 188.54/30.04 | | (27) all_252_24 = e0 & op(e0, e0) = e0 % 188.54/30.04 | | % 188.54/30.04 | | ALPHA: (27) implies: % 188.54/30.04 | | (28) all_252_24 = e0 % 188.54/30.04 | | % 188.54/30.04 | | REF_CLOSE: (3), (5), (7), (10), (12), (17), (21), (24), (25), (26), (28) are % 188.54/30.04 | | inconsistent by sub-proof #257. % 188.54/30.04 | | % 188.54/30.04 | Case 2: % 188.54/30.04 | | % 188.54/30.04 | | (29) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) % 188.54/30.04 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & % 188.54/30.04 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) | % 188.54/30.04 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, % 188.54/30.04 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)) % 188.54/30.04 | | % 188.54/30.04 | | ALPHA: (29) implies: % 188.54/30.04 | | (30) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 188.54/30.04 | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.04 | | op(e0, e1) = e0) % 188.54/30.04 | | % 188.54/30.04 | | BETA: splitting (30) gives: % 188.54/30.04 | | % 188.54/30.04 | | Case 1: % 188.54/30.04 | | | % 188.54/30.04 | | | (31) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, % 188.54/30.04 | | | e3) = e0) % 188.54/30.04 | | | % 188.54/30.04 | | | BETA: splitting (31) gives: % 188.54/30.04 | | | % 188.54/30.04 | | | Case 1: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (32) all_252_20 = e0 & op(e0, e4) = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | REF_CLOSE: (3), (16), (23), (32) are inconsistent by sub-proof #255. % 188.54/30.04 | | | | % 188.54/30.04 | | | Case 2: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (33) all_252_21 = e0 & op(e0, e3) = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | ALPHA: (33) implies: % 188.54/30.04 | | | | (34) all_252_21 = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | COMBINE_EQS: (26), (34) imply: % 188.54/30.04 | | | | (35) e4 = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | SIMP: (35) implies: % 188.54/30.04 | | | | (36) e4 = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | REDUCE: (6), (36) imply: % 188.54/30.04 | | | | (37) $false % 188.54/30.04 | | | | % 188.54/30.04 | | | | CLOSE: (37) is inconsistent. % 188.54/30.04 | | | | % 188.54/30.04 | | | End of split % 188.54/30.04 | | | % 188.54/30.04 | | Case 2: % 188.54/30.04 | | | % 188.54/30.04 | | | (38) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, % 188.54/30.04 | | | e1) = e0) % 188.54/30.04 | | | % 188.54/30.04 | | | BETA: splitting (38) gives: % 188.54/30.04 | | | % 188.54/30.04 | | | Case 1: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (39) all_252_22 = e0 & op(e0, e2) = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | ALPHA: (39) implies: % 188.54/30.04 | | | | (40) op(e0, e2) = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | REF_CLOSE: (3), (5), (6), (40) are inconsistent by sub-proof #520. % 188.54/30.04 | | | | % 188.54/30.04 | | | Case 2: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (41) all_252_23 = e0 & op(e0, e1) = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | ALPHA: (41) implies: % 188.54/30.04 | | | | (42) all_252_23 = e0 % 188.54/30.04 | | | | % 188.54/30.04 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (11), (13), (14), (15), (18), % 188.54/30.04 | | | | (19), (22), (42) are inconsistent by sub-proof #172. % 188.54/30.04 | | | | % 188.54/30.04 | | | End of split % 188.54/30.04 | | | % 188.54/30.04 | | End of split % 188.54/30.04 | | % 188.54/30.04 | End of split % 188.54/30.04 | % 188.54/30.04 End of proof % 188.54/30.04 % 188.54/30.04 Sub-proof #48 shows that the following formulas are inconsistent: % 188.54/30.04 ---------------------------------------------------------------- % 188.54/30.04 (1) all_252_8 = e3 & op(e2, e2) = e3 % 188.54/30.04 (2) all_252_8 = e2 % 188.54/30.04 (3) ~ (e3 = e2) % 188.54/30.04 % 188.54/30.04 Begin of proof % 188.54/30.04 | % 188.54/30.04 | ALPHA: (1) implies: % 188.54/30.04 | (4) all_252_8 = e3 % 188.54/30.04 | % 188.54/30.04 | COMBINE_EQS: (2), (4) imply: % 188.54/30.04 | (5) e3 = e2 % 188.54/30.04 | % 188.54/30.04 | REDUCE: (3), (5) imply: % 188.54/30.04 | (6) $false % 188.54/30.04 | % 188.54/30.04 | CLOSE: (6) is inconsistent. % 188.54/30.04 | % 188.54/30.04 End of proof % 188.54/30.04 % 188.54/30.04 Sub-proof #49 shows that the following formulas are inconsistent: % 188.54/30.04 ---------------------------------------------------------------- % 188.54/30.04 (1) all_252_20 = e2 % 188.54/30.04 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.04 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.04 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.04 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.04 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.04 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.04 (5) ~ (all_20_2 = e4) % 188.54/30.04 (6) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.04 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.04 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.04 (7) op(e0, e2) = e4 % 188.54/30.04 (8) op(e3, e1) = all_36_2 % 188.54/30.04 (9) ~ (e2 = e1) % 188.54/30.04 (10) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.04 (11) all_252_12 = e0 % 188.54/30.04 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.04 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.04 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.04 (13) op(e2, e1) = e0 % 188.54/30.04 (14) all_252_15 = e3 % 188.54/30.04 (15) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.04 all_250_23 = e0 % 188.54/30.04 (16) ~ (e4 = e0) % 188.54/30.04 (17) ~ (e4 = e3) % 188.54/30.04 (18) ~ (all_36_2 = e2) % 188.54/30.04 (19) ~ (all_40_2 = all_34_2) % 188.54/30.04 (20) ~ (all_244_24 = all_20_2) % 188.54/30.04 (21) op(e1, e4) = e0 % 188.54/30.04 (22) all_252_23 = e1 % 188.54/30.04 (23) ~ (all_20_2 = e3) % 188.54/30.04 (24) op(all_20_2, e4) = e1 % 188.54/30.04 (25) op(e0, e0) = all_244_24 % 188.54/30.04 (26) op(e0, e1) = all_20_2 % 188.54/30.04 (27) all_252_19 = e4 % 188.54/30.04 (28) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.04 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.04 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.04 (29) ~ (all_20_2 = e0) % 188.54/30.04 (30) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.04 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.04 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.04 (31) ~ (all_20_2 = e2) % 188.54/30.04 (32) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.04 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.04 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.04 (33) op(e1, e3) = e4 % 188.54/30.04 (34) op(e0, e4) = e2 % 188.54/30.04 (35) ~ (e3 = e0) % 188.54/30.04 (36) ~ (all_20_2 = all_8_1) % 188.54/30.04 (37) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.04 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.04 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.04 (38) all_252_10 = e0 % 188.54/30.04 (39) all_252_6 = e4 % 188.54/30.04 (40) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.04 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.04 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.04 (41) ~ (e3 = e2) % 188.54/30.04 (42) op(e4, all_20_2) = e0 % 188.54/30.04 (43) op(e0, e3) = all_8_1 % 188.54/30.04 (44) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.04 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.04 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.04 (45) ~ (e4 = e2) % 188.54/30.04 (46) op(e2, e0) = all_40_2 % 188.54/30.04 (47) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.04 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.04 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.04 (48) ~ (e1 = e0) % 188.54/30.04 (49) op(e0, e4) = all_12_2 % 188.54/30.04 (50) all_250_23 = all_20_2 % 188.54/30.04 (51) ~ (e3 = e1) % 188.54/30.04 (52) ~ (e2 = e0) % 188.54/30.04 (53) op(e1, e0) = all_34_2 % 188.54/30.04 (54) ~ (all_12_2 = e3) % 188.54/30.04 (55) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.04 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.04 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.04 (56) ~ (all_34_2 = e2) % 188.54/30.04 (57) all_252_9 = e4 % 188.54/30.04 (58) ~ (e4 = e1) % 188.54/30.04 (59) op(e2, e0) = e1 % 188.54/30.04 % 188.54/30.04 Begin of proof % 188.54/30.04 | % 188.54/30.04 | BETA: splitting (30) gives: % 188.54/30.04 | % 188.54/30.04 | Case 1: % 188.54/30.04 | | % 188.54/30.04 | | (60) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 188.54/30.04 | | = e2) % 188.54/30.04 | | % 188.54/30.04 | | BETA: splitting (60) gives: % 188.54/30.04 | | % 188.54/30.04 | | Case 1: % 188.54/30.04 | | | % 188.54/30.04 | | | (61) all_252_12 = e2 & op(e1, e4) = e2 % 188.54/30.04 | | | % 188.54/30.04 | | | ALPHA: (61) implies: % 188.54/30.04 | | | (62) all_252_12 = e2 % 188.54/30.04 | | | % 188.54/30.04 | | | REF_CLOSE: (11), (52), (62) are inconsistent by sub-proof #81. % 188.54/30.04 | | | % 188.54/30.04 | | Case 2: % 188.54/30.04 | | | % 188.54/30.04 | | | (63) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.04 | | | % 188.54/30.04 | | | ALPHA: (63) implies: % 188.54/30.04 | | | (64) all_252_13 = e2 % 188.54/30.04 | | | % 188.54/30.04 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.04 | | | (13), (14), (16), (17), (18), (19), (20), (21), (23), (24), % 188.54/30.04 | | | (25), (26), (28), (29), (31), (32), (34), (35), (36), (39), % 188.54/30.04 | | | (40), (41), (42), (43), (44), (45), (46), (47), (48), (49), % 188.54/30.04 | | | (50), (51), (52), (53), (54), (55), (57), (58), (59), (64) are % 188.54/30.04 | | | inconsistent by sub-proof #51. % 188.54/30.04 | | | % 188.54/30.04 | | End of split % 188.54/30.04 | | % 188.54/30.04 | Case 2: % 188.54/30.04 | | % 188.54/30.04 | | (65) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) % 188.54/30.04 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.04 | | % 188.54/30.04 | | BETA: splitting (65) gives: % 188.54/30.04 | | % 188.54/30.04 | | Case 1: % 188.54/30.04 | | | % 188.54/30.04 | | | (66) all_252_14 = e2 & op(e1, e2) = e2 % 188.54/30.04 | | | % 188.54/30.04 | | | ALPHA: (66) implies: % 188.54/30.04 | | | (67) all_252_14 = e2 % 188.54/30.04 | | | % 188.54/30.04 | | | BETA: splitting (47) gives: % 188.54/30.04 | | | % 188.54/30.04 | | | Case 1: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (68) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, % 188.54/30.04 | | | | e3) = e1) % 188.54/30.04 | | | | % 188.54/30.04 | | | | BETA: splitting (68) gives: % 188.54/30.04 | | | | % 188.54/30.04 | | | | Case 1: % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | (69) all_252_12 = e1 & op(e1, e4) = e1 % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | REF_CLOSE: (1), (4), (5), (7), (10), (11), (20), (22), (25), (28), % 188.54/30.04 | | | | | (29), (31), (36), (43), (50), (69) are inconsistent by % 188.54/30.04 | | | | | sub-proof #181. % 188.54/30.04 | | | | | % 188.54/30.04 | | | | Case 2: % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | (70) all_252_13 = e1 & op(e1, e3) = e1 % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | REF_CLOSE: (4), (33), (58), (70) are inconsistent by sub-proof #423. % 188.54/30.04 | | | | | % 188.54/30.04 | | | | End of split % 188.54/30.04 | | | | % 188.54/30.04 | | | Case 2: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (71) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.04 | | | | e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.04 | | | | % 188.54/30.04 | | | | BETA: splitting (71) gives: % 188.54/30.04 | | | | % 188.54/30.04 | | | | Case 1: % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | (72) all_252_14 = e1 & op(e1, e2) = e1 % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | REF_CLOSE: (9), (67), (72) are inconsistent by sub-proof #395. % 188.54/30.04 | | | | | % 188.54/30.04 | | | | Case 2: % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | (73) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 188.54/30.04 | | | | | op(e1, e0) = e1) % 188.54/30.04 | | | | | % 188.54/30.04 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), % 188.54/30.04 | | | | | (13), (15), (16), (17), (18), (19), (20), (21), (23), (24), % 188.54/30.04 | | | | | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), % 188.54/30.04 | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 188.54/30.04 | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), % 188.54/30.04 | | | | | (56), (57), (58), (59), (73) are inconsistent by sub-proof % 188.54/30.04 | | | | | #50. % 188.54/30.04 | | | | | % 188.54/30.04 | | | | End of split % 188.54/30.04 | | | | % 188.54/30.04 | | | End of split % 188.54/30.04 | | | % 188.54/30.04 | | Case 2: % 188.54/30.04 | | | % 188.54/30.04 | | | (74) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, % 188.54/30.04 | | | e0) = e2) % 188.54/30.04 | | | % 188.54/30.04 | | | BETA: splitting (74) gives: % 188.54/30.04 | | | % 188.54/30.04 | | | Case 1: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (75) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.04 | | | | % 188.54/30.04 | | | | REF_CLOSE: (14), (41), (75) are inconsistent by sub-proof #114. % 188.54/30.04 | | | | % 188.54/30.04 | | | Case 2: % 188.54/30.04 | | | | % 188.54/30.04 | | | | (76) all_252_19 = e2 & op(e1, e0) = e2 % 188.54/30.04 | | | | % 188.54/30.04 | | | | REF_CLOSE: (4), (53), (56), (76) are inconsistent by sub-proof #438. % 188.54/30.04 | | | | % 188.54/30.04 | | | End of split % 188.54/30.04 | | | % 188.54/30.04 | | End of split % 188.54/30.04 | | % 188.54/30.04 | End of split % 188.54/30.04 | % 188.54/30.04 End of proof % 188.54/30.04 % 188.54/30.04 Sub-proof #50 shows that the following formulas are inconsistent: % 188.54/30.04 ---------------------------------------------------------------- % 188.54/30.04 (1) all_252_20 = e2 % 188.54/30.04 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.04 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.04 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.04 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.04 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.04 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.04 (5) ~ (all_20_2 = e4) % 188.54/30.04 (6) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.04 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.04 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.04 (7) op(e0, e2) = e4 % 188.54/30.04 (8) op(e3, e1) = all_36_2 % 188.54/30.04 (9) ~ (e2 = e1) % 188.54/30.04 (10) all_252_12 = e0 % 188.54/30.04 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.04 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.04 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.05 (12) op(e2, e1) = e0 % 188.54/30.05 (13) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.05 all_250_23 = e0 % 188.54/30.05 (14) ~ (e4 = e0) % 188.54/30.05 (15) ~ (e4 = e3) % 188.54/30.05 (16) ~ (all_36_2 = e2) % 188.54/30.05 (17) ~ (all_40_2 = all_34_2) % 188.54/30.05 (18) ~ (all_244_24 = all_20_2) % 188.54/30.05 (19) op(e1, e4) = e0 % 188.54/30.05 (20) ~ (all_20_2 = e3) % 188.54/30.05 (21) op(all_20_2, e4) = e1 % 188.54/30.05 (22) op(e0, e0) = all_244_24 % 188.54/30.05 (23) op(e0, e1) = all_20_2 % 188.54/30.05 (24) all_252_19 = e4 % 188.54/30.05 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.05 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.05 (26) ~ (all_20_2 = e0) % 188.54/30.05 (27) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.05 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.05 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.05 (28) ~ (all_20_2 = e2) % 188.54/30.05 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.05 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.05 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.05 (30) op(e0, e4) = e2 % 188.54/30.05 (31) ~ (e3 = e0) % 188.54/30.05 (32) ~ (all_20_2 = all_8_1) % 188.54/30.05 (33) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.05 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.05 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.05 (34) all_252_10 = e0 % 188.54/30.05 (35) all_252_6 = e4 % 188.54/30.05 (36) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.05 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.05 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.05 (37) ~ (e3 = e2) % 188.54/30.05 (38) op(e4, all_20_2) = e0 % 188.54/30.05 (39) op(e0, e3) = all_8_1 % 188.54/30.05 (40) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = % 188.54/30.05 e1) % 188.54/30.05 (41) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.05 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.05 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.05 (42) ~ (e4 = e2) % 188.54/30.05 (43) op(e2, e0) = all_40_2 % 188.54/30.05 (44) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.05 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.05 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.05 (45) ~ (e1 = e0) % 188.54/30.05 (46) op(e0, e4) = all_12_2 % 188.54/30.05 (47) all_250_23 = all_20_2 % 188.54/30.05 (48) ~ (e3 = e1) % 188.54/30.05 (49) ~ (e2 = e0) % 188.54/30.05 (50) op(e1, e0) = all_34_2 % 188.54/30.05 (51) ~ (all_12_2 = e3) % 188.54/30.05 (52) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.05 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.05 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.05 (53) ~ (all_34_2 = e2) % 188.54/30.05 (54) all_252_9 = e4 % 188.54/30.05 (55) ~ (e4 = e1) % 188.54/30.05 (56) op(e2, e0) = e1 % 188.54/30.05 % 188.54/30.05 Begin of proof % 188.54/30.05 | % 188.54/30.05 | BETA: splitting (40) gives: % 188.54/30.05 | % 188.54/30.05 | Case 1: % 188.54/30.05 | | % 188.54/30.05 | | (57) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.05 | | % 188.54/30.05 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.05 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 188.54/30.05 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 188.54/30.05 | | (35), (36), (37), (38), (39), (41), (42), (43), (44), (45), (46), % 188.54/30.05 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57) % 188.54/30.05 | | are inconsistent by sub-proof #55. % 188.54/30.05 | | % 188.54/30.05 | Case 2: % 188.54/30.05 | | % 188.54/30.05 | | (58) all_252_19 = e1 & op(e1, e0) = e1 % 188.54/30.05 | | % 188.54/30.05 | | ALPHA: (58) implies: % 188.54/30.05 | | (59) op(e1, e0) = e1 % 188.54/30.05 | | % 188.54/30.05 | | REF_CLOSE: (4), (17), (43), (50), (56), (59) are inconsistent by sub-proof % 188.54/30.05 | | #352. % 188.54/30.05 | | % 188.54/30.05 | End of split % 188.54/30.05 | % 188.54/30.05 End of proof % 188.54/30.05 % 188.54/30.05 Sub-proof #51 shows that the following formulas are inconsistent: % 188.54/30.05 ---------------------------------------------------------------- % 188.54/30.05 (1) all_252_13 = e2 % 188.54/30.05 (2) all_252_20 = e2 % 188.54/30.05 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.05 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.05 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.05 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.05 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.05 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.05 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.05 (6) ~ (all_20_2 = e4) % 188.54/30.05 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.05 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.05 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.05 (8) op(e0, e2) = e4 % 188.54/30.05 (9) op(e3, e1) = all_36_2 % 188.54/30.05 (10) ~ (e2 = e1) % 188.54/30.05 (11) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.05 (12) all_252_12 = e0 % 188.54/30.05 (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.05 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.05 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.05 (14) op(e2, e1) = e0 % 188.54/30.05 (15) all_252_15 = e3 % 188.54/30.05 (16) ~ (e4 = e0) % 188.54/30.05 (17) ~ (e4 = e3) % 188.54/30.05 (18) ~ (all_36_2 = e2) % 188.54/30.05 (19) ~ (all_40_2 = all_34_2) % 188.54/30.05 (20) ~ (all_244_24 = all_20_2) % 188.54/30.05 (21) op(e1, e4) = e0 % 188.54/30.05 (22) ~ (all_20_2 = e3) % 188.54/30.05 (23) op(all_20_2, e4) = e1 % 188.54/30.05 (24) op(e0, e0) = all_244_24 % 188.54/30.05 (25) op(e0, e1) = all_20_2 % 188.54/30.05 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.05 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.05 (27) ~ (all_20_2 = e0) % 188.54/30.05 (28) ~ (all_20_2 = e2) % 188.54/30.05 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.05 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.05 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.05 (30) op(e0, e4) = e2 % 188.54/30.05 (31) ~ (e3 = e0) % 188.54/30.05 (32) ~ (all_20_2 = all_8_1) % 188.54/30.05 (33) all_252_6 = e4 % 188.54/30.05 (34) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.05 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.05 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.05 (35) ~ (e3 = e2) % 188.54/30.05 (36) op(e4, all_20_2) = e0 % 188.54/30.05 (37) op(e0, e3) = all_8_1 % 188.54/30.05 (38) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.05 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.05 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.05 (39) ~ (e4 = e2) % 188.54/30.05 (40) op(e2, e0) = all_40_2 % 188.54/30.05 (41) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.05 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.05 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.05 (42) ~ (e1 = e0) % 188.54/30.05 (43) op(e0, e4) = all_12_2 % 188.54/30.05 (44) all_250_23 = all_20_2 % 188.54/30.05 (45) ~ (e3 = e1) % 188.54/30.05 (46) ~ (e2 = e0) % 188.54/30.05 (47) op(e1, e0) = all_34_2 % 188.54/30.05 (48) ~ (all_12_2 = e3) % 188.54/30.05 (49) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.05 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.05 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.05 (50) all_252_9 = e4 % 188.54/30.05 (51) ~ (e4 = e1) % 188.54/30.05 (52) op(e2, e0) = e1 % 188.54/30.05 % 188.54/30.05 Begin of proof % 188.54/30.05 | % 188.54/30.05 | BETA: splitting (7) gives: % 188.54/30.05 | % 188.54/30.05 | Case 1: % 188.54/30.05 | | % 188.54/30.05 | | (53) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 188.54/30.05 | | e2) % 188.54/30.05 | | % 188.54/30.05 | | BETA: splitting (53) gives: % 188.54/30.05 | | % 188.54/30.05 | | Case 1: % 188.54/30.05 | | | % 188.54/30.05 | | | (54) all_252_9 = e2 & op(e4, e1) = e2 % 188.54/30.05 | | | % 188.54/30.05 | | | REF_CLOSE: (2), (3), (4), (5), (10), (12), (16), (17), (30), (31), (33), % 188.54/30.05 | | | (35), (38), (39), (42), (43), (45), (46), (48), (49), (50), % 188.54/30.05 | | | (51), (54) are inconsistent by sub-proof #52. % 188.54/30.05 | | | % 188.54/30.05 | | Case 2: % 188.54/30.05 | | | % 188.54/30.05 | | | (55) all_252_10 = e2 & op(e3, e1) = e2 % 188.54/30.05 | | | % 188.54/30.05 | | | ALPHA: (55) implies: % 188.54/30.05 | | | (56) op(e3, e1) = e2 % 188.54/30.05 | | | % 188.54/30.05 | | | REF_CLOSE: (5), (9), (18), (56) are inconsistent by sub-proof #557. % 188.54/30.05 | | | % 188.54/30.05 | | End of split % 188.54/30.05 | | % 188.54/30.05 | Case 2: % 188.54/30.05 | | % 188.54/30.05 | | (57) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) % 188.54/30.05 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.05 | | % 188.54/30.05 | | BETA: splitting (57) gives: % 188.54/30.05 | | % 188.54/30.05 | | Case 1: % 188.54/30.05 | | | % 188.54/30.05 | | | (58) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.05 | | | % 188.54/30.05 | | | ALPHA: (58) implies: % 188.54/30.05 | | | (59) all_252_11 = e2 % 188.54/30.05 | | | (60) op(e2, e1) = e2 % 188.54/30.05 | | | % 188.54/30.05 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 188.54/30.05 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 188.54/30.05 | | | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), % 188.54/30.05 | | | (36), (37), (39), (40), (41), (44), (46), (47), (52), (59), % 188.54/30.05 | | | (60) are inconsistent by sub-proof #119. % 188.54/30.05 | | | % 188.54/30.05 | | Case 2: % 188.54/30.05 | | | % 188.54/30.05 | | | (61) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, % 188.54/30.05 | | | e1) = e2) % 188.54/30.05 | | | % 188.54/30.05 | | | BETA: splitting (61) gives: % 188.54/30.05 | | | % 188.54/30.05 | | | Case 1: % 188.54/30.05 | | | | % 188.54/30.05 | | | | (62) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.05 | | | | % 188.54/30.05 | | | | REF_CLOSE: (15), (35), (62) are inconsistent by sub-proof #202. % 188.54/30.05 | | | | % 188.54/30.05 | | | Case 2: % 188.54/30.05 | | | | % 188.54/30.05 | | | | (63) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.05 | | | | % 188.54/30.05 | | | | REF_CLOSE: (5), (25), (28), (63) are inconsistent by sub-proof #540. % 188.54/30.05 | | | | % 188.54/30.05 | | | End of split % 188.54/30.05 | | | % 188.54/30.05 | | End of split % 188.54/30.05 | | % 188.54/30.05 | End of split % 188.54/30.05 | % 188.54/30.05 End of proof % 188.54/30.05 % 188.54/30.05 Sub-proof #52 shows that the following formulas are inconsistent: % 188.54/30.05 ---------------------------------------------------------------- % 188.54/30.05 (1) all_252_20 = e2 % 188.54/30.05 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.05 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.05 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.05 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.05 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.05 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.05 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.05 (5) ~ (e2 = e1) % 188.54/30.05 (6) all_252_12 = e0 % 188.54/30.05 (7) ~ (e4 = e0) % 188.54/30.05 (8) ~ (e4 = e3) % 188.54/30.05 (9) op(e0, e4) = e2 % 188.54/30.05 (10) ~ (e3 = e0) % 188.54/30.05 (11) all_252_9 = e2 & op(e4, e1) = e2 % 188.54/30.05 (12) all_252_6 = e4 % 188.54/30.05 (13) ~ (e3 = e2) % 188.54/30.05 (14) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.05 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.05 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.05 (15) ~ (e4 = e2) % 188.54/30.05 (16) ~ (e1 = e0) % 188.54/30.05 (17) op(e0, e4) = all_12_2 % 188.54/30.05 (18) ~ (e3 = e1) % 188.54/30.05 (19) ~ (e2 = e0) % 188.54/30.05 (20) ~ (all_12_2 = e3) % 188.54/30.05 (21) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.05 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.05 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.05 (22) all_252_9 = e4 % 188.54/30.05 (23) ~ (e4 = e1) % 188.54/30.05 % 188.54/30.05 Begin of proof % 188.54/30.05 | % 188.54/30.05 | ALPHA: (11) implies: % 188.54/30.05 | (24) all_252_9 = e2 % 188.54/30.05 | % 188.54/30.05 | COMBINE_EQS: (22), (24) imply: % 188.54/30.05 | (25) e4 = e2 % 188.54/30.05 | % 188.54/30.05 | SIMP: (25) implies: % 188.54/30.05 | (26) e4 = e2 % 188.54/30.05 | % 188.54/30.05 | COMBINE_EQS: (12), (26) imply: % 188.54/30.05 | (27) all_252_6 = e2 % 188.54/30.05 | % 188.54/30.05 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), % 188.54/30.05 | (15), (16), (17), (18), (19), (20), (21), (23), (27) are % 188.54/30.05 | inconsistent by sub-proof #223. % 188.54/30.05 | % 188.54/30.05 End of proof % 188.54/30.05 % 188.54/30.05 Sub-proof #53 shows that the following formulas are inconsistent: % 188.54/30.05 ---------------------------------------------------------------- % 188.54/30.05 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.54/30.05 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.54/30.05 (all_252_16 = e1 & op(e4, e0) = e1) % 188.54/30.05 (2) all_252_20 = e2 % 188.54/30.05 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.05 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.05 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.05 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.05 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.05 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.05 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.05 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.05 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.05 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.05 (7) ~ (all_20_2 = e4) % 188.54/30.05 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.05 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.05 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.05 (9) op(e0, e2) = e4 % 188.54/30.05 (10) op(e0, e2) = all_28_2 % 188.54/30.05 (11) op(e3, e1) = all_36_2 % 188.54/30.05 (12) all_252_12 = e0 % 188.54/30.05 (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.05 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.05 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.05 (14) op(e1, e3) = all_62_2 % 188.54/30.05 (15) op(e2, e1) = e0 % 188.54/30.05 (16) all_252_7 = e0 % 188.54/30.05 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.05 all_250_23 = e0 % 188.54/30.05 (18) ~ (e4 = e0) % 188.54/30.05 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.54/30.05 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.54/30.05 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.54/30.05 (20) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.05 (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.05 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.05 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.05 (22) ~ (e4 = e3) % 188.54/30.05 (23) ~ (all_36_2 = e2) % 188.54/30.05 (24) ~ (all_40_2 = all_34_2) % 188.54/30.05 (25) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.54/30.05 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.54/30.05 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.54/30.05 (26) ~ (all_244_24 = all_20_2) % 188.54/30.05 (27) all_252_8 = e2 % 188.54/30.05 (28) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.54/30.05 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.54/30.05 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.54/30.05 (29) op(e1, e4) = e0 % 188.54/30.05 (30) ~ (all_6_2 = e4) % 188.54/30.05 (31) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.54/30.05 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.54/30.05 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.54/30.05 (32) ~ (all_20_2 = e3) % 188.54/30.05 (33) op(all_20_2, e4) = e1 % 188.54/30.05 (34) op(e0, e0) = all_244_24 % 188.54/30.05 (35) op(e0, e1) = all_20_2 % 188.54/30.05 (36) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.05 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.05 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.05 (37) all_252_19 = e4 % 188.54/30.05 (38) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.05 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.05 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.05 (39) ~ (all_8_1 = e2) % 188.54/30.05 (40) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.05 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.05 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.05 (41) ~ (all_20_2 = e0) % 188.54/30.05 (42) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.05 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.05 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.05 (43) all_252_17 = e2 % 188.54/30.05 (44) ~ (all_20_2 = e2) % 188.54/30.05 (45) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.05 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.05 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.05 (46) op(e4, e4) = all_244_0 % 188.54/30.05 (47) op(e0, e4) = e2 % 188.54/30.05 (48) ~ (e3 = e0) % 188.54/30.05 (49) ~ (all_20_2 = all_8_1) % 188.54/30.05 (50) ~ (all_28_2 = e0) % 188.54/30.05 (51) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.05 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.05 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.05 (52) ~ (all_244_0 = e2) % 188.54/30.05 (53) op(e2, all_40_2) = e0 % 188.54/30.05 (54) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.05 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.05 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.54/30.05 (55) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.05 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.05 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.05 (56) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.54/30.05 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.05 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.54/30.06 (57) ~ (e3 = e2) % 188.54/30.06 (58) all_252_22 = e4 % 188.54/30.06 (59) op(e4, all_20_2) = e0 % 188.54/30.06 (60) op(e0, e3) = all_8_1 % 188.54/30.06 (61) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.06 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.06 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.06 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.06 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.06 op(e0, e1) = e0))) % 188.54/30.06 (62) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.06 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.06 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.06 (63) ~ (e4 = e2) % 188.54/30.06 (64) op(e2, e0) = all_40_2 % 188.54/30.06 (65) op(all_28_2, all_40_2) = e2 % 188.54/30.06 (66) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.06 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.06 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.06 (67) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.06 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.06 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.06 (68) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.54/30.06 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.54/30.06 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.06 (69) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.06 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.54/30.06 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.54/30.06 (70) op(e0, e4) = all_12_2 % 188.54/30.06 (71) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.54/30.06 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.54/30.06 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.54/30.06 (72) all_250_23 = all_20_2 % 188.54/30.06 (73) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.54/30.06 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.54/30.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.54/30.06 (74) ~ (e2 = e0) % 188.54/30.06 (75) op(e1, e0) = all_34_2 % 188.54/30.06 (76) ~ (all_12_2 = e3) % 188.54/30.06 (77) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.06 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.06 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.54/30.06 (78) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.06 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.06 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.06 (79) ~ (all_34_2 = e2) % 188.54/30.06 (80) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.06 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.06 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.06 (81) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.06 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.06 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.06 (82) op(e4, e2) = all_6_2 % 188.54/30.06 (83) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.54/30.06 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.54/30.06 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.54/30.06 (84) all_252_5 = e0 % 188.54/30.06 (85) all_252_9 = e4 % 188.54/30.06 (86) op(e2, e0) = e1 % 188.54/30.06 % 188.54/30.06 Begin of proof % 188.54/30.06 | % 188.54/30.06 | ALPHA: (20) implies: % 188.54/30.06 | (87) all_252_7 = e4 % 188.54/30.06 | % 188.54/30.06 | COMBINE_EQS: (16), (87) imply: % 188.54/30.06 | (88) e4 = e0 % 188.54/30.06 | % 188.54/30.06 | SIMP: (88) implies: % 188.54/30.06 | (89) e4 = e0 % 188.54/30.06 | % 188.54/30.06 | COMBINE_EQS: (85), (89) imply: % 188.54/30.06 | (90) all_252_9 = e0 % 188.54/30.06 | % 188.54/30.06 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.06 | (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), % 188.54/30.06 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 188.54/30.06 | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.06 | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 188.54/30.06 | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 188.54/30.06 | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 188.54/30.06 | (80), (81), (82), (83), (84), (86), (90) are inconsistent by % 188.54/30.06 | sub-proof #77. % 188.54/30.06 | % 188.54/30.06 End of proof % 188.54/30.06 % 188.54/30.06 Sub-proof #54 shows that the following formulas are inconsistent: % 188.54/30.06 ---------------------------------------------------------------- % 188.54/30.06 (1) ~ (e2 = e1) % 188.54/30.06 (2) ~ (e4 = e0) % 188.54/30.06 (3) ~ (e4 = e3) % 188.54/30.06 (4) all_252_3 = e4 & op(e3, e3) = e4 % 188.54/30.06 (5) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 188.54/30.06 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.06 | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.06 (6) all_252_17 = e2 % 188.54/30.06 (7) ~ (e3 = e0) % 188.54/30.06 (8) all_252_10 = e0 % 188.54/30.06 (9) ~ (e3 = e2) % 188.54/30.06 (10) ~ (e4 = e2) % 188.54/30.06 (11) ~ (e1 = e0) % 188.54/30.06 (12) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.06 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.06 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.06 (13) ~ (e3 = e1) % 188.54/30.06 (14) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.06 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.06 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.06 (15) all_252_5 = e0 % 188.54/30.06 (16) ~ (e4 = e1) % 188.54/30.06 % 188.54/30.06 Begin of proof % 188.54/30.06 | % 188.54/30.06 | ALPHA: (4) implies: % 188.54/30.06 | (17) all_252_3 = e4 % 188.54/30.06 | % 188.54/30.06 | BETA: splitting (5) gives: % 188.54/30.06 | % 188.54/30.06 | Case 1: % 188.54/30.06 | | % 188.54/30.06 | | (18) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = % 188.54/30.06 | | e1) % 188.54/30.06 | | % 188.54/30.06 | | BETA: splitting (18) gives: % 188.54/30.06 | | % 188.54/30.06 | | Case 1: % 188.54/30.06 | | | % 188.54/30.06 | | | (19) all_252_2 = e1 & op(e3, e4) = e1 % 188.54/30.06 | | | % 188.54/30.06 | | | ALPHA: (19) implies: % 188.54/30.06 | | | (20) all_252_2 = e1 % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 188.54/30.06 | | | (14), (15), (16), (20) are inconsistent by sub-proof #88. % 188.54/30.06 | | | % 188.54/30.06 | | Case 2: % 188.54/30.06 | | | % 188.54/30.06 | | | (21) all_252_3 = e1 & op(e3, e3) = e1 % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (16), (17), (21) are inconsistent by sub-proof #149. % 188.54/30.06 | | | % 188.54/30.06 | | End of split % 188.54/30.06 | | % 188.54/30.06 | Case 2: % 188.54/30.06 | | % 188.54/30.06 | | (22) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.06 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.06 | | % 188.54/30.06 | | REF_CLOSE: (1), (6), (8), (11), (15), (22) are inconsistent by sub-proof % 188.54/30.06 | | #93. % 188.54/30.06 | | % 188.54/30.06 | End of split % 188.54/30.06 | % 188.54/30.06 End of proof % 188.54/30.06 % 188.54/30.06 Sub-proof #55 shows that the following formulas are inconsistent: % 188.54/30.06 ---------------------------------------------------------------- % 188.54/30.06 (1) all_252_20 = e2 % 188.54/30.06 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.06 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.06 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.06 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.06 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.06 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.06 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.06 (5) ~ (all_20_2 = e4) % 188.54/30.06 (6) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.06 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.06 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.06 (7) op(e0, e2) = e4 % 188.54/30.06 (8) op(e3, e1) = all_36_2 % 188.54/30.06 (9) ~ (e2 = e1) % 188.54/30.06 (10) all_252_12 = e0 % 188.54/30.06 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.06 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.06 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.06 (12) op(e2, e1) = e0 % 188.54/30.06 (13) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.06 all_250_23 = e0 % 188.54/30.06 (14) ~ (e4 = e0) % 188.54/30.06 (15) ~ (e4 = e3) % 188.54/30.06 (16) ~ (all_36_2 = e2) % 188.54/30.06 (17) ~ (all_40_2 = all_34_2) % 188.54/30.06 (18) ~ (all_244_24 = all_20_2) % 188.54/30.06 (19) op(e1, e4) = e0 % 188.54/30.06 (20) ~ (all_20_2 = e3) % 188.54/30.06 (21) op(all_20_2, e4) = e1 % 188.54/30.06 (22) op(e0, e0) = all_244_24 % 188.54/30.06 (23) op(e0, e1) = all_20_2 % 188.54/30.06 (24) all_252_19 = e4 % 188.54/30.06 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.06 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.06 (26) ~ (all_20_2 = e0) % 188.54/30.06 (27) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.06 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.06 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.06 (28) ~ (all_20_2 = e2) % 188.54/30.06 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.06 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.06 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.06 (30) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.06 (31) op(e0, e4) = e2 % 188.54/30.06 (32) ~ (e3 = e0) % 188.54/30.06 (33) ~ (all_20_2 = all_8_1) % 188.54/30.06 (34) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.06 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.06 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.06 (35) all_252_10 = e0 % 188.54/30.06 (36) all_252_6 = e4 % 188.54/30.06 (37) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.06 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.06 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.06 (38) ~ (e3 = e2) % 188.54/30.06 (39) op(e4, all_20_2) = e0 % 188.54/30.06 (40) op(e0, e3) = all_8_1 % 188.54/30.06 (41) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.06 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.06 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.06 (42) ~ (e4 = e2) % 188.54/30.06 (43) op(e2, e0) = all_40_2 % 188.54/30.06 (44) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.06 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.06 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.06 (45) ~ (e1 = e0) % 188.54/30.06 (46) op(e0, e4) = all_12_2 % 188.54/30.06 (47) all_250_23 = all_20_2 % 188.54/30.06 (48) ~ (e3 = e1) % 188.54/30.06 (49) ~ (e2 = e0) % 188.54/30.06 (50) op(e1, e0) = all_34_2 % 188.54/30.06 (51) ~ (all_12_2 = e3) % 188.54/30.06 (52) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.06 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.06 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.06 (53) ~ (all_34_2 = e2) % 188.54/30.06 (54) all_252_9 = e4 % 188.54/30.06 (55) ~ (e4 = e1) % 188.54/30.06 (56) op(e2, e0) = e1 % 188.54/30.06 % 188.54/30.06 Begin of proof % 188.54/30.06 | % 188.54/30.06 | ALPHA: (30) implies: % 188.54/30.06 | (57) all_252_15 = e1 % 188.54/30.06 | % 188.54/30.06 | BETA: splitting (6) gives: % 188.54/30.06 | % 188.54/30.06 | Case 1: % 188.54/30.06 | | % 188.54/30.06 | | (58) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 188.54/30.06 | | e2) % 188.54/30.06 | | % 188.54/30.06 | | BETA: splitting (58) gives: % 188.54/30.06 | | % 188.54/30.06 | | Case 1: % 188.54/30.06 | | | % 188.54/30.06 | | | (59) all_252_9 = e2 & op(e4, e1) = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | ALPHA: (59) implies: % 188.54/30.06 | | | (60) all_252_9 = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | COMBINE_EQS: (54), (60) imply: % 188.54/30.06 | | | (61) e4 = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | COMBINE_EQS: (36), (61) imply: % 188.54/30.06 | | | (62) all_252_6 = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (14), (15), (31), (32), (38), % 188.54/30.06 | | | (41), (42), (45), (46), (48), (49), (51), (52), (55), (62) are % 188.54/30.06 | | | inconsistent by sub-proof #223. % 188.54/30.06 | | | % 188.54/30.06 | | Case 2: % 188.54/30.06 | | | % 188.54/30.06 | | | (63) all_252_10 = e2 & op(e3, e1) = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | ALPHA: (63) implies: % 188.54/30.06 | | | (64) op(e3, e1) = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (4), (8), (16), (64) are inconsistent by sub-proof #557. % 188.54/30.06 | | | % 188.54/30.06 | | End of split % 188.54/30.06 | | % 188.54/30.06 | Case 2: % 188.54/30.06 | | % 188.54/30.06 | | (65) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) % 188.54/30.06 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.06 | | % 188.54/30.06 | | BETA: splitting (65) gives: % 188.54/30.06 | | % 188.54/30.06 | | Case 1: % 188.54/30.06 | | | % 188.54/30.06 | | | (66) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | ALPHA: (66) implies: % 188.54/30.06 | | | (67) all_252_11 = e2 % 188.54/30.06 | | | (68) op(e2, e1) = e2 % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), % 188.54/30.06 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 188.54/30.06 | | | (25), (26), (27), (28), (29), (31), (32), (33), (34), (35), % 188.54/30.06 | | | (37), (38), (39), (40), (42), (43), (44), (47), (49), (50), % 188.54/30.06 | | | (53), (56), (67), (68) are inconsistent by sub-proof #56. % 188.54/30.06 | | | % 188.54/30.06 | | Case 2: % 188.54/30.06 | | | % 188.54/30.06 | | | (69) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, % 188.54/30.06 | | | e1) = e2) % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (4), (9), (23), (28), (57), (69) are inconsistent by sub-proof % 188.54/30.06 | | | #194. % 188.54/30.06 | | | % 188.54/30.06 | | End of split % 188.54/30.06 | | % 188.54/30.06 | End of split % 188.54/30.06 | % 188.54/30.06 End of proof % 188.54/30.06 % 188.54/30.06 Sub-proof #56 shows that the following formulas are inconsistent: % 188.54/30.06 ---------------------------------------------------------------- % 188.54/30.06 (1) all_252_20 = e2 % 188.54/30.06 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.06 (3) ~ (all_20_2 = e4) % 188.54/30.06 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.06 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.06 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.06 (5) op(e0, e2) = e4 % 188.54/30.06 (6) op(e3, e1) = all_36_2 % 188.54/30.06 (7) all_252_12 = e0 % 188.54/30.06 (8) op(e2, e1) = e2 % 188.54/30.06 (9) all_252_11 = e2 % 188.54/30.06 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.06 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.06 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.06 (11) op(e2, e1) = e0 % 188.54/30.06 (12) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.06 all_250_23 = e0 % 188.54/30.06 (13) ~ (e4 = e0) % 188.54/30.06 (14) ~ (e4 = e3) % 188.54/30.06 (15) ~ (all_36_2 = e2) % 188.54/30.06 (16) ~ (all_40_2 = all_34_2) % 188.54/30.06 (17) ~ (all_244_24 = all_20_2) % 188.54/30.06 (18) op(e1, e4) = e0 % 188.54/30.06 (19) ~ (all_20_2 = e3) % 188.54/30.06 (20) op(all_20_2, e4) = e1 % 188.54/30.06 (21) op(e0, e0) = all_244_24 % 188.54/30.06 (22) op(e0, e1) = all_20_2 % 188.54/30.06 (23) all_252_19 = e4 % 188.54/30.06 (24) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.06 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.06 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.06 (25) ~ (all_20_2 = e0) % 188.54/30.06 (26) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.06 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.06 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.06 (27) ~ (all_20_2 = e2) % 188.54/30.06 (28) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.06 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.06 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.06 (29) op(e0, e4) = e2 % 188.54/30.06 (30) ~ (e3 = e0) % 188.54/30.06 (31) ~ (all_20_2 = all_8_1) % 188.54/30.06 (32) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.06 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.06 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.06 (33) all_252_10 = e0 % 188.54/30.06 (34) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.06 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.06 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.06 (35) ~ (e3 = e2) % 188.54/30.06 (36) op(e4, all_20_2) = e0 % 188.54/30.06 (37) op(e0, e3) = all_8_1 % 188.54/30.06 (38) ~ (e4 = e2) % 188.54/30.06 (39) op(e2, e0) = all_40_2 % 188.54/30.06 (40) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.06 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.06 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.06 (41) all_250_23 = all_20_2 % 188.54/30.06 (42) ~ (e2 = e0) % 188.54/30.06 (43) op(e1, e0) = all_34_2 % 188.54/30.06 (44) ~ (all_34_2 = e2) % 188.54/30.06 (45) op(e2, e0) = e1 % 188.54/30.06 % 188.54/30.06 Begin of proof % 188.54/30.06 | % 188.54/30.06 | BETA: splitting (12) gives: % 188.54/30.06 | % 188.54/30.06 | Case 1: % 188.54/30.06 | | % 188.54/30.06 | | (46) all_250_23 = e4 % 188.54/30.06 | | % 188.54/30.06 | | REF_CLOSE: (3), (41), (46) are inconsistent by sub-proof #489. % 188.54/30.06 | | % 188.54/30.06 | Case 2: % 188.54/30.06 | | % 188.54/30.06 | | (47) ~ (all_250_23 = e4) % 188.54/30.06 | | (48) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 188.54/30.06 | | e0 % 188.54/30.06 | | % 188.54/30.06 | | BETA: splitting (48) gives: % 188.54/30.06 | | % 188.54/30.06 | | Case 1: % 188.54/30.06 | | | % 188.54/30.06 | | | (49) all_250_23 = e3 % 188.54/30.06 | | | % 188.54/30.06 | | | REF_CLOSE: (19), (41), (49) are inconsistent by sub-proof #488. % 188.54/30.06 | | | % 188.54/30.06 | | Case 2: % 188.54/30.06 | | | % 188.54/30.06 | | | (50) ~ (all_250_23 = e3) % 188.54/30.06 | | | (51) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.06 | | | % 188.54/30.06 | | | BETA: splitting (28) gives: % 188.54/30.06 | | | % 188.54/30.06 | | | Case 1: % 188.54/30.06 | | | | % 188.54/30.06 | | | | (52) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, % 188.54/30.06 | | | | e1) = e4) % 188.54/30.06 | | | | % 188.54/30.06 | | | | BETA: splitting (52) gives: % 188.54/30.07 | | | | % 188.54/30.07 | | | | Case 1: % 188.54/30.07 | | | | | % 188.54/30.07 | | | | | (53) all_252_9 = e4 & op(e4, e1) = e4 % 188.54/30.07 | | | | | % 188.54/30.07 | | | | | ALPHA: (53) implies: % 188.54/30.07 | | | | | (54) all_252_9 = e4 % 188.54/30.07 | | | | | % 188.54/30.07 | | | | | BETA: splitting (10) gives: % 188.54/30.07 | | | | | % 188.54/30.07 | | | | | Case 1: % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | | (55) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & % 188.54/30.07 | | | | | | op(e3, e1) = e3) % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | | BETA: splitting (55) gives: % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | | Case 1: % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | (56) all_252_9 = e3 & op(e4, e1) = e3 % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | REF_CLOSE: (14), (54), (56) are inconsistent by sub-proof #398. % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | Case 2: % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | (57) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | REF_CLOSE: (30), (33), (57) are inconsistent by sub-proof #59. % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | End of split % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | Case 2: % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | | (58) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 188.54/30.07 | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | | BETA: splitting (58) gives: % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | | Case 1: % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | (59) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | REF_CLOSE: (9), (35), (59) are inconsistent by sub-proof #356. % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | Case 2: % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | (60) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 188.54/30.07 | | | | | | | op(e0, e1) = e3) % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | BETA: splitting (60) gives: % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | (61) all_252_15 = e3 & op(e1, e1) = e3 % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | ALPHA: (61) implies: % 188.54/30.07 | | | | | | | | (62) all_252_15 = e3 % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | BETA: splitting (51) gives: % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | | (63) all_250_23 = e2 % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | | REF_CLOSE: (27), (41), (63) are inconsistent by sub-proof % 188.54/30.07 | | | | | | | | | #487. % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | | (64) ~ (all_250_23 = e2) % 188.54/30.07 | | | | | | | | | (65) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | | BETA: splitting (65) gives: % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | (66) all_250_23 = e1 % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | COMBINE_EQS: (41), (66) imply: % 188.54/30.07 | | | | | | | | | | (67) all_20_2 = e1 % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | SIMP: (67) implies: % 188.54/30.07 | | | | | | | | | | (68) all_20_2 = e1 % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REDUCE: (3), (68) imply: % 188.54/30.07 | | | | | | | | | | (69) ~ (e4 = e1) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | SIMP: (69) implies: % 188.54/30.07 | | | | | | | | | | (70) ~ (e4 = e1) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REDUCE: (19), (68) imply: % 188.54/30.07 | | | | | | | | | | (71) ~ (e3 = e1) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | SIMP: (71) implies: % 188.54/30.07 | | | | | | | | | | (72) ~ (e3 = e1) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REDUCE: (27), (68) imply: % 188.54/30.07 | | | | | | | | | | (73) ~ (e2 = e1) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | SIMP: (73) implies: % 188.54/30.07 | | | | | | | | | | (74) ~ (e2 = e1) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REDUCE: (25), (68) imply: % 188.54/30.07 | | | | | | | | | | (75) ~ (e1 = e0) % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REDUCE: (20), (68) imply: % 188.54/30.07 | | | | | | | | | | (76) op(e1, e4) = e1 % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REDUCE: (36), (68) imply: % 188.54/30.07 | | | | | | | | | | (77) op(e4, e1) = e0 % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | BETA: splitting (34) gives: % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | (78) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 188.54/30.07 | | | | | | | | | | | e1 & op(e3, e1) = e1) % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | REF_CLOSE: (33), (54), (70), (75), (78) are inconsistent by % 188.54/30.07 | | | | | | | | | | | sub-proof #57. % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | (79) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 188.54/30.07 | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 188.54/30.07 | | | | | | | | | | | op(e0, e1) = e1) % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | BETA: splitting (79) gives: % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | (80) all_252_11 = e1 & op(e2, e1) = e1 % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | REF_CLOSE: (9), (74), (80) are inconsistent by sub-proof % 188.54/30.07 | | | | | | | | | | | | #357. % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | (81) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 188.54/30.07 | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | BETA: splitting (81) gives: % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | (82) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | REF_CLOSE: (62), (72), (82) are inconsistent by sub-proof % 188.54/30.07 | | | | | | | | | | | | | #123. % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | (83) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | ALPHA: (83) implies: % 188.54/30.07 | | | | | | | | | | | | | (84) all_252_23 = e1 % 188.54/30.07 | | | | | | | | | | | | | (85) op(e0, e1) = e1 % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | BETA: splitting (26) gives: % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | (86) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 188.54/30.07 | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | BETA: splitting (86) gives: % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | (87) all_252_12 = e2 & op(e1, e4) = e2 % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.54/30.07 | | | | | | | | | | | | | | | (13), (14), (15), (17), (18), (19), (21), (22), % 188.54/30.07 | | | | | | | | | | | | | | | (24), (25), (27), (28), (30), (31), (34), (35), % 188.54/30.07 | | | | | | | | | | | | | | | (37), (38), (41), (42), (65), (70), (72), (74), % 188.54/30.07 | | | | | | | | | | | | | | | (75), (76), (77), (85), (87) are inconsistent by % 188.54/30.07 | | | | | | | | | | | | | | | sub-proof #183. % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | (88) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | ALPHA: (88) implies: % 188.54/30.07 | | | | | | | | | | | | | | | (89) all_252_13 = e2 % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.07 | | | | | | | | | | | | | | | (11), (13), (14), (15), (16), (17), (18), (19), % 188.54/30.07 | | | | | | | | | | | | | | | (21), (22), (24), (25), (27), (28), (30), (31), % 188.54/30.07 | | | | | | | | | | | | | | | (34), (35), (37), (38), (39), (40), (41), (42), % 188.54/30.07 | | | | | | | | | | | | | | | (43), (45), (62), (65), (70), (72), (74), (75), % 188.54/30.07 | | | | | | | | | | | | | | | (76), (77), (84), (85), (89) are inconsistent by % 188.54/30.07 | | | | | | | | | | | | | | | sub-proof #121. % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | (90) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 188.54/30.07 | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 188.54/30.07 | | | | | | | | | | | | | | op(e1, e0) = e2) % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | BETA: splitting (90) gives: % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | (91) all_252_14 = e2 & op(e1, e2) = e2 % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | ALPHA: (91) implies: % 188.54/30.07 | | | | | | | | | | | | | | | (92) all_252_14 = e2 % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.07 | | | | | | | | | | | | | | | (11), (13), (14), (15), (16), (17), (18), (19), % 188.54/30.07 | | | | | | | | | | | | | | | (20), (21), (22), (24), (25), (27), (28), (30), % 188.54/30.07 | | | | | | | | | | | | | | | (31), (34), (35), (36), (37), (38), (39), (40), % 188.54/30.07 | | | | | | | | | | | | | | | (41), (42), (43), (45), (51), (62), (84), (92) are % 188.54/30.07 | | | | | | | | | | | | | | | inconsistent by sub-proof #64. % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | (93) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 188.54/30.07 | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | BETA: splitting (93) gives: % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | Case 1: % 188.54/30.07 | | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | | (94) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.07 | | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (62), (94) are inconsistent by sub-proof % 188.54/30.07 | | | | | | | | | | | | | | | | #202. % 188.54/30.07 | | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | | (95) all_252_19 = e2 & op(e1, e0) = e2 % 188.54/30.07 | | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (43), (44), (95) are inconsistent by % 188.54/30.07 | | | | | | | | | | | | | | | | sub-proof #438. % 188.54/30.07 | | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | (96) all_250_23 = e0 % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | | REF_CLOSE: (25), (41), (96) are inconsistent by sub-proof % 188.54/30.07 | | | | | | | | | | #486. % 188.54/30.07 | | | | | | | | | | % 188.54/30.07 | | | | | | | | | End of split % 188.54/30.07 | | | | | | | | | % 188.54/30.07 | | | | | | | | End of split % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | Case 2: % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | (97) all_252_23 = e3 & op(e0, e1) = e3 % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | ALPHA: (97) implies: % 188.54/30.07 | | | | | | | | (98) op(e0, e1) = e3 % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | | REF_CLOSE: (2), (19), (22), (98) are inconsistent by sub-proof % 188.54/30.07 | | | | | | | | #508. % 188.54/30.07 | | | | | | | | % 188.54/30.07 | | | | | | | End of split % 188.54/30.07 | | | | | | | % 188.54/30.07 | | | | | | End of split % 188.54/30.07 | | | | | | % 188.54/30.07 | | | | | End of split % 188.54/30.07 | | | | | % 188.54/30.07 | | | | Case 2: % 188.54/30.07 | | | | | % 188.54/30.07 | | | | | (99) all_252_10 = e4 & op(e3, e1) = e4 % 188.54/30.07 | | | | | % 188.54/30.07 | | | | | REF_CLOSE: (13), (33), (99) are inconsistent by sub-proof #91. % 188.54/30.07 | | | | | % 188.54/30.07 | | | | End of split % 188.54/30.07 | | | | % 188.54/30.07 | | | Case 2: % 188.54/30.07 | | | | % 188.54/30.07 | | | | (100) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, % 188.54/30.07 | | | | e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.07 | | | | % 188.54/30.07 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (13), (14), % 188.54/30.07 | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 188.54/30.07 | | | | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), % 188.54/30.07 | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 188.54/30.07 | | | | (51), (100) are inconsistent by sub-proof #116. % 188.54/30.07 | | | | % 188.54/30.07 | | | End of split % 188.54/30.07 | | | % 188.54/30.07 | | End of split % 188.54/30.07 | | % 188.54/30.07 | End of split % 188.54/30.07 | % 188.54/30.07 End of proof % 188.54/30.07 % 188.54/30.07 Sub-proof #57 shows that the following formulas are inconsistent: % 188.54/30.07 ---------------------------------------------------------------- % 188.54/30.07 (1) all_252_10 = e0 % 188.54/30.07 (2) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.07 (3) ~ (e1 = e0) % 188.54/30.07 (4) all_252_9 = e4 % 188.54/30.07 (5) ~ (e4 = e1) % 188.54/30.07 % 188.54/30.07 Begin of proof % 188.54/30.07 | % 188.54/30.07 | BETA: splitting (2) gives: % 188.54/30.07 | % 188.54/30.07 | Case 1: % 188.54/30.07 | | % 188.54/30.07 | | (6) all_252_9 = e1 & op(e4, e1) = e1 % 188.54/30.07 | | % 188.54/30.07 | | ALPHA: (6) implies: % 188.54/30.07 | | (7) all_252_9 = e1 % 188.54/30.07 | | % 188.54/30.07 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #204. % 188.54/30.07 | | % 188.54/30.07 | Case 2: % 188.54/30.07 | | % 188.54/30.07 | | (8) all_252_10 = e1 & op(e3, e1) = e1 % 188.54/30.07 | | % 188.54/30.07 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #58. % 188.54/30.07 | | % 188.54/30.07 | End of split % 188.54/30.07 | % 188.54/30.07 End of proof % 188.54/30.07 % 188.54/30.07 Sub-proof #58 shows that the following formulas are inconsistent: % 188.54/30.07 ---------------------------------------------------------------- % 188.54/30.07 (1) all_252_10 = e1 & op(e3, e1) = e1 % 188.54/30.07 (2) all_252_10 = e0 % 188.54/30.07 (3) ~ (e1 = e0) % 188.54/30.07 % 188.54/30.07 Begin of proof % 188.54/30.07 | % 188.54/30.07 | ALPHA: (1) implies: % 188.54/30.07 | (4) all_252_10 = e1 % 188.54/30.07 | % 188.54/30.07 | COMBINE_EQS: (2), (4) imply: % 188.54/30.07 | (5) e1 = e0 % 188.54/30.07 | % 188.54/30.07 | REDUCE: (3), (5) imply: % 188.54/30.07 | (6) $false % 188.54/30.07 | % 188.54/30.07 | CLOSE: (6) is inconsistent. % 188.54/30.07 | % 188.54/30.07 End of proof % 188.54/30.07 % 188.54/30.07 Sub-proof #59 shows that the following formulas are inconsistent: % 188.54/30.07 ---------------------------------------------------------------- % 188.54/30.07 (1) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.07 (2) all_252_10 = e0 % 188.54/30.07 (3) ~ (e3 = e0) % 188.54/30.07 % 188.54/30.07 Begin of proof % 188.54/30.07 | % 188.54/30.07 | ALPHA: (1) implies: % 188.54/30.07 | (4) all_252_10 = e3 % 188.54/30.07 | % 188.54/30.07 | COMBINE_EQS: (2), (4) imply: % 188.54/30.07 | (5) e3 = e0 % 188.54/30.07 | % 188.54/30.07 | REDUCE: (3), (5) imply: % 188.54/30.07 | (6) $false % 188.54/30.07 | % 188.54/30.07 | CLOSE: (6) is inconsistent. % 188.54/30.07 | % 188.54/30.07 End of proof % 188.54/30.07 % 188.54/30.07 Sub-proof #60 shows that the following formulas are inconsistent: % 188.54/30.07 ---------------------------------------------------------------- % 188.54/30.07 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.54/30.07 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.54/30.07 (all_252_16 = e1 & op(e4, e0) = e1) % 188.54/30.07 (2) all_252_20 = e2 % 188.54/30.07 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.07 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.07 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.07 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.07 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.07 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.07 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.07 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.07 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.07 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.07 (7) ~ (all_20_2 = e4) % 188.54/30.07 (8) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) | % 188.54/30.07 (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 188.54/30.07 | (all_252_21 = e0 & op(e0, e3) = e0) % 188.54/30.07 (9) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.07 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.07 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.07 (10) op(e0, e2) = e4 % 188.54/30.07 (11) op(e0, e2) = all_28_2 % 188.54/30.07 (12) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) % 188.54/30.07 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) = % 188.54/30.07 e0) | (all_252_18 = e0 & op(e2, e0) = e0) % 188.54/30.07 (13) op(e3, e1) = all_36_2 % 188.54/30.07 (14) ~ (all_40_2 = e2) % 188.54/30.07 (15) ~ (e2 = e1) % 188.54/30.07 (16) ~ (all_62_2 = e0) % 188.54/30.07 (17) all_252_12 = e0 % 188.54/30.07 (18) op(e4, e1) = e0 % 188.54/30.07 (19) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.07 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.07 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.07 (20) op(e1, e3) = all_62_2 % 188.54/30.07 (21) op(e2, e1) = e0 % 188.54/30.07 (22) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 188.54/30.07 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = % 188.54/30.07 e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 188.54/30.07 (23) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.07 all_250_23 = e0 % 188.54/30.07 (24) ~ (e4 = e0) % 188.54/30.07 (25) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.54/30.07 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.54/30.07 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.54/30.07 (26) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.07 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.07 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.07 (27) ~ (e4 = e3) % 188.54/30.07 (28) ~ (all_36_2 = e2) % 188.54/30.07 (29) all_252_9 = e0 % 188.54/30.07 (30) ~ (all_40_2 = all_34_2) % 188.54/30.07 (31) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.54/30.07 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.54/30.07 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.54/30.07 (32) ~ (all_244_24 = all_20_2) % 188.54/30.07 (33) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.54/30.07 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.54/30.07 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.54/30.07 (34) op(e1, e4) = e0 % 188.54/30.07 (35) ~ (all_6_2 = e4) % 188.54/30.07 (36) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.54/30.07 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.54/30.07 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.54/30.07 (37) ~ (all_20_2 = e3) % 188.54/30.07 (38) op(all_20_2, e4) = e1 % 188.54/30.07 (39) op(e0, e0) = all_244_24 % 188.54/30.07 (40) op(e0, e1) = all_20_2 % 188.54/30.07 (41) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.07 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.07 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.07 (42) all_252_19 = e4 % 188.54/30.07 (43) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.07 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.07 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.07 (44) ~ (all_8_1 = e2) % 188.54/30.07 (45) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.07 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.07 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.07 (46) ~ (all_20_2 = e0) % 188.54/30.07 (47) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.07 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.07 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.07 (48) all_252_17 = e2 % 188.54/30.07 (49) ~ (all_20_2 = e2) % 188.54/30.07 (50) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.07 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.07 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.07 (51) op(e4, e4) = all_244_0 % 188.54/30.07 (52) op(e0, e4) = e2 % 188.54/30.07 (53) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) % 188.54/30.07 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.54/30.07 e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.54/30.07 (54) ~ (e3 = e0) % 188.54/30.07 (55) ~ (all_20_2 = all_8_1) % 188.54/30.07 (56) ~ (all_28_2 = e0) % 188.54/30.07 (57) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.07 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.07 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.07 (58) ~ (all_244_0 = e2) % 188.54/30.07 (59) op(e2, all_40_2) = e0 % 188.54/30.07 (60) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.07 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.07 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.54/30.07 (61) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.07 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.07 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.07 (62) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.54/30.07 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.07 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.54/30.07 (63) ~ (e3 = e2) % 188.54/30.07 (64) all_252_22 = e4 % 188.54/30.07 (65) op(e4, all_20_2) = e0 % 188.54/30.07 (66) op(e0, e3) = all_8_1 % 188.54/30.07 (67) op(e2, e4) = all_64_2 % 188.54/30.07 (68) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.07 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.07 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.07 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.07 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.07 op(e0, e1) = e0))) % 188.54/30.07 (69) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.07 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.07 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.07 (70) ~ (e4 = e2) % 188.54/30.07 (71) op(e2, e0) = all_40_2 % 188.54/30.07 (72) op(all_28_2, all_40_2) = e2 % 188.54/30.07 (73) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.07 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.07 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.07 (74) ~ (e1 = e0) % 188.54/30.07 (75) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.07 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.07 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.07 (76) ~ (all_64_2 = e0) % 188.54/30.07 (77) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.54/30.08 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.54/30.08 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.08 (78) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.08 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.54/30.08 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.54/30.08 (79) op(e0, e4) = all_12_2 % 188.54/30.08 (80) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.54/30.08 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.54/30.08 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.54/30.08 (81) all_250_23 = all_20_2 % 188.54/30.08 (82) ~ (e3 = e1) % 188.54/30.08 (83) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.54/30.08 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.54/30.08 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.54/30.08 (84) ~ (e2 = e0) % 188.54/30.08 (85) op(e1, e0) = all_34_2 % 188.54/30.08 (86) ~ (all_12_2 = e3) % 188.54/30.08 (87) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.08 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.08 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.54/30.08 (88) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.08 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.08 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.08 (89) ~ (all_34_2 = e2) % 188.54/30.08 (90) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.08 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.08 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.08 (91) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.08 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.08 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.08 (92) op(e4, e2) = all_6_2 % 188.54/30.08 (93) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.54/30.08 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.54/30.08 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.54/30.08 (94) all_252_5 = e0 % 188.54/30.08 (95) ~ (e4 = e1) % 188.54/30.08 (96) op(e2, e0) = e1 % 188.54/30.08 % 188.54/30.08 Begin of proof % 188.54/30.08 | % 188.54/30.08 | BETA: splitting (12) gives: % 188.54/30.08 | % 188.54/30.08 | Case 1: % 188.54/30.08 | | % 188.54/30.08 | | (97) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = % 188.54/30.08 | | e0) % 188.54/30.08 | | % 188.54/30.08 | | BETA: splitting (97) gives: % 188.54/30.08 | | % 188.54/30.08 | | Case 1: % 188.54/30.08 | | | % 188.54/30.08 | | | (98) all_252_6 = e0 & op(e2, e4) = e0 % 188.54/30.08 | | | % 188.54/30.08 | | | ALPHA: (98) implies: % 188.54/30.08 | | | (99) op(e2, e4) = e0 % 188.54/30.08 | | | % 188.54/30.08 | | | REF_CLOSE: (6), (67), (76), (99) are inconsistent by sub-proof #382. % 188.54/30.08 | | | % 188.54/30.08 | | Case 2: % 188.54/30.08 | | | % 188.54/30.08 | | | (100) all_252_7 = e0 & op(e2, e3) = e0 % 188.54/30.08 | | | % 188.54/30.08 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), % 188.54/30.08 | | | (15), (17), (18), (19), (20), (21), (23), (24), (25), (26), % 188.54/30.08 | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.08 | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.08 | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 188.54/30.08 | | | (57), (58), (59), (60), (61), (62), (63), (64), (65), (66), % 188.54/30.08 | | | (68), (69), (70), (71), (72), (73), (74), (75), (77), (78), % 188.54/30.08 | | | (79), (80), (81), (82), (83), (84), (85), (86), (87), (88), % 188.54/30.08 | | | (89), (90), (91), (92), (93), (94), (95), (96), (100) are % 188.54/30.08 | | | inconsistent by sub-proof #75. % 188.54/30.08 | | | % 188.54/30.08 | | End of split % 188.54/30.08 | | % 188.54/30.08 | Case 2: % 188.54/30.08 | | % 188.54/30.08 | | (101) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_11 = e0 & op(e2, e1) % 188.54/30.08 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) % 188.54/30.08 | | % 188.54/30.08 | | BETA: splitting (101) gives: % 188.54/30.08 | | % 188.54/30.08 | | Case 1: % 188.54/30.08 | | | % 188.54/30.08 | | | (102) all_252_8 = e0 & op(e2, e2) = e0 % 188.54/30.08 | | | % 188.54/30.08 | | | ALPHA: (102) implies: % 188.54/30.08 | | | (103) all_252_8 = e0 % 188.54/30.08 | | | % 188.54/30.08 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 188.54/30.08 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 188.54/30.08 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 188.54/30.08 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 188.54/30.08 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), % 188.54/30.08 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.08 | | | (64), (65), (66), (68), (69), (70), (71), (72), (73), (74), % 188.54/30.08 | | | (75), (77), (78), (79), (80), (81), (82), (83), (84), (85), % 188.54/30.08 | | | (86), (87), (88), (89), (90), (91), (92), (93), (94), (95), % 188.54/30.08 | | | (96), (103) are inconsistent by sub-proof #63. % 188.54/30.08 | | | % 188.54/30.08 | | Case 2: % 188.54/30.08 | | | % 188.54/30.08 | | | (104) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_18 = e0 & op(e2, % 188.54/30.08 | | | e0) = e0) % 188.54/30.08 | | | % 188.54/30.08 | | | BETA: splitting (104) gives: % 188.54/30.08 | | | % 188.54/30.08 | | | Case 1: % 188.54/30.08 | | | | % 188.54/30.08 | | | | (105) all_252_11 = e0 & op(e2, e1) = e0 % 188.54/30.08 | | | | % 188.54/30.08 | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (19), (23), (24), (27), (28), % 188.54/30.08 | | | | (32), (34), (37), (38), (39), (40), (43), (46), (49), (50), % 188.54/30.08 | | | | (54), (55), (61), (63), (65), (66), (70), (81), (84), (105) % 188.54/30.08 | | | | are inconsistent by sub-proof #62. % 188.54/30.08 | | | | % 188.54/30.08 | | | Case 2: % 188.54/30.08 | | | | % 188.54/30.08 | | | | (106) all_252_18 = e0 & op(e2, e0) = e0 % 188.54/30.08 | | | | % 188.54/30.08 | | | | ALPHA: (106) implies: % 188.54/30.08 | | | | (107) all_252_18 = e0 % 188.54/30.08 | | | | % 188.54/30.08 | | | | BETA: splitting (45) gives: % 188.54/30.08 | | | | % 188.54/30.08 | | | | Case 1: % 188.54/30.08 | | | | | % 188.54/30.08 | | | | | (108) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & % 188.54/30.08 | | | | | op(e3, e0) = e3) % 188.54/30.08 | | | | | % 188.54/30.08 | | | | | BETA: splitting (108) gives: % 188.54/30.08 | | | | | % 188.54/30.08 | | | | | Case 1: % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | (109) all_252_16 = e3 & op(e4, e0) = e3 % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | ALPHA: (109) implies: % 188.54/30.08 | | | | | | (110) op(e4, e0) = e3 % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | REF_CLOSE: (6), (7), (15), (23), (26), (30), (32), (37), (39), (46), % 188.54/30.08 | | | | | | (48), (49), (71), (74), (81), (82), (85), (96), (107), % 188.54/30.08 | | | | | | (110) are inconsistent by sub-proof #141. % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | Case 2: % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | (111) all_252_17 = e3 & op(e3, e0) = e3 % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | REF_CLOSE: (48), (63), (111) are inconsistent by sub-proof #159. % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | End of split % 188.54/30.08 | | | | | % 188.54/30.08 | | | | Case 2: % 188.54/30.08 | | | | | % 188.54/30.08 | | | | | (112) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & % 188.54/30.08 | | | | | op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.08 | | | | | % 188.54/30.08 | | | | | BETA: splitting (112) gives: % 188.54/30.08 | | | | | % 188.54/30.08 | | | | | Case 1: % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | (113) all_252_18 = e3 & op(e2, e0) = e3 % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | REF_CLOSE: (54), (107), (113) are inconsistent by sub-proof #61. % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | Case 2: % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | (114) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 188.54/30.08 | | | | | | op(e0, e0) = e3) % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | BETA: splitting (114) gives: % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | | Case 1: % 188.54/30.08 | | | | | | | % 188.54/30.08 | | | | | | | (115) all_252_19 = e3 & op(e1, e0) = e3 % 188.54/30.08 | | | | | | | % 188.54/30.08 | | | | | | | REF_CLOSE: (27), (42), (115) are inconsistent by sub-proof #177. % 188.54/30.08 | | | | | | | % 188.54/30.08 | | | | | | Case 2: % 188.54/30.08 | | | | | | | % 188.54/30.08 | | | | | | | (116) all_252_24 = e3 & op(e0, e0) = e3 % 188.54/30.08 | | | | | | | % 188.54/30.08 | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (13), (17), (19), (21), (23), % 188.54/30.08 | | | | | | | (24), (27), (28), (29), (30), (32), (34), (37), (38), % 188.54/30.08 | | | | | | | (39), (40), (42), (43), (46), (47), (49), (50), (52), % 188.54/30.08 | | | | | | | (54), (55), (57), (61), (63), (64), (65), (66), (68), % 188.54/30.08 | | | | | | | (70), (71), (73), (81), (84), (85), (89), (96), (116) % 188.54/30.08 | | | | | | | are inconsistent by sub-proof #169. % 188.54/30.08 | | | | | | | % 188.54/30.08 | | | | | | End of split % 188.54/30.08 | | | | | | % 188.54/30.08 | | | | | End of split % 188.54/30.08 | | | | | % 188.54/30.08 | | | | End of split % 188.54/30.08 | | | | % 188.54/30.08 | | | End of split % 188.54/30.08 | | | % 188.54/30.08 | | End of split % 188.54/30.08 | | % 188.54/30.08 | End of split % 188.54/30.08 | % 188.54/30.08 End of proof % 188.54/30.08 % 188.54/30.08 Sub-proof #61 shows that the following formulas are inconsistent: % 188.54/30.08 ---------------------------------------------------------------- % 188.54/30.08 (1) all_252_18 = e3 & op(e2, e0) = e3 % 188.54/30.08 (2) all_252_18 = e0 % 188.54/30.08 (3) ~ (e3 = e0) % 188.54/30.08 % 188.54/30.08 Begin of proof % 188.54/30.08 | % 188.54/30.08 | ALPHA: (1) implies: % 188.54/30.08 | (4) all_252_18 = e3 % 188.54/30.08 | % 188.54/30.08 | COMBINE_EQS: (2), (4) imply: % 188.54/30.08 | (5) e3 = e0 % 188.54/30.08 | % 188.54/30.08 | REDUCE: (3), (5) imply: % 188.54/30.08 | (6) $false % 188.54/30.08 | % 188.54/30.08 | CLOSE: (6) is inconsistent. % 188.54/30.08 | % 188.54/30.08 End of proof % 188.54/30.08 % 188.54/30.08 Sub-proof #62 shows that the following formulas are inconsistent: % 188.54/30.08 ---------------------------------------------------------------- % 188.54/30.08 (1) all_252_20 = e2 % 188.54/30.08 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.08 (3) ~ (all_20_2 = e4) % 188.54/30.08 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.08 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.08 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.08 (5) op(e0, e2) = e4 % 188.54/30.08 (6) op(e3, e1) = all_36_2 % 188.54/30.08 (7) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.08 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.08 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.08 (8) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.08 all_250_23 = e0 % 188.54/30.08 (9) ~ (e4 = e0) % 188.54/30.08 (10) ~ (e4 = e3) % 188.54/30.08 (11) ~ (all_36_2 = e2) % 188.54/30.08 (12) ~ (all_244_24 = all_20_2) % 188.54/30.08 (13) all_252_11 = e0 & op(e2, e1) = e0 % 188.54/30.08 (14) op(e1, e4) = e0 % 188.54/30.08 (15) ~ (all_20_2 = e3) % 188.54/30.08 (16) op(all_20_2, e4) = e1 % 188.54/30.08 (17) op(e0, e0) = all_244_24 % 188.54/30.08 (18) op(e0, e1) = all_20_2 % 188.54/30.08 (19) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.08 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.08 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.08 (20) ~ (all_20_2 = e0) % 188.54/30.08 (21) ~ (all_20_2 = e2) % 188.54/30.08 (22) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.08 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.08 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.08 (23) ~ (e3 = e0) % 188.54/30.08 (24) ~ (all_20_2 = all_8_1) % 188.54/30.08 (25) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.08 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.08 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.08 (26) ~ (e3 = e2) % 188.54/30.08 (27) op(e4, all_20_2) = e0 % 188.54/30.08 (28) op(e0, e3) = all_8_1 % 188.54/30.08 (29) ~ (e4 = e2) % 188.54/30.08 (30) all_250_23 = all_20_2 % 188.54/30.08 (31) ~ (e2 = e0) % 188.54/30.08 % 188.54/30.08 Begin of proof % 188.54/30.08 | % 188.54/30.08 | ALPHA: (13) implies: % 188.54/30.08 | (32) all_252_11 = e0 % 188.54/30.08 | % 188.54/30.08 | BETA: splitting (8) gives: % 188.54/30.08 | % 188.54/30.08 | Case 1: % 188.54/30.08 | | % 188.54/30.08 | | (33) all_250_23 = e4 % 188.54/30.08 | | % 188.54/30.08 | | REF_CLOSE: (3), (30), (33) are inconsistent by sub-proof #489. % 188.54/30.08 | | % 188.54/30.08 | Case 2: % 188.54/30.08 | | % 188.54/30.08 | | (34) ~ (all_250_23 = e4) % 188.54/30.08 | | (35) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 188.54/30.08 | | e0 % 188.54/30.08 | | % 188.54/30.08 | | BETA: splitting (35) gives: % 188.54/30.08 | | % 188.54/30.08 | | Case 1: % 188.54/30.08 | | | % 188.54/30.08 | | | (36) all_250_23 = e3 % 188.54/30.08 | | | % 188.54/30.08 | | | REF_CLOSE: (15), (30), (36) are inconsistent by sub-proof #488. % 188.54/30.08 | | | % 188.54/30.08 | | Case 2: % 188.54/30.08 | | | % 188.54/30.08 | | | (37) ~ (all_250_23 = e3) % 188.54/30.08 | | | (38) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.08 | | | % 188.54/30.08 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14), % 188.54/30.08 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 188.54/30.08 | | | (25), (26), (27), (28), (29), (30), (31), (32), (38) are % 188.54/30.08 | | | inconsistent by sub-proof #126. % 188.54/30.08 | | | % 188.54/30.08 | | End of split % 188.54/30.08 | | % 188.54/30.08 | End of split % 188.54/30.08 | % 188.54/30.08 End of proof % 188.54/30.08 % 188.54/30.08 Sub-proof #63 shows that the following formulas are inconsistent: % 188.54/30.08 ---------------------------------------------------------------- % 188.54/30.08 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.54/30.08 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.54/30.08 (all_252_16 = e1 & op(e4, e0) = e1) % 188.54/30.08 (2) all_252_20 = e2 % 188.54/30.08 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.08 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.08 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.08 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.08 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.08 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.08 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.08 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.08 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.08 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.08 (7) ~ (all_20_2 = e4) % 188.54/30.08 (8) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) | % 188.54/30.08 (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 188.54/30.08 | (all_252_21 = e0 & op(e0, e3) = e0) % 188.54/30.08 (9) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.08 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.08 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.08 (10) op(e0, e2) = e4 % 188.54/30.08 (11) op(e0, e2) = all_28_2 % 188.54/30.08 (12) op(e3, e1) = all_36_2 % 188.54/30.08 (13) ~ (all_40_2 = e2) % 188.54/30.08 (14) ~ (e2 = e1) % 188.54/30.08 (15) ~ (all_62_2 = e0) % 188.54/30.08 (16) all_252_12 = e0 % 188.54/30.08 (17) op(e4, e1) = e0 % 188.54/30.08 (18) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.08 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.08 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.08 (19) op(e1, e3) = all_62_2 % 188.54/30.08 (20) op(e2, e1) = e0 % 188.54/30.08 (21) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 188.54/30.08 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = e1 & op(e2, e1) = % 188.54/30.08 e1) | (all_252_18 = e1 & op(e2, e0) = e1) % 188.54/30.08 (22) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.08 all_250_23 = e0 % 188.54/30.08 (23) ~ (e4 = e0) % 188.54/30.08 (24) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.54/30.08 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.54/30.08 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.54/30.08 (25) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.08 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.08 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.08 (26) ~ (e4 = e3) % 188.54/30.08 (27) ~ (all_36_2 = e2) % 188.54/30.08 (28) all_252_9 = e0 % 188.54/30.08 (29) ~ (all_40_2 = all_34_2) % 188.54/30.08 (30) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.54/30.08 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.54/30.08 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.54/30.08 (31) ~ (all_244_24 = all_20_2) % 188.54/30.08 (32) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.54/30.08 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.54/30.08 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.54/30.08 (33) op(e1, e4) = e0 % 188.54/30.08 (34) ~ (all_6_2 = e4) % 188.54/30.08 (35) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.54/30.08 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.54/30.08 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.54/30.08 (36) ~ (all_20_2 = e3) % 188.54/30.08 (37) op(all_20_2, e4) = e1 % 188.54/30.08 (38) op(e0, e0) = all_244_24 % 188.54/30.08 (39) op(e0, e1) = all_20_2 % 188.54/30.08 (40) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.08 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.08 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.08 (41) all_252_19 = e4 % 188.54/30.08 (42) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.08 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.08 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.08 (43) ~ (all_8_1 = e2) % 188.54/30.08 (44) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.08 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.08 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.08 (45) ~ (all_20_2 = e0) % 188.54/30.08 (46) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.08 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.08 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.08 (47) all_252_17 = e2 % 188.54/30.08 (48) ~ (all_20_2 = e2) % 188.54/30.08 (49) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.08 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.08 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.08 (50) op(e4, e4) = all_244_0 % 188.54/30.08 (51) op(e0, e4) = e2 % 188.54/30.08 (52) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) % 188.54/30.08 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.54/30.08 e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.54/30.08 (53) ~ (e3 = e0) % 188.54/30.08 (54) ~ (all_20_2 = all_8_1) % 188.54/30.08 (55) all_252_8 = e0 % 188.54/30.08 (56) ~ (all_28_2 = e0) % 188.54/30.08 (57) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.08 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.08 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.08 (58) ~ (all_244_0 = e2) % 188.54/30.09 (59) op(e2, all_40_2) = e0 % 188.54/30.09 (60) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.09 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.09 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.54/30.09 (61) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.09 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.09 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.09 (62) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.54/30.09 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.09 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.54/30.09 (63) ~ (e3 = e2) % 188.54/30.09 (64) all_252_22 = e4 % 188.54/30.09 (65) op(e4, all_20_2) = e0 % 188.54/30.09 (66) op(e0, e3) = all_8_1 % 188.54/30.09 (67) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.09 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.09 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.09 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.09 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.09 op(e0, e1) = e0))) % 188.54/30.09 (68) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.09 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.09 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.09 (69) ~ (e4 = e2) % 188.54/30.09 (70) op(e2, e0) = all_40_2 % 188.54/30.09 (71) op(all_28_2, all_40_2) = e2 % 188.54/30.09 (72) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.09 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.09 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.09 (73) ~ (e1 = e0) % 188.54/30.09 (74) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.09 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.09 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.09 (75) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.54/30.09 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.54/30.09 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.09 (76) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.09 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.54/30.09 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.54/30.09 (77) op(e0, e4) = all_12_2 % 188.54/30.09 (78) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.54/30.09 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.54/30.09 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.54/30.09 (79) all_250_23 = all_20_2 % 188.54/30.09 (80) ~ (e3 = e1) % 188.54/30.09 (81) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.54/30.09 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.54/30.09 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.54/30.09 (82) ~ (e2 = e0) % 188.54/30.09 (83) op(e1, e0) = all_34_2 % 188.54/30.09 (84) ~ (all_12_2 = e3) % 188.54/30.09 (85) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.09 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.09 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.54/30.09 (86) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.09 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.09 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.09 (87) ~ (all_34_2 = e2) % 188.54/30.09 (88) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.09 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.09 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.09 (89) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.09 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.09 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.09 (90) op(e4, e2) = all_6_2 % 188.54/30.09 (91) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.54/30.09 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.54/30.09 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.54/30.09 (92) all_252_5 = e0 % 188.54/30.09 (93) ~ (e4 = e1) % 188.54/30.09 (94) op(e2, e0) = e1 % 188.54/30.09 % 188.54/30.09 Begin of proof % 188.54/30.09 | % 188.54/30.09 | BETA: splitting (52) gives: % 188.54/30.09 | % 188.54/30.09 | Case 1: % 188.54/30.09 | | % 188.54/30.09 | | (95) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = % 188.54/30.09 | | e2) % 188.54/30.09 | | % 188.54/30.09 | | BETA: splitting (95) gives: % 188.54/30.09 | | % 188.54/30.09 | | Case 1: % 188.54/30.09 | | | % 188.54/30.09 | | | (96) all_252_6 = e2 & op(e2, e4) = e2 % 188.54/30.09 | | | % 188.54/30.09 | | | ALPHA: (96) implies: % 188.54/30.09 | | | (97) all_252_6 = e2 % 188.54/30.09 | | | % 188.54/30.09 | | | REF_CLOSE: (2), (3), (4), (6), (14), (16), (23), (26), (51), (53), (63), % 188.54/30.09 | | | (68), (69), (73), (77), (80), (82), (84), (86), (93), (97) are % 188.54/30.09 | | | inconsistent by sub-proof #223. % 188.54/30.09 | | | % 188.54/30.09 | | Case 2: % 188.54/30.09 | | | % 188.54/30.09 | | | (98) all_252_7 = e2 & op(e2, e3) = e2 % 188.54/30.09 | | | % 188.54/30.09 | | | ALPHA: (98) implies: % 188.54/30.09 | | | (99) all_252_7 = e2 % 188.54/30.09 | | | % 188.54/30.09 | | | BETA: splitting (22) gives: % 188.54/30.09 | | | % 188.54/30.09 | | | Case 1: % 188.54/30.09 | | | | % 188.54/30.09 | | | | (100) all_250_23 = e4 % 188.54/30.09 | | | | % 188.54/30.09 | | | | REF_CLOSE: (7), (79), (100) are inconsistent by sub-proof #489. % 188.54/30.09 | | | | % 188.54/30.09 | | | Case 2: % 188.54/30.09 | | | | % 188.54/30.09 | | | | (101) ~ (all_250_23 = e4) % 188.54/30.09 | | | | (102) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.09 | | | | all_250_23 = e0 % 188.54/30.09 | | | | % 188.54/30.09 | | | | BETA: splitting (102) gives: % 188.54/30.09 | | | | % 188.54/30.09 | | | | Case 1: % 188.54/30.09 | | | | | % 188.54/30.09 | | | | | (103) all_250_23 = e3 % 188.54/30.09 | | | | | % 188.54/30.09 | | | | | REF_CLOSE: (36), (79), (103) are inconsistent by sub-proof #488. % 188.54/30.09 | | | | | % 188.54/30.09 | | | | Case 2: % 188.54/30.09 | | | | | % 188.54/30.09 | | | | | (104) ~ (all_250_23 = e3) % 188.54/30.09 | | | | | (105) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.09 | | | | | % 188.54/30.09 | | | | | BETA: splitting (105) gives: % 188.54/30.09 | | | | | % 188.54/30.09 | | | | | Case 1: % 188.54/30.09 | | | | | | % 188.54/30.09 | | | | | | (106) all_250_23 = e2 % 188.54/30.09 | | | | | | % 188.54/30.09 | | | | | | REF_CLOSE: (48), (79), (106) are inconsistent by sub-proof #487. % 188.54/30.09 | | | | | | % 188.54/30.09 | | | | | Case 2: % 188.54/30.09 | | | | | | % 188.54/30.09 | | | | | | (107) ~ (all_250_23 = e2) % 188.54/30.09 | | | | | | (108) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.09 | | | | | | % 188.54/30.09 | | | | | | BETA: splitting (108) gives: % 188.54/30.09 | | | | | | % 188.54/30.09 | | | | | | Case 1: % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | (109) all_250_23 = e1 % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | COMBINE_EQS: (79), (109) imply: % 188.54/30.09 | | | | | | | (110) all_20_2 = e1 % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | SIMP: (110) implies: % 188.54/30.09 | | | | | | | (111) all_20_2 = e1 % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (31), (111) imply: % 188.54/30.09 | | | | | | | (112) ~ (all_244_24 = e1) % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (54), (111) imply: % 188.54/30.09 | | | | | | | (113) ~ (all_8_1 = e1) % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | SIMP: (113) implies: % 188.54/30.09 | | | | | | | (114) ~ (all_8_1 = e1) % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (7), (111) imply: % 188.54/30.09 | | | | | | | (115) ~ (e4 = e1) % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (36), (111) imply: % 188.54/30.09 | | | | | | | (116) ~ (e3 = e1) % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (48), (111) imply: % 188.54/30.09 | | | | | | | (117) ~ (e2 = e1) % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (37), (111) imply: % 188.54/30.09 | | | | | | | (118) op(e1, e4) = e1 % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | REDUCE: (39), (111) imply: % 188.54/30.09 | | | | | | | (119) op(e0, e1) = e1 % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | BETA: splitting (49) gives: % 188.54/30.09 | | | | | | | % 188.54/30.09 | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | % 188.54/30.09 | | | | | | | | (120) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & % 188.54/30.09 | | | | | | | | op(e3, e1) = e4) % 188.54/30.09 | | | | | | | | % 188.54/30.09 | | | | | | | | BETA: splitting (120) gives: % 188.54/30.09 | | | | | | | | % 188.54/30.09 | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | | (121) all_252_9 = e4 & op(e4, e1) = e4 % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | | REF_CLOSE: (23), (28), (121) are inconsistent by sub-proof % 188.54/30.09 | | | | | | | | | #220. % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | | (122) all_252_10 = e4 & op(e3, e1) = e4 % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | | ALPHA: (122) implies: % 188.54/30.09 | | | | | | | | | (123) all_252_10 = e4 % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | | BETA: splitting (42) gives: % 188.54/30.09 | | | | | | | | | % 188.54/30.09 | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | (124) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = % 188.54/30.09 | | | | | | | | | | e1 & op(e0, e3) = e1) % 188.54/30.09 | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | REF_CLOSE: (6), (14), (51), (66), (114), (124) are % 188.54/30.09 | | | | | | | | | | inconsistent by sub-proof #244. % 188.54/30.09 | | | | | | | | | | % 188.54/30.09 | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | (125) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = % 188.54/30.09 | | | | | | | | | | e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 188.54/30.09 | | | | | | | | | | e0) = e1) % 188.54/30.09 | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | BETA: splitting (125) gives: % 188.54/30.09 | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | (126) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | ALPHA: (126) implies: % 188.54/30.09 | | | | | | | | | | | (127) op(e0, e2) = e1 % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | REF_CLOSE: (6), (10), (93), (127) are inconsistent by % 188.54/30.09 | | | | | | | | | | | sub-proof #256. % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | (128) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.54/30.09 | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | BETA: splitting (128) gives: % 188.54/30.09 | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | (129) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.09 | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | ALPHA: (129) implies: % 188.54/30.09 | | | | | | | | | | | | (130) all_252_23 = e1 % 188.54/30.09 | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | BETA: splitting (18) gives: % 188.54/30.09 | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | (131) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 188.54/30.09 | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 188.54/30.09 | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | REF_CLOSE: (6), (17), (26), (53), (123), (131) are % 188.54/30.09 | | | | | | | | | | | | | inconsistent by sub-proof #218. % 188.54/30.09 | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | (132) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 188.54/30.09 | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 188.54/30.09 | | | | | | | | | | | | | op(e0, e1) = e3) % 188.54/30.09 | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | BETA: splitting (132) gives: % 188.54/30.09 | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | (133) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.09 | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | ALPHA: (133) implies: % 188.54/30.09 | | | | | | | | | | | | | | (134) all_252_11 = e3 % 188.54/30.09 | | | | | | | | | | | | | | (135) op(e2, e1) = e3 % 188.54/30.09 | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | BETA: splitting (75) gives: % 188.54/30.09 | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | (136) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.54/30.09 | | | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.54/30.09 | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | BETA: splitting (136) gives: % 188.54/30.09 | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | (137) all_252_6 = e4 & op(e2, e4) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | ALPHA: (137) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | (138) all_252_6 = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | (139) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = % 188.54/30.09 | | | | | | | | | | | | | | | | | e1 & op(e2, e3) = e1) % 188.54/30.09 | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (93), (99), (138), (139) are inconsistent by % 188.54/30.09 | | | | | | | | | | | | | | | | | sub-proof #74. % 188.54/30.09 | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | (140) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_11 = % 188.54/30.09 | | | | | | | | | | | | | | | | | e1 & op(e2, e1) = e1) | (all_252_18 = e1 & % 188.54/30.09 | | | | | | | | | | | | | | | | | op(e2, e0) = e1) % 188.54/30.09 | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | (141) all_252_8 = e1 & op(e2, e2) = e1 % 188.54/30.09 | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (10), (31), (38), (42), (45), (48), % 188.54/30.09 | | | | | | | | | | | | | | | | | | (54), (55), (66), (79), (108), (130), (141) are % 188.54/30.09 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #73. % 188.54/30.09 | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | (142) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_18 % 188.54/30.09 | | | | | | | | | | | | | | | | | | = e1 & op(e2, e0) = e1) % 188.54/30.09 | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | (143) all_252_11 = e1 & op(e2, e1) = e1 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (134), (143) are inconsistent by sub-proof % 188.54/30.09 | | | | | | | | | | | | | | | | | | | #72. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | (144) all_252_18 = e1 & op(e2, e0) = e1 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | (145) all_252_18 = e1 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | (146) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | (147) all_252_16 = e3 & op(e4, e0) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | (148) op(e4, e0) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | (149) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | (150) all_252_20 = e3 & op(e0, e4) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | (151) op(e0, e4) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (77), (84), (151) are inconsistent by % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #512. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | (152) all_252_21 = e3 & op(e0, e3) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | (153) all_252_21 = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | (154) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e3, e3) = e0) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | (155) all_252_1 = e0 & op(e4, e3) = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | (156) all_252_1 = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (24) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (157) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_0 = e4 & op(e4, e4) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_0 = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (14), (16), (23), (26), (47), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (51), (53), (63), (68), (69), (73), (74), (77), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (84), (86), (92), (93), (123), (138), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (159) are inconsistent by sub-proof #213. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_1 = e4 & op(e4, e3) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (161) all_252_1 = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (156), (161) imply: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) e4 = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (162) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) e4 = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (163) imply: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) $false % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 & % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_252_4 = e4 & op(e4, e2) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (34), (90), (166) are inconsistent by % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #388. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (167) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) all_252_9 = e4 & op(e4, e1) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (28), (168) are inconsistent by sub-proof % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #211. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_252_16 = e4 & op(e4, e0) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) op(e4, e0) = e4 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (12), (14), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (16), (18), (20), (22), (23), (26), (27), (28), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (29), (31), (33), (36), (37), (38), (39), (41), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (42), (44), (45), (46), (47), (48), (49), (51), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (57), (61), (63), (64), (65), (66), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (67), (68), (69), (70), (72), (73), (77), (79), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (82), (83), (84), (86), (87), (93), (94), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (145), (170) are inconsistent by sub-proof % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #167. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_252_3 = e0 & op(e3, e3) = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_3 = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (173) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_2 = e1 & op(e3, e4) = e1 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_2 = e1 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_252_0 = e3 & op(e4, e4) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_0 = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (74) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_252_2 = e3 & op(e3, e4) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (175), (180) are inconsistent by sub-proof % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_3 = e3 & op(e3, e3) = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_3 = e3 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (182) imply: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) e3 = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (183) imply: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_252_0 = e0 % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (16), (26), (53), (77), (80), (84), % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (175), (184) are inconsistent by sub-proof % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #71. % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3) % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives: % 188.54/30.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_252_5 = e3 & op(e3, e2) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_5 = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (187) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) e3 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (188) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) e3 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (178), (189) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_0 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (6), (16), (26), (53), (77), (80), (84), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (175), (190) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #71. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_252_10 = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (14), (23), (26), (33), (40), (47), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (64), (67), (69), (73), (80), (82), (89), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (92), (93), (118), (130), (153), (175), (193) are % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #85. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_252_17 = e3 & op(e3, e0) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (63), (194) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_252_2 = e3 & op(e3, e4) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (175), (195) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_6 = e3 & op(e2, e4) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_252_6 = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (198) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) e4 = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (199) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_10 = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (14), (23), (26), (33), (40), (47), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (64), (67), (69), (73), (80), (82), (89), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (92), (93), (118), (130), (153), (175), (200) are % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #85. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_252_12 = e3 & op(e1, e4) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (16), (17), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (18), (23), (26), (27), (31), (33), (36), (38), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (42), (45), (48), (49), (53), (54), (61), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (63), (66), (69), (73), (79), (80), (82), (93), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (108), (118), (119), (134), (202) are inconsistent % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #70. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_20 = e3 & op(e0, e4) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) op(e0, e4) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (77), (84), (204) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #512. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_252_3 = e1 & op(e3, e3) = e1 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_252_3 = e1 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (206) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) e1 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (14), (22), (25), (29), (31), (36), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (45), (47), (48), (70), (73), (79), (80), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (94), (145), (148), (207) are inconsistent % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #69. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (208) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_252_5 = e1 & op(e3, e2) = e1 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_5 = e1 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (92), (210) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) e1 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (14), (22), (25), (29), (31), (36), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (45), (47), (48), (70), (73), (79), (80), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (83), (94), (145), (148), (211) are inconsistent % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #69. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (47), (93), (123), (212) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #128. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | (213) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e3) = e0) | (all_252_21 = e0 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e0) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_7 = e0 & op(e2, e3) = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (14), (16), (17), (18), (19), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (20), (22), (23), (24), (25), (26), (27), (28), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (53), (54), (56), (57), (58), (59), (60), (61), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (77), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (78), (79), (80), (81), (82), (83), (84), (85), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (94), (214) are inconsistent by sub-proof #75. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | (215) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_252_13 = e0 & op(e1, e3) = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (15), (19), (216) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #319. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_21 = e0 & op(e0, e3) = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) op(e0, e3) = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (17), (18), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (23), (26), (27), (31), (33), (36), (38), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (42), (45), (48), (49), (51), (53), (54), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (63), (66), (69), (73), (79), (80), (82), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (93), (108), (112), (118), (134), (135), (218) are % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #189. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (219) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (16), (18), (20), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (22), (23), (26), (27), (28), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (36), (37), (38), (39), (41), (42), (45), (46), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (53), (54), (57), (61), (63), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (69), (70), (72), (79), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (82), (83), (87), (94), (219) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | sub-proof #138. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | (220) all_252_17 = e3 & op(e3, e0) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (63), (220) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | #159. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | (221) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | (222) all_252_18 = e3 & op(e2, e0) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (80), (145), (222) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | #209. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | (223) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e0) = e3) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (224) all_252_19 = e3 & op(e1, e0) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (41), (224) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | #177. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (225) all_252_24 = e3 & op(e0, e0) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (16), (18), (20), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (22), (23), (26), (27), (28), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (36), (37), (38), (39), (41), (42), (45), (46), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (48), (49), (51), (53), (54), (57), (61), (63), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (69), (70), (72), (79), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | (82), (83), (87), (94), (225) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | sub-proof #169. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | (226) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | REF_CLOSE: (69), (99), (226) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | #68. % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | (227) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.54/30.10 | | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.54/30.10 | | | | | | | | | | | | | | | op(e2, e0) = e4) % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | BETA: splitting (227) gives: % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | (228) all_252_8 = e4 & op(e2, e2) = e4 % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | REF_CLOSE: (23), (55), (228) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | #418. % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | (229) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 188.54/30.10 | | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (16), (18), % 188.54/30.10 | | | | | | | | | | | | | | | | (20), (22), (23), (25), (26), (27), (28), (29), % 188.54/30.10 | | | | | | | | | | | | | | | | (31), (33), (36), (37), (38), (39), (41), (42), % 188.54/30.10 | | | | | | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (51), (53), % 188.54/30.10 | | | | | | | | | | | | | | | | (54), (57), (61), (63), (64), (65), (66), (67), % 188.54/30.10 | | | | | | | | | | | | | | | | (69), (70), (72), (73), (79), (80), (82), (83), % 188.54/30.10 | | | | | | | | | | | | | | | | (87), (93), (94), (134), (229) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | sub-proof #157. % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | (230) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 188.54/30.10 | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 188.54/30.10 | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | BETA: splitting (230) gives: % 188.54/30.10 | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | (231) all_252_15 = e3 & op(e1, e1) = e3 % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | ALPHA: (231) implies: % 188.54/30.10 | | | | | | | | | | | | | | | (232) all_252_15 = e3 % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | BETA: splitting (46) gives: % 188.54/30.10 | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | (233) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 188.54/30.10 | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | BETA: splitting (233) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | (234) all_252_12 = e2 & op(e1, e4) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | ALPHA: (234) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | (235) all_252_12 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (235) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | (236) e2 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (236) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | (237) all_252_7 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), % 188.54/30.10 | | | | | | | | | | | | | | | | | (12), (14), (16), (17), (18), (20), (22), (23), % 188.54/30.10 | | | | | | | | | | | | | | | | | (24), (25), (26), (27), (28), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (41), % 188.54/30.10 | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), % 188.54/30.10 | | | | | | | | | | | | | | | | | (50), (51), (53), (54), (56), (57), (58), (59), % 188.54/30.10 | | | | | | | | | | | | | | | | | (61), (62), (63), (64), (65), (66), (67), (68), % 188.54/30.10 | | | | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), % 188.54/30.10 | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), % 188.54/30.10 | | | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), % 188.54/30.10 | | | | | | | | | | | | | | | | | (94), (232), (237) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | #113. % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | (238) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | ALPHA: (238) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | (239) all_252_13 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | BETA: splitting (9) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | (240) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 188.54/30.10 | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (241) all_252_9 = e2 & op(e4, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (242) all_252_9 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (242) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (243) e2 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (243) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (244) all_252_7 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (12), (14), (16), (17), (18), (20), (22), (23), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (24), (25), (26), (27), (28), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (41), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (50), (51), (53), (54), (56), (57), (58), (59), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (61), (62), (63), (64), (65), (66), (67), (68), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (94), (105), (108), (112), (114), (118), (123), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (239), (244) are inconsistent by sub-proof #106. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (245) all_252_10 = e2 & op(e3, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | ALPHA: (245) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (246) op(e3, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (27), (246) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | sub-proof #557. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | (247) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 188.54/30.10 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (248) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (249) all_252_11 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (250) op(e2, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (16), (17), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (18), (20), (23), (26), (27), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (36), (38), (39), (42), (45), (48), (49), (51), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (53), (54), (61), (63), (66), (69), (70), (72), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (73), (79), (80), (82), (83), (93), (94), (108), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (112), (114), (118), (232), (239), (249), (250) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #120. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (251) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | (252) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (232), (252) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | #114. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | (253) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (48), (253) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | sub-proof #540. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | (254) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 188.54/30.10 | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 188.54/30.10 | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | BETA: splitting (254) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | (255) all_252_14 = e2 & op(e1, e2) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | (256) all_252_14 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | BETA: splitting (9) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | (257) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 188.54/30.10 | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | BETA: splitting (257) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (258) all_252_9 = e2 & op(e4, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (259) all_252_9 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (259) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (260) e2 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (260) imply: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (261) all_252_7 = e0 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (12), (14), (16), (17), (18), (20), (22), (23), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (24), (25), (26), (27), (28), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (41), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (42), (43), (44), (45), (46), (47), (48), (49), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (50), (51), (53), (54), (56), (57), (58), (59), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (61), (62), (63), (64), (65), (66), (67), (68), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (69), (70), (71), (72), (73), (74), (75), (76), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (77), (78), (79), (80), (81), (82), (83), (84), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (86), (87), (88), (89), (90), (91), (92), (93), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (94), (232), (261) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | #113. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (262) all_252_10 = e2 & op(e3, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (263) op(e3, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (27), (263) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | sub-proof #557. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | (264) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 188.54/30.10 | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.10 | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (265) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (266) all_252_11 = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (267) op(e2, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (16), (17), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (18), (20), (23), (26), (27), (29), (31), (33), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (36), (38), (39), (42), (45), (48), (49), (53), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (54), (61), (63), (66), (69), (70), (72), (73), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (79), (80), (82), (83), (93), (94), (108), (118), % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (119), (130), (232), (256), (266), (267) are % 188.54/30.10 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | (268) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | (269) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (232), (269) are inconsistent by sub-proof % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | #114. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | (270) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (39), (48), (270) are inconsistent by % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | sub-proof #540. % 188.54/30.10 | | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | | End of split % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.10 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.10 | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | (271) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 188.54/30.11 | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 188.54/30.11 | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | BETA: splitting (271) gives: % 188.54/30.11 | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | | (272) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.11 | | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (232), (272) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | | | | | #114. % 188.54/30.11 | | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | | (273) all_252_19 = e2 & op(e1, e0) = e2 % 188.54/30.11 | | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (83), (87), (273) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | | | | | | | sub-proof #438. % 188.54/30.11 | | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (274) all_252_23 = e3 & op(e0, e1) = e3 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | ALPHA: (274) implies: % 188.54/30.11 | | | | | | | | | | | | | | | (275) op(e0, e1) = e3 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (39), (275) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | | | | sub-proof #508. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | (276) all_252_24 = e1 & op(e0, e0) = e1 % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | ALPHA: (276) implies: % 188.54/30.11 | | | | | | | | | | | | (277) op(e0, e0) = e1 % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | REF_CLOSE: (6), (38), (112), (277) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | sub-proof #474. % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | End of split % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | (278) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 % 188.54/30.11 | | | | | | | | & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = % 188.54/30.11 | | | | | | | | e4) % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | BETA: splitting (278) gives: % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | (279) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (17), (18), % 188.54/30.11 | | | | | | | | | (20), (23), (26), (27), (31), (33), (36), (38), % 188.54/30.11 | | | | | | | | | (39), (42), (45), (48), (49), (51), (53), (54), % 188.54/30.11 | | | | | | | | | (61), (63), (66), (69), (73), (79), (80), (82), % 188.54/30.11 | | | | | | | | | (93), (108), (112), (114), (118), (279) are % 188.54/30.11 | | | | | | | | | inconsistent by sub-proof #67. % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | (280) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = % 188.54/30.11 | | | | | | | | | e4 & op(e0, e1) = e4) % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | BETA: splitting (280) gives: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | (281) all_252_15 = e4 & op(e1, e1) = e4 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | ALPHA: (281) implies: % 188.54/30.11 | | | | | | | | | | (282) all_252_15 = e4 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | BETA: splitting (42) gives: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | (283) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 188.54/30.11 | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | REF_CLOSE: (6), (14), (51), (66), (114), (283) are % 188.54/30.11 | | | | | | | | | | | inconsistent by sub-proof #244. % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | (284) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 188.54/30.11 | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 188.54/30.11 | | | | | | | | | | | op(e0, e0) = e1) % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | BETA: splitting (284) gives: % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | (285) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | ALPHA: (285) implies: % 188.54/30.11 | | | | | | | | | | | | (286) op(e0, e2) = e1 % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | REF_CLOSE: (6), (10), (93), (286) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | sub-proof #256. % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | (287) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 188.54/30.11 | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | BETA: splitting (287) gives: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | (288) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | ALPHA: (288) implies: % 188.54/30.11 | | | | | | | | | | | | | (289) all_252_23 = e1 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | BETA: splitting (75) gives: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | (290) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.54/30.11 | | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | BETA: splitting (290) gives: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (291) all_252_6 = e4 & op(e2, e4) = e4 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | ALPHA: (291) implies: % 188.54/30.11 | | | | | | | | | | | | | | | (292) all_252_6 = e4 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (10), (14), (16), (23), % 188.54/30.11 | | | | | | | | | | | | | | | (26), (29), (31), (38), (41), (42), (45), (46), % 188.54/30.11 | | | | | | | | | | | | | | | (48), (51), (53), (54), (57), (63), (66), (68), % 188.54/30.11 | | | | | | | | | | | | | | | (69), (70), (72), (73), (77), (79), (80), (82), % 188.54/30.11 | | | | | | | | | | | | | | | (83), (84), (86), (87), (93), (94), (108), (282), % 188.54/30.11 | | | | | | | | | | | | | | | (289), (292) are inconsistent by sub-proof #80. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (293) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REF_CLOSE: (69), (99), (293) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | | #68. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | (294) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.54/30.11 | | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.54/30.11 | | | | | | | | | | | | | | op(e2, e0) = e4) % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | BETA: splitting (294) gives: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (295) all_252_8 = e4 & op(e2, e2) = e4 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REF_CLOSE: (23), (55), (295) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | | #418. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (296) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 188.54/30.11 | | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | BETA: splitting (296) gives: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | (297) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | ALPHA: (297) implies: % 188.54/30.11 | | | | | | | | | | | | | | | | (298) all_252_11 = e4 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (16), (17), % 188.54/30.11 | | | | | | | | | | | | | | | | (18), (23), (26), (27), (28), (29), (31), (33), % 188.54/30.11 | | | | | | | | | | | | | | | | (36), (38), (39), (41), (42), (45), (46), (48), % 188.54/30.11 | | | | | | | | | | | | | | | | (49), (53), (54), (57), (61), (63), (66), (69), % 188.54/30.11 | | | | | | | | | | | | | | | | (70), (72), (73), (79), (80), (82), (83), (87), % 188.54/30.11 | | | | | | | | | | | | | | | | (93), (94), (108), (118), (119), (282), (289), % 188.54/30.11 | | | | | | | | | | | | | | | | (298) are inconsistent by sub-proof #78. % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | (299) all_252_18 = e4 & op(e2, e0) = e4 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 188.54/30.11 | | | | | | | | | | | | | | | | (300) all_252_18 = e4 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (14), (16), (18), % 188.54/30.11 | | | | | | | | | | | | | | | | (20), (22), (23), (25), (26), (27), (28), (29), % 188.54/30.11 | | | | | | | | | | | | | | | | (31), (33), (36), (37), (38), (39), (41), (42), % 188.54/30.11 | | | | | | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (51), (53), % 188.54/30.11 | | | | | | | | | | | | | | | | (54), (57), (61), (63), (64), (65), (66), (67), % 188.54/30.11 | | | | | | | | | | | | | | | | (69), (70), (72), (73), (79), (80), (82), (83), % 188.54/30.11 | | | | | | | | | | | | | | | | (87), (93), (94), (300) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | | | | | sub-proof #158. % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | (301) all_252_24 = e1 & op(e0, e0) = e1 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | ALPHA: (301) implies: % 188.54/30.11 | | | | | | | | | | | | | (302) op(e0, e0) = e1 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | REF_CLOSE: (6), (38), (112), (302) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | | sub-proof #474. % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | (303) all_252_23 = e4 & op(e0, e1) = e4 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | ALPHA: (303) implies: % 188.54/30.11 | | | | | | | | | | (304) op(e0, e1) = e4 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | REF_CLOSE: (6), (39), (93), (119), (304) are inconsistent by % 188.54/30.11 | | | | | | | | | | sub-proof #401. % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | End of split % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | End of split % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | Case 2: % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | (305) all_250_23 = e0 % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | REF_CLOSE: (45), (79), (305) are inconsistent by sub-proof #486. % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | End of split % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | End of split % 188.54/30.11 | | | | | % 188.54/30.11 | | | | End of split % 188.54/30.11 | | | | % 188.54/30.11 | | | End of split % 188.54/30.11 | | | % 188.54/30.11 | | End of split % 188.54/30.11 | | % 188.54/30.11 | Case 2: % 188.54/30.11 | | % 188.54/30.11 | | (306) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) % 188.54/30.11 | | = e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.54/30.11 | | % 188.54/30.11 | | BETA: splitting (306) gives: % 188.54/30.11 | | % 188.54/30.11 | | Case 1: % 188.54/30.11 | | | % 188.54/30.11 | | | (307) all_252_8 = e2 & op(e2, e2) = e2 % 188.54/30.11 | | | % 188.54/30.11 | | | REF_CLOSE: (55), (82), (307) are inconsistent by sub-proof #66. % 188.54/30.11 | | | % 188.54/30.11 | | Case 2: % 188.54/30.11 | | | % 188.54/30.11 | | | (308) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, % 188.54/30.11 | | | e0) = e2) % 188.54/30.11 | | | % 188.54/30.11 | | | BETA: splitting (308) gives: % 188.54/30.11 | | | % 188.54/30.11 | | | Case 1: % 188.54/30.11 | | | | % 188.54/30.11 | | | | (309) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.11 | | | | % 188.54/30.11 | | | | ALPHA: (309) implies: % 188.54/30.11 | | | | (310) all_252_11 = e2 % 188.54/30.11 | | | | (311) op(e2, e1) = e2 % 188.54/30.11 | | | | % 188.54/30.11 | | | | BETA: splitting (22) gives: % 188.54/30.11 | | | | % 188.54/30.11 | | | | Case 1: % 188.54/30.11 | | | | | % 188.54/30.11 | | | | | (312) all_250_23 = e4 % 188.54/30.11 | | | | | % 188.54/30.11 | | | | | REF_CLOSE: (7), (79), (312) are inconsistent by sub-proof #489. % 188.54/30.11 | | | | | % 188.54/30.11 | | | | Case 2: % 188.54/30.11 | | | | | % 188.54/30.11 | | | | | (313) ~ (all_250_23 = e4) % 188.54/30.11 | | | | | (314) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.11 | | | | | all_250_23 = e0 % 188.54/30.11 | | | | | % 188.54/30.11 | | | | | BETA: splitting (314) gives: % 188.54/30.11 | | | | | % 188.54/30.11 | | | | | Case 1: % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | | (315) all_250_23 = e3 % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | | REF_CLOSE: (36), (79), (315) are inconsistent by sub-proof #488. % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | Case 2: % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | | (316) ~ (all_250_23 = e3) % 188.54/30.11 | | | | | | (317) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | | BETA: splitting (49) gives: % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | | Case 1: % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | (318) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & % 188.54/30.11 | | | | | | | op(e3, e1) = e4) % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | BETA: splitting (318) gives: % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | (319) all_252_9 = e4 & op(e4, e1) = e4 % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | REF_CLOSE: (23), (28), (319) are inconsistent by sub-proof #211. % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | (320) all_252_10 = e4 & op(e3, e1) = e4 % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | ALPHA: (320) implies: % 188.54/30.11 | | | | | | | | (321) all_252_10 = e4 % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | BETA: splitting (18) gives: % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | (322) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 % 188.54/30.11 | | | | | | | | | & op(e3, e1) = e3) % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | BETA: splitting (322) gives: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | (323) all_252_9 = e3 & op(e4, e1) = e3 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | REF_CLOSE: (6), (17), (53), (323) are inconsistent by % 188.54/30.11 | | | | | | | | | | sub-proof #275. % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | (324) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | REF_CLOSE: (26), (321), (324) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | #274. % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | (325) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = % 188.54/30.11 | | | | | | | | | e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.11 | | | | | | | | | e1) = e3) % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | BETA: splitting (325) gives: % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | (326) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | REF_CLOSE: (63), (310), (326) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | #356. % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | (327) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = % 188.54/30.11 | | | | | | | | | | e3 & op(e0, e1) = e3) % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | BETA: splitting (327) gives: % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | (328) all_252_15 = e3 & op(e1, e1) = e3 % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | ALPHA: (328) implies: % 188.54/30.11 | | | | | | | | | | | (329) all_252_15 = e3 % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | BETA: splitting (46) gives: % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | (330) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 188.54/30.11 | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | BETA: splitting (330) gives: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | (331) all_252_12 = e2 & op(e1, e4) = e2 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | ALPHA: (331) implies: % 188.54/30.11 | | | | | | | | | | | | | (332) all_252_12 = e2 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | COMBINE_EQS: (16), (332) imply: % 188.54/30.11 | | | | | | | | | | | | | (333) e2 = e0 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | COMBINE_EQS: (310), (333) imply: % 188.54/30.11 | | | | | | | | | | | | | (334) all_252_11 = e0 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (18), (23), (26), % 188.54/30.11 | | | | | | | | | | | | | (27), (31), (33), (36), (37), (38), (39), (42), % 188.54/30.11 | | | | | | | | | | | | | (45), (48), (49), (53), (54), (61), (63), (65), % 188.54/30.11 | | | | | | | | | | | | | (66), (69), (79), (82), (317), (334) are % 188.54/30.11 | | | | | | | | | | | | | inconsistent by sub-proof #126. % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | (335) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | ALPHA: (335) implies: % 188.54/30.11 | | | | | | | | | | | | | (336) all_252_13 = e2 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (16), (18), (20), % 188.54/30.11 | | | | | | | | | | | | | (23), (26), (27), (29), (31), (33), (36), (37), % 188.54/30.11 | | | | | | | | | | | | | (38), (39), (42), (45), (48), (49), (51), (53), % 188.54/30.11 | | | | | | | | | | | | | (54), (61), (63), (65), (66), (69), (70), (72), % 188.54/30.11 | | | | | | | | | | | | | (79), (82), (83), (94), (310), (311), (317), % 188.54/30.11 | | | | | | | | | | | | | (329), (336) are inconsistent by sub-proof #118. % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | (337) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 188.54/30.11 | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 188.54/30.11 | | | | | | | | | | | | op(e1, e0) = e2) % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | BETA: splitting (337) gives: % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | (338) all_252_14 = e2 & op(e1, e2) = e2 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | ALPHA: (338) implies: % 188.54/30.11 | | | | | | | | | | | | | (339) all_252_14 = e2 % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | BETA: splitting (61) gives: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | (340) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 188.54/30.11 | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | BETA: splitting (340) gives: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (341) all_252_9 = e1 & op(e4, e1) = e1 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | ALPHA: (341) implies: % 188.54/30.11 | | | | | | | | | | | | | | | (342) all_252_9 = e1 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | COMBINE_EQS: (28), (342) imply: % 188.54/30.11 | | | | | | | | | | | | | | | (343) e1 = e0 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | SIMP: (343) implies: % 188.54/30.11 | | | | | | | | | | | | | | | (344) e1 = e0 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REDUCE: (73), (344) imply: % 188.54/30.11 | | | | | | | | | | | | | | | (345) $false % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | CLOSE: (345) is inconsistent. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (346) all_252_10 = e1 & op(e3, e1) = e1 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | ALPHA: (346) implies: % 188.54/30.11 | | | | | | | | | | | | | | | (347) all_252_10 = e1 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REF_CLOSE: (93), (321), (347) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | | #197. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | (348) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 % 188.54/30.11 | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & % 188.54/30.11 | | | | | | | | | | | | | | op(e0, e1) = e1) % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | BETA: splitting (348) gives: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (349) all_252_11 = e1 & op(e2, e1) = e1 % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | REF_CLOSE: (14), (310), (349) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | | #357. % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | (350) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 188.54/30.11 | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | BETA: splitting (350) gives: % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | (351) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | REF_CLOSE: (80), (329), (351) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | | | #143. % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | (352) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | ALPHA: (352) implies: % 188.54/30.11 | | | | | | | | | | | | | | | | (353) all_252_23 = e1 % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (16), (18), (20), % 188.54/30.11 | | | | | | | | | | | | | | | | (23), (26), (27), (29), (31), (33), (36), (37), % 188.54/30.11 | | | | | | | | | | | | | | | | (38), (39), (42), (45), (48), (49), (53), (54), % 188.54/30.11 | | | | | | | | | | | | | | | | (61), (63), (65), (66), (69), (70), (72), (79), % 188.54/30.11 | | | | | | | | | | | | | | | | (82), (83), (94), (310), (311), (317), (329), % 188.54/30.11 | | | | | | | | | | | | | | | | (339), (353) are inconsistent by sub-proof #64. % 188.54/30.11 | | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | (354) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 188.54/30.11 | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | BETA: splitting (354) gives: % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | Case 1: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | (355) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | REF_CLOSE: (63), (329), (355) are inconsistent by sub-proof % 188.54/30.11 | | | | | | | | | | | | | | #202. % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | (356) all_252_19 = e2 & op(e1, e0) = e2 % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | | REF_CLOSE: (6), (83), (87), (356) are inconsistent by % 188.54/30.11 | | | | | | | | | | | | | | sub-proof #438. % 188.54/30.11 | | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | Case 2: % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | (357) all_252_23 = e3 & op(e0, e1) = e3 % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | ALPHA: (357) implies: % 188.54/30.11 | | | | | | | | | | | (358) op(e0, e1) = e3 % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | | REF_CLOSE: (6), (36), (39), (358) are inconsistent by % 188.54/30.11 | | | | | | | | | | | sub-proof #508. % 188.54/30.11 | | | | | | | | | | | % 188.54/30.11 | | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | | % 188.54/30.11 | | | | | | | | | End of split % 188.54/30.11 | | | | | | | | | % 188.54/30.11 | | | | | | | | End of split % 188.54/30.11 | | | | | | | | % 188.54/30.11 | | | | | | | End of split % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | Case 2: % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | (359) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & % 188.54/30.11 | | | | | | | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | | REF_CLOSE: (2), (6), (7), (9), (10), (12), (16), (18), (23), (26), % 188.54/30.11 | | | | | | | (27), (29), (31), (33), (36), (37), (38), (39), (41), % 188.54/30.11 | | | | | | | (42), (45), (46), (48), (49), (51), (53), (54), (57), % 188.54/30.11 | | | | | | | (61), (63), (65), (66), (69), (70), (72), (79), (82), % 188.54/30.11 | | | | | | | (83), (87), (94), (310), (317), (359) are inconsistent % 188.54/30.11 | | | | | | | by sub-proof #116. % 188.54/30.11 | | | | | | | % 188.54/30.11 | | | | | | End of split % 188.54/30.11 | | | | | | % 188.54/30.11 | | | | | End of split % 188.54/30.11 | | | | | % 188.54/30.11 | | | | End of split % 188.54/30.11 | | | | % 188.54/30.11 | | | Case 2: % 188.54/30.11 | | | | % 188.54/30.11 | | | | (360) all_252_18 = e2 & op(e2, e0) = e2 % 188.54/30.11 | | | | % 188.54/30.11 | | | | REF_CLOSE: (6), (13), (70), (360) are inconsistent by sub-proof #76. % 188.54/30.11 | | | | % 188.54/30.11 | | | End of split % 188.54/30.11 | | | % 188.54/30.11 | | End of split % 188.54/30.11 | | % 188.54/30.11 | End of split % 188.54/30.11 | % 188.54/30.11 End of proof % 188.54/30.11 % 188.54/30.11 Sub-proof #64 shows that the following formulas are inconsistent: % 188.54/30.11 ---------------------------------------------------------------- % 188.54/30.11 (1) all_252_20 = e2 % 188.54/30.11 (2) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.11 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.11 (4) ~ (all_20_2 = e4) % 188.54/30.11 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.11 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.11 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.11 (6) op(e0, e2) = e4 % 188.54/30.11 (7) op(e3, e1) = all_36_2 % 188.54/30.11 (8) all_252_12 = e0 % 188.54/30.11 (9) op(e2, e1) = e2 % 188.54/30.11 (10) all_252_11 = e2 % 188.54/30.11 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.11 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.11 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.11 (12) op(e2, e1) = e0 % 188.54/30.11 (13) all_252_15 = e3 % 188.54/30.11 (14) ~ (e4 = e0) % 188.54/30.11 (15) all_252_14 = e2 % 188.54/30.11 (16) ~ (e4 = e3) % 188.54/30.11 (17) ~ (all_36_2 = e2) % 188.54/30.11 (18) ~ (all_40_2 = all_34_2) % 188.54/30.11 (19) ~ (all_244_24 = all_20_2) % 188.54/30.11 (20) op(e1, e4) = e0 % 188.54/30.11 (21) all_252_23 = e1 % 188.54/30.11 (22) ~ (all_20_2 = e3) % 188.54/30.11 (23) op(all_20_2, e4) = e1 % 188.54/30.11 (24) op(e0, e0) = all_244_24 % 188.54/30.11 (25) op(e0, e1) = all_20_2 % 188.54/30.12 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.12 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.12 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.12 (27) ~ (all_20_2 = e0) % 188.54/30.12 (28) ~ (all_20_2 = e2) % 188.54/30.12 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.12 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.12 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.12 (30) ~ (e3 = e0) % 188.54/30.12 (31) ~ (all_20_2 = all_8_1) % 188.54/30.12 (32) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.12 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.12 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.12 (33) ~ (e3 = e2) % 188.54/30.12 (34) op(e4, all_20_2) = e0 % 188.54/30.12 (35) op(e0, e3) = all_8_1 % 188.54/30.12 (36) ~ (e4 = e2) % 188.54/30.12 (37) op(e2, e0) = all_40_2 % 188.54/30.12 (38) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.12 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.12 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.12 (39) all_250_23 = all_20_2 % 188.54/30.12 (40) ~ (e2 = e0) % 188.54/30.12 (41) op(e1, e0) = all_34_2 % 188.54/30.12 (42) op(e2, e0) = e1 % 188.54/30.12 % 188.54/30.12 Begin of proof % 188.54/30.12 | % 188.54/30.12 | BETA: splitting (2) gives: % 188.54/30.12 | % 188.54/30.12 | Case 1: % 188.54/30.12 | | % 188.54/30.12 | | (43) all_250_23 = e2 % 188.54/30.12 | | % 188.54/30.12 | | COMBINE_EQS: (39), (43) imply: % 188.54/30.12 | | (44) all_20_2 = e2 % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (28), (44) imply: % 188.54/30.12 | | (45) $false % 188.54/30.12 | | % 188.54/30.12 | | CLOSE: (45) is inconsistent. % 188.54/30.12 | | % 188.54/30.12 | Case 2: % 188.54/30.12 | | % 188.54/30.12 | | (46) ~ (all_250_23 = e2) % 188.54/30.12 | | (47) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.12 | | % 188.54/30.12 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 188.54/30.12 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 188.54/30.12 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 188.54/30.12 | | (36), (37), (38), (39), (40), (41), (42), (47) are inconsistent % 188.54/30.12 | | by sub-proof #65. % 188.54/30.12 | | % 188.54/30.12 | End of split % 188.54/30.12 | % 188.54/30.12 End of proof % 188.54/30.12 % 188.54/30.12 Sub-proof #65 shows that the following formulas are inconsistent: % 188.54/30.12 ---------------------------------------------------------------- % 188.54/30.12 (1) all_252_20 = e2 % 188.54/30.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.12 (3) ~ (all_20_2 = e4) % 188.54/30.12 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.12 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.12 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.12 (5) op(e0, e2) = e4 % 188.54/30.12 (6) op(e3, e1) = all_36_2 % 188.54/30.12 (7) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.12 (8) all_252_12 = e0 % 188.54/30.12 (9) op(e2, e1) = e2 % 188.54/30.12 (10) all_252_11 = e2 % 188.54/30.12 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.12 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.12 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.12 (12) op(e2, e1) = e0 % 188.54/30.12 (13) all_252_15 = e3 % 188.54/30.12 (14) ~ (e4 = e0) % 188.54/30.12 (15) all_252_14 = e2 % 188.54/30.12 (16) ~ (e4 = e3) % 188.54/30.12 (17) ~ (all_36_2 = e2) % 188.54/30.12 (18) ~ (all_40_2 = all_34_2) % 188.54/30.12 (19) ~ (all_244_24 = all_20_2) % 188.54/30.12 (20) op(e1, e4) = e0 % 188.54/30.12 (21) all_252_23 = e1 % 188.54/30.12 (22) ~ (all_20_2 = e3) % 188.54/30.12 (23) op(all_20_2, e4) = e1 % 188.54/30.12 (24) op(e0, e0) = all_244_24 % 188.54/30.12 (25) op(e0, e1) = all_20_2 % 188.54/30.12 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.12 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.12 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.12 (27) ~ (all_20_2 = e0) % 188.54/30.12 (28) ~ (all_20_2 = e2) % 188.54/30.12 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.12 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.12 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.12 (30) ~ (e3 = e0) % 188.54/30.12 (31) ~ (all_20_2 = all_8_1) % 188.54/30.12 (32) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.12 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.12 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.12 (33) ~ (e3 = e2) % 188.54/30.12 (34) op(e4, all_20_2) = e0 % 188.54/30.12 (35) op(e0, e3) = all_8_1 % 188.54/30.12 (36) ~ (e4 = e2) % 188.54/30.12 (37) op(e2, e0) = all_40_2 % 188.54/30.12 (38) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.12 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.12 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.12 (39) all_250_23 = all_20_2 % 188.54/30.12 (40) ~ (e2 = e0) % 188.54/30.12 (41) op(e1, e0) = all_34_2 % 188.54/30.12 (42) op(e2, e0) = e1 % 188.54/30.12 % 188.54/30.12 Begin of proof % 188.54/30.12 | % 188.54/30.12 | BETA: splitting (7) gives: % 188.54/30.12 | % 188.54/30.12 | Case 1: % 188.54/30.12 | | % 188.54/30.12 | | (43) all_250_23 = e1 % 188.54/30.12 | | % 188.54/30.12 | | COMBINE_EQS: (39), (43) imply: % 188.54/30.12 | | (44) all_20_2 = e1 % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (3), (44) imply: % 188.54/30.12 | | (45) ~ (e4 = e1) % 188.54/30.12 | | % 188.54/30.12 | | SIMP: (45) implies: % 188.54/30.12 | | (46) ~ (e4 = e1) % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (22), (44) imply: % 188.54/30.12 | | (47) ~ (e3 = e1) % 188.54/30.12 | | % 188.54/30.12 | | SIMP: (47) implies: % 188.54/30.12 | | (48) ~ (e3 = e1) % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (28), (44) imply: % 188.54/30.12 | | (49) ~ (e2 = e1) % 188.54/30.12 | | % 188.54/30.12 | | SIMP: (49) implies: % 188.54/30.12 | | (50) ~ (e2 = e1) % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (27), (44) imply: % 188.54/30.12 | | (51) ~ (e1 = e0) % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (23), (44) imply: % 188.54/30.12 | | (52) op(e1, e4) = e1 % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (34), (44) imply: % 188.54/30.12 | | (53) op(e4, e1) = e0 % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (25), (44) imply: % 188.54/30.12 | | (54) op(e0, e1) = e1 % 188.54/30.12 | | % 188.54/30.12 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 188.54/30.12 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), % 188.54/30.12 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), % 188.54/30.12 | | (37), (38), (39), (40), (41), (42), (46), (48), (50), (51), (52), % 188.54/30.12 | | (53), (54) are inconsistent by sub-proof #142. % 188.54/30.12 | | % 188.54/30.12 | Case 2: % 188.54/30.12 | | % 188.54/30.12 | | (55) all_250_23 = e0 % 188.54/30.12 | | % 188.54/30.12 | | COMBINE_EQS: (39), (55) imply: % 188.54/30.12 | | (56) all_20_2 = e0 % 188.54/30.12 | | % 188.54/30.12 | | REDUCE: (27), (56) imply: % 188.54/30.12 | | (57) $false % 188.54/30.12 | | % 188.54/30.12 | | CLOSE: (57) is inconsistent. % 188.54/30.12 | | % 188.54/30.12 | End of split % 188.54/30.12 | % 188.54/30.12 End of proof % 188.54/30.12 % 188.54/30.12 Sub-proof #66 shows that the following formulas are inconsistent: % 188.54/30.12 ---------------------------------------------------------------- % 188.54/30.12 (1) all_252_8 = e2 & op(e2, e2) = e2 % 188.54/30.12 (2) all_252_8 = e0 % 188.54/30.12 (3) ~ (e2 = e0) % 188.54/30.12 % 188.54/30.12 Begin of proof % 188.54/30.12 | % 188.54/30.12 | ALPHA: (1) implies: % 188.54/30.12 | (4) all_252_8 = e2 % 188.54/30.12 | % 188.54/30.12 | COMBINE_EQS: (2), (4) imply: % 188.54/30.12 | (5) e2 = e0 % 188.54/30.12 | % 188.54/30.12 | SIMP: (5) implies: % 188.54/30.12 | (6) e2 = e0 % 188.54/30.12 | % 188.54/30.12 | REDUCE: (3), (6) imply: % 188.54/30.12 | (7) $false % 188.54/30.12 | % 188.54/30.12 | CLOSE: (7) is inconsistent. % 188.54/30.12 | % 188.54/30.12 End of proof % 188.54/30.12 % 188.54/30.12 Sub-proof #67 shows that the following formulas are inconsistent: % 188.54/30.12 ---------------------------------------------------------------- % 188.54/30.12 (1) all_252_20 = e2 % 188.54/30.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.12 (3) ~ (all_20_2 = e4) % 188.54/30.12 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.12 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.12 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.12 (5) op(e0, e2) = e4 % 188.54/30.12 (6) op(e3, e1) = all_36_2 % 188.54/30.12 (7) ~ (e2 = e1) % 188.54/30.12 (8) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.12 (9) op(e4, e1) = e0 % 188.54/30.12 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.12 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.12 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.12 (11) op(e2, e1) = e0 % 188.54/30.12 (12) ~ (e4 = e0) % 188.54/30.12 (13) ~ (e4 = e3) % 188.54/30.12 (14) ~ (all_36_2 = e2) % 188.54/30.12 (15) ~ (all_244_24 = all_20_2) % 188.54/30.12 (16) op(e1, e4) = e0 % 188.54/30.12 (17) ~ (all_20_2 = e3) % 188.54/30.12 (18) op(e0, e0) = all_244_24 % 188.54/30.12 (19) op(e0, e1) = all_20_2 % 188.54/30.12 (20) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.12 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.12 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.12 (21) ~ (all_20_2 = e0) % 188.54/30.12 (22) ~ (all_20_2 = e2) % 188.54/30.12 (23) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.12 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.12 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.12 (24) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.12 (25) op(e0, e4) = e2 % 188.54/30.12 (26) ~ (e3 = e0) % 188.54/30.12 (27) ~ (all_20_2 = all_8_1) % 188.54/30.12 (28) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.12 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.12 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.12 (29) ~ (e3 = e2) % 188.54/30.12 (30) op(e0, e3) = all_8_1 % 188.54/30.12 (31) op(e1, e4) = e1 % 188.54/30.12 (32) ~ (e4 = e2) % 188.54/30.12 (33) ~ (e1 = e0) % 188.54/30.12 (34) all_250_23 = all_20_2 % 188.54/30.12 (35) ~ (e3 = e1) % 188.54/30.12 (36) ~ (e2 = e0) % 188.54/30.12 (37) ~ (all_244_24 = e1) % 188.54/30.12 (38) ~ (all_8_1 = e1) % 188.54/30.12 (39) ~ (e4 = e1) % 188.54/30.12 % 188.54/30.12 Begin of proof % 188.54/30.12 | % 188.54/30.12 | BETA: splitting (20) gives: % 188.54/30.12 | % 188.54/30.12 | Case 1: % 188.54/30.12 | | % 188.54/30.12 | | (40) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 188.54/30.12 | | = e1) % 188.54/30.12 | | % 188.54/30.12 | | REF_CLOSE: (2), (7), (25), (30), (38), (40) are inconsistent by sub-proof % 188.54/30.12 | | #244. % 188.54/30.12 | | % 188.54/30.12 | Case 2: % 188.54/30.12 | | % 188.54/30.12 | | (41) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 188.54/30.12 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.12 | | % 188.54/30.12 | | BETA: splitting (41) gives: % 188.54/30.12 | | % 188.54/30.12 | | Case 1: % 188.54/30.12 | | | % 188.54/30.12 | | | (42) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.12 | | | % 188.54/30.12 | | | ALPHA: (42) implies: % 188.54/30.12 | | | (43) op(e0, e2) = e1 % 188.54/30.12 | | | % 188.54/30.12 | | | REF_CLOSE: (2), (5), (39), (43) are inconsistent by sub-proof #256. % 188.54/30.12 | | | % 188.54/30.12 | | Case 2: % 188.54/30.12 | | | % 188.54/30.12 | | | (44) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 188.54/30.12 | | | e0) = e1) % 188.54/30.12 | | | % 188.54/30.12 | | | BETA: splitting (44) gives: % 188.54/30.12 | | | % 188.54/30.12 | | | Case 1: % 188.54/30.12 | | | | % 188.54/30.12 | | | | (45) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.12 | | | | % 188.54/30.12 | | | | ALPHA: (45) implies: % 188.54/30.12 | | | | (46) op(e0, e1) = e1 % 188.54/30.12 | | | | % 188.54/30.12 | | | | ALPHA: (24) implies: % 188.54/30.12 | | | | (47) all_252_11 = e4 % 188.54/30.12 | | | | (48) op(e2, e1) = e4 % 188.54/30.12 | | | | % 188.54/30.12 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 188.54/30.12 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 188.54/30.12 | | | | (22), (23), (26), (27), (28), (29), (30), (31), (32), (33), % 188.54/30.12 | | | | (34), (35), (36), (39), (46), (47), (48) are inconsistent by % 188.54/30.12 | | | | sub-proof #184. % 188.54/30.12 | | | | % 188.54/30.12 | | | Case 2: % 188.54/30.12 | | | | % 188.54/30.12 | | | | (49) all_252_24 = e1 & op(e0, e0) = e1 % 188.54/30.12 | | | | % 188.54/30.12 | | | | ALPHA: (49) implies: % 188.54/30.12 | | | | (50) op(e0, e0) = e1 % 188.54/30.12 | | | | % 188.54/30.12 | | | | REF_CLOSE: (2), (18), (37), (50) are inconsistent by sub-proof #474. % 188.54/30.12 | | | | % 188.54/30.12 | | | End of split % 188.54/30.12 | | | % 188.54/30.12 | | End of split % 188.54/30.12 | | % 188.54/30.12 | End of split % 188.54/30.12 | % 188.54/30.12 End of proof % 188.54/30.12 % 188.54/30.12 Sub-proof #68 shows that the following formulas are inconsistent: % 188.54/30.12 ---------------------------------------------------------------- % 188.54/30.12 (1) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.12 (2) all_252_7 = e2 % 188.54/30.12 (3) ~ (e4 = e2) % 188.54/30.12 % 188.54/30.12 Begin of proof % 188.54/30.12 | % 188.54/30.12 | ALPHA: (1) implies: % 188.54/30.12 | (4) all_252_7 = e4 % 188.54/30.12 | % 188.54/30.12 | COMBINE_EQS: (2), (4) imply: % 188.54/30.12 | (5) e4 = e2 % 188.54/30.12 | % 188.54/30.12 | SIMP: (5) implies: % 188.54/30.12 | (6) e4 = e2 % 188.54/30.12 | % 188.54/30.12 | REDUCE: (3), (6) imply: % 188.54/30.12 | (7) $false % 188.54/30.12 | % 188.54/30.12 | CLOSE: (7) is inconsistent. % 188.54/30.12 | % 188.54/30.12 End of proof % 188.54/30.12 % 188.54/30.12 Sub-proof #69 shows that the following formulas are inconsistent: % 188.54/30.12 ---------------------------------------------------------------- % 188.54/30.12 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.12 (2) all_252_18 = e1 % 188.54/30.12 (3) ~ (all_20_2 = e4) % 188.54/30.12 (4) ~ (e2 = e1) % 188.54/30.12 (5) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.12 all_250_23 = e0 % 188.54/30.12 (6) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.12 | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0) = % 188.54/30.12 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.12 (7) ~ (all_40_2 = all_34_2) % 188.54/30.12 (8) ~ (all_244_24 = all_20_2) % 188.54/30.12 (9) ~ (all_20_2 = e3) % 188.54/30.12 (10) op(e0, e0) = all_244_24 % 188.54/30.12 (11) op(e4, e0) = e3 % 188.54/30.12 (12) ~ (all_20_2 = e0) % 188.54/30.12 (13) all_252_17 = e2 % 188.54/30.12 (14) ~ (all_20_2 = e2) % 188.54/30.12 (15) op(e2, e0) = all_40_2 % 188.54/30.12 (16) ~ (e1 = e0) % 188.54/30.12 (17) all_250_23 = all_20_2 % 188.54/30.12 (18) ~ (e3 = e1) % 188.54/30.12 (19) op(e1, e0) = all_34_2 % 188.54/30.12 (20) e1 = e0 % 188.54/30.12 (21) op(e2, e0) = e1 % 188.54/30.12 % 188.54/30.12 Begin of proof % 188.54/30.12 | % 188.54/30.12 | SIMP: (20) implies: % 188.54/30.12 | (22) e1 = e0 % 188.54/30.12 | % 188.54/30.12 | COMBINE_EQS: (2), (22) imply: % 188.54/30.12 | (23) all_252_18 = e0 % 188.54/30.12 | % 188.54/30.12 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 188.54/30.12 | (14), (15), (16), (17), (18), (19), (21), (23) are inconsistent by % 188.54/30.12 | sub-proof #141. % 188.54/30.12 | % 188.54/30.12 End of proof % 188.54/30.12 % 188.54/30.12 Sub-proof #70 shows that the following formulas are inconsistent: % 188.54/30.12 ---------------------------------------------------------------- % 188.54/30.12 (1) all_252_20 = e2 % 188.54/30.12 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.12 (3) ~ (all_20_2 = e4) % 188.54/30.12 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.12 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.12 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.12 (5) op(e0, e2) = e4 % 188.54/30.12 (6) op(e3, e1) = all_36_2 % 188.54/30.12 (7) ~ (e2 = e1) % 188.54/30.12 (8) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.12 (9) all_252_12 = e0 % 188.54/30.12 (10) op(e4, e1) = e0 % 188.54/30.12 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.12 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.12 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.12 (12) ~ (e4 = e0) % 188.54/30.12 (13) ~ (e4 = e3) % 188.54/30.12 (14) ~ (all_36_2 = e2) % 188.54/30.12 (15) ~ (all_244_24 = all_20_2) % 188.54/30.12 (16) op(e1, e4) = e0 % 188.54/30.12 (17) ~ (all_20_2 = e3) % 188.54/30.12 (18) all_252_12 = e3 & op(e1, e4) = e3 % 188.54/30.12 (19) op(e0, e0) = all_244_24 % 188.54/30.12 (20) op(e0, e1) = all_20_2 % 188.54/30.12 (21) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.12 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.12 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.12 (22) ~ (all_20_2 = e0) % 188.54/30.12 (23) all_252_11 = e3 % 188.54/30.12 (24) ~ (all_20_2 = e2) % 188.54/30.12 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.12 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.12 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.12 (26) ~ (e3 = e0) % 188.54/30.12 (27) ~ (all_20_2 = all_8_1) % 188.54/30.12 (28) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.12 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.12 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.12 (29) ~ (e3 = e2) % 188.54/30.12 (30) op(e0, e3) = all_8_1 % 188.54/30.12 (31) op(e1, e4) = e1 % 188.54/30.12 (32) ~ (e4 = e2) % 188.54/30.12 (33) ~ (e1 = e0) % 188.54/30.13 (34) all_250_23 = all_20_2 % 188.54/30.13 (35) ~ (e3 = e1) % 188.54/30.13 (36) ~ (e2 = e0) % 188.54/30.13 (37) op(e0, e1) = e1 % 188.54/30.13 (38) ~ (e4 = e1) % 188.54/30.13 % 188.54/30.13 Begin of proof % 188.54/30.13 | % 188.54/30.13 | ALPHA: (18) implies: % 188.54/30.13 | (39) all_252_12 = e3 % 188.54/30.13 | % 188.54/30.13 | COMBINE_EQS: (9), (39) imply: % 188.54/30.13 | (40) e3 = e0 % 188.54/30.13 | % 188.54/30.13 | COMBINE_EQS: (23), (40) imply: % 188.54/30.13 | (41) all_252_11 = e0 % 188.54/30.13 | % 188.54/30.13 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 188.54/30.13 | (14), (15), (16), (17), (19), (20), (21), (22), (24), (25), (26), % 188.54/30.13 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 188.54/30.13 | (38), (41) are inconsistent by sub-proof #191. % 188.54/30.13 | % 188.54/30.13 End of proof % 188.54/30.13 % 188.54/30.13 Sub-proof #71 shows that the following formulas are inconsistent: % 188.54/30.13 ---------------------------------------------------------------- % 188.54/30.13 (1) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.13 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.13 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.13 (3) all_252_12 = e0 % 188.54/30.13 (4) ~ (e4 = e3) % 188.54/30.13 (5) all_252_2 = e1 % 188.54/30.13 (6) ~ (e3 = e0) % 188.54/30.13 (7) all_252_0 = e0 % 188.54/30.13 (8) all_252_6 = e4 % 188.54/30.13 (9) op(e0, e4) = all_12_2 % 188.54/30.13 (10) ~ (e3 = e1) % 188.54/30.13 (11) ~ (all_12_2 = e3) % 188.54/30.13 % 188.54/30.13 Begin of proof % 188.54/30.13 | % 188.54/30.13 | BETA: splitting (1) gives: % 188.54/30.13 | % 188.54/30.13 | Case 1: % 188.54/30.13 | | % 188.54/30.13 | | (12) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = % 188.54/30.13 | | e3) % 188.54/30.13 | | % 188.54/30.13 | | BETA: splitting (12) gives: % 188.54/30.13 | | % 188.54/30.13 | | Case 1: % 188.54/30.13 | | | % 188.54/30.13 | | | (13) all_252_0 = e3 & op(e4, e4) = e3 % 188.54/30.13 | | | % 188.54/30.13 | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #148. % 188.54/30.13 | | | % 188.54/30.13 | | Case 2: % 188.54/30.13 | | | % 188.54/30.13 | | | (14) all_252_2 = e3 & op(e3, e4) = e3 % 188.54/30.13 | | | % 188.54/30.13 | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #234. % 188.54/30.13 | | | % 188.54/30.13 | | End of split % 188.54/30.13 | | % 188.54/30.13 | Case 2: % 188.54/30.13 | | % 188.54/30.13 | | (15) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = % 188.54/30.13 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.13 | | % 188.54/30.13 | | BETA: splitting (15) gives: % 188.54/30.13 | | % 188.54/30.13 | | Case 1: % 188.54/30.13 | | | % 188.54/30.13 | | | (16) all_252_6 = e3 & op(e2, e4) = e3 % 188.54/30.13 | | | % 188.54/30.13 | | | ALPHA: (16) implies: % 188.54/30.13 | | | (17) all_252_6 = e3 % 188.54/30.13 | | | % 188.54/30.13 | | | COMBINE_EQS: (8), (17) imply: % 188.54/30.13 | | | (18) e4 = e3 % 188.54/30.13 | | | % 188.54/30.13 | | | REDUCE: (4), (18) imply: % 188.54/30.13 | | | (19) $false % 188.54/30.13 | | | % 188.54/30.13 | | | CLOSE: (19) is inconsistent. % 188.54/30.13 | | | % 188.54/30.13 | | Case 2: % 188.54/30.13 | | | % 188.54/30.13 | | | (20) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, % 188.54/30.13 | | | e4) = e3) % 188.54/30.13 | | | % 188.54/30.13 | | | REF_CLOSE: (2), (3), (6), (9), (11), (20) are inconsistent by sub-proof % 188.54/30.13 | | | #237. % 188.54/30.13 | | | % 188.54/30.13 | | End of split % 188.54/30.13 | | % 188.54/30.13 | End of split % 188.54/30.13 | % 188.54/30.13 End of proof % 188.54/30.13 % 188.54/30.13 Sub-proof #72 shows that the following formulas are inconsistent: % 188.54/30.13 ---------------------------------------------------------------- % 188.54/30.13 (1) all_252_11 = e1 & op(e2, e1) = e1 % 188.54/30.13 (2) all_252_11 = e3 % 188.54/30.13 (3) ~ (e3 = e1) % 188.54/30.13 % 188.54/30.13 Begin of proof % 188.54/30.13 | % 188.54/30.13 | ALPHA: (1) implies: % 188.54/30.13 | (4) all_252_11 = e1 % 188.54/30.13 | % 188.54/30.13 | COMBINE_EQS: (2), (4) imply: % 188.54/30.13 | (5) e3 = e1 % 188.54/30.13 | % 188.54/30.13 | SIMP: (5) implies: % 188.54/30.13 | (6) e3 = e1 % 188.54/30.13 | % 188.54/30.13 | REDUCE: (3), (6) imply: % 188.54/30.13 | (7) $false % 188.54/30.13 | % 188.54/30.13 | CLOSE: (7) is inconsistent. % 188.54/30.13 | % 188.54/30.13 End of proof % 188.54/30.13 % 188.54/30.13 Sub-proof #73 shows that the following formulas are inconsistent: % 188.54/30.13 ---------------------------------------------------------------- % 188.54/30.13 (1) all_252_20 = e2 % 188.54/30.13 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.13 (3) ~ (all_20_2 = e4) % 188.54/30.13 (4) op(e0, e2) = e4 % 188.54/30.13 (5) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.13 (6) all_252_8 = e1 & op(e2, e2) = e1 % 188.54/30.13 (7) ~ (all_244_24 = all_20_2) % 188.54/30.13 (8) all_252_23 = e1 % 188.54/30.13 (9) op(e0, e0) = all_244_24 % 188.54/30.13 (10) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.13 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.13 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.13 (11) ~ (all_20_2 = e0) % 188.54/30.13 (12) ~ (all_20_2 = e2) % 188.54/30.13 (13) ~ (all_20_2 = all_8_1) % 188.54/30.13 (14) all_252_8 = e0 % 188.54/30.13 (15) op(e0, e3) = all_8_1 % 188.54/30.13 (16) all_250_23 = all_20_2 % 188.54/30.13 % 188.54/30.13 Begin of proof % 188.54/30.13 | % 188.54/30.13 | ALPHA: (6) implies: % 188.54/30.13 | (17) all_252_8 = e1 % 188.54/30.13 | % 188.54/30.13 | COMBINE_EQS: (14), (17) imply: % 188.54/30.13 | (18) e1 = e0 % 188.54/30.13 | % 188.54/30.13 | SIMP: (18) implies: % 188.54/30.13 | (19) e1 = e0 % 188.54/30.13 | % 188.54/30.13 | COMBINE_EQS: (8), (19) imply: % 188.54/30.13 | (20) all_252_23 = e0 % 188.54/30.13 | % 188.54/30.13 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (15), % 188.54/30.13 | (16), (20) are inconsistent by sub-proof #192. % 188.54/30.13 | % 188.54/30.13 End of proof % 188.54/30.13 % 188.54/30.13 Sub-proof #74 shows that the following formulas are inconsistent: % 188.54/30.13 ---------------------------------------------------------------- % 188.54/30.13 (1) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 188.54/30.13 (2) ~ (e2 = e1) % 188.54/30.13 (3) all_252_6 = e4 % 188.54/30.13 (4) all_252_7 = e2 % 188.54/30.13 (5) ~ (e4 = e1) % 188.54/30.13 % 188.54/30.13 Begin of proof % 188.54/30.13 | % 188.54/30.13 | BETA: splitting (1) gives: % 188.54/30.13 | % 188.54/30.13 | Case 1: % 188.54/30.13 | | % 188.54/30.13 | | (6) all_252_6 = e1 & op(e2, e4) = e1 % 188.54/30.13 | | % 188.54/30.13 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #215. % 188.54/30.13 | | % 188.54/30.13 | Case 2: % 188.54/30.13 | | % 188.54/30.13 | | (7) all_252_7 = e1 & op(e2, e3) = e1 % 188.54/30.13 | | % 188.54/30.13 | | ALPHA: (7) implies: % 188.54/30.13 | | (8) all_252_7 = e1 % 188.54/30.13 | | % 188.54/30.13 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #301. % 188.54/30.13 | | % 188.54/30.13 | End of split % 188.54/30.13 | % 188.54/30.13 End of proof % 188.54/30.13 % 188.54/30.13 Sub-proof #75 shows that the following formulas are inconsistent: % 188.54/30.13 ---------------------------------------------------------------- % 188.54/30.13 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.54/30.13 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.54/30.13 (all_252_16 = e1 & op(e4, e0) = e1) % 188.54/30.13 (2) all_252_20 = e2 % 188.54/30.13 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.13 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.13 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.13 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.13 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.13 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.13 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.13 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.13 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.13 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.13 (7) ~ (all_20_2 = e4) % 188.54/30.13 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.13 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.13 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.13 (9) op(e0, e2) = e4 % 188.54/30.13 (10) op(e0, e2) = all_28_2 % 188.54/30.13 (11) op(e3, e1) = all_36_2 % 188.54/30.13 (12) ~ (all_40_2 = e2) % 188.54/30.13 (13) ~ (e2 = e1) % 188.54/30.13 (14) all_252_12 = e0 % 188.54/30.13 (15) op(e4, e1) = e0 % 188.54/30.13 (16) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.13 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.13 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.13 (17) op(e1, e3) = all_62_2 % 188.54/30.13 (18) op(e2, e1) = e0 % 188.54/30.13 (19) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.13 all_250_23 = e0 % 188.54/30.13 (20) ~ (e4 = e0) % 188.54/30.13 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.54/30.13 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.54/30.13 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.54/30.13 (22) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.13 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.13 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.13 (23) ~ (e4 = e3) % 188.54/30.13 (24) ~ (all_36_2 = e2) % 188.54/30.13 (25) all_252_7 = e0 & op(e2, e3) = e0 % 188.54/30.13 (26) all_252_9 = e0 % 188.54/30.13 (27) ~ (all_40_2 = all_34_2) % 188.54/30.13 (28) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.54/30.13 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.54/30.13 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.54/30.13 (29) ~ (all_244_24 = all_20_2) % 188.54/30.13 (30) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.54/30.13 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.54/30.13 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.54/30.13 (31) op(e1, e4) = e0 % 188.54/30.13 (32) ~ (all_6_2 = e4) % 188.54/30.13 (33) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.54/30.13 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.54/30.13 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.54/30.13 (34) ~ (all_20_2 = e3) % 188.54/30.13 (35) op(all_20_2, e4) = e1 % 188.54/30.13 (36) op(e0, e0) = all_244_24 % 188.54/30.13 (37) op(e0, e1) = all_20_2 % 188.54/30.13 (38) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.13 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.13 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.13 (39) all_252_19 = e4 % 188.54/30.13 (40) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.13 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.13 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.13 (41) ~ (all_8_1 = e2) % 188.54/30.13 (42) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.13 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.13 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.13 (43) ~ (all_20_2 = e0) % 188.54/30.13 (44) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.13 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.13 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.13 (45) all_252_17 = e2 % 188.54/30.13 (46) ~ (all_20_2 = e2) % 188.54/30.13 (47) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.13 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.13 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.13 (48) op(e4, e4) = all_244_0 % 188.54/30.13 (49) op(e0, e4) = e2 % 188.54/30.13 (50) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) % 188.54/30.13 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.54/30.13 e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.54/30.13 (51) ~ (e3 = e0) % 188.54/30.13 (52) ~ (all_20_2 = all_8_1) % 188.54/30.13 (53) ~ (all_28_2 = e0) % 188.54/30.13 (54) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.13 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.13 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.13 (55) ~ (all_244_0 = e2) % 188.54/30.13 (56) op(e2, all_40_2) = e0 % 188.54/30.13 (57) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.13 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.13 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.54/30.13 (58) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.13 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.13 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.13 (59) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.54/30.13 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.13 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.54/30.13 (60) ~ (e3 = e2) % 188.54/30.13 (61) all_252_22 = e4 % 188.54/30.13 (62) op(e4, all_20_2) = e0 % 188.54/30.13 (63) op(e0, e3) = all_8_1 % 188.54/30.13 (64) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.13 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.13 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.13 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.13 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.13 op(e0, e1) = e0))) % 188.54/30.13 (65) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.13 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.13 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.13 (66) ~ (e4 = e2) % 188.54/30.13 (67) op(e2, e0) = all_40_2 % 188.54/30.13 (68) op(all_28_2, all_40_2) = e2 % 188.54/30.13 (69) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.13 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.13 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.13 (70) ~ (e1 = e0) % 188.54/30.13 (71) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.13 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.13 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.13 (72) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.54/30.13 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.54/30.13 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.13 (73) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.13 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.54/30.13 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.54/30.13 (74) op(e0, e4) = all_12_2 % 188.54/30.13 (75) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.54/30.13 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.54/30.13 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.54/30.13 (76) all_250_23 = all_20_2 % 188.54/30.13 (77) ~ (e3 = e1) % 188.54/30.13 (78) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.54/30.13 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.54/30.13 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.54/30.13 (79) ~ (e2 = e0) % 188.54/30.13 (80) op(e1, e0) = all_34_2 % 188.54/30.13 (81) ~ (all_12_2 = e3) % 188.54/30.13 (82) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.13 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.13 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.54/30.13 (83) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.13 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.13 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.13 (84) ~ (all_34_2 = e2) % 188.54/30.13 (85) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.13 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.13 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.13 (86) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.13 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.13 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.13 (87) op(e4, e2) = all_6_2 % 188.54/30.13 (88) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.54/30.13 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.54/30.13 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.54/30.13 (89) all_252_5 = e0 % 188.54/30.13 (90) ~ (e4 = e1) % 188.54/30.13 (91) op(e2, e0) = e1 % 188.54/30.13 % 188.54/30.13 Begin of proof % 188.54/30.13 | % 188.54/30.13 | ALPHA: (25) implies: % 188.54/30.13 | (92) all_252_7 = e0 % 188.54/30.13 | % 188.54/30.13 | BETA: splitting (50) gives: % 188.54/30.13 | % 188.54/30.13 | Case 1: % 188.54/30.13 | | % 188.54/30.13 | | (93) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = % 188.54/30.13 | | e2) % 188.54/30.13 | | % 188.54/30.13 | | REF_CLOSE: (2), (3), (4), (6), (13), (14), (20), (23), (49), (51), (60), % 188.54/30.13 | | (65), (66), (70), (74), (77), (79), (81), (83), (90), (92), (93) % 188.54/30.13 | | are inconsistent by sub-proof #221. % 188.54/30.13 | | % 188.54/30.13 | Case 2: % 188.54/30.13 | | % 188.54/30.13 | | (94) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_11 = e2 & op(e2, e1) = % 188.54/30.13 | | e2) | (all_252_18 = e2 & op(e2, e0) = e2) % 188.54/30.13 | | % 188.54/30.13 | | BETA: splitting (94) gives: % 188.54/30.13 | | % 188.54/30.13 | | Case 1: % 188.54/30.13 | | | % 188.54/30.13 | | | (95) all_252_8 = e2 & op(e2, e2) = e2 % 188.54/30.13 | | | % 188.54/30.13 | | | ALPHA: (95) implies: % 188.54/30.13 | | | (96) all_252_8 = e2 % 188.54/30.13 | | | % 188.54/30.13 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), % 188.54/30.13 | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (26), % 188.54/30.13 | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.13 | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.13 | | | (47), (48), (49), (51), (52), (53), (54), (55), (56), (57), % 188.54/30.13 | | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 188.54/30.13 | | | (68), (69), (71), (72), (73), (74), (75), (76), (78), (79), % 188.54/30.13 | | | (80), (81), (82), (83), (84), (85), (86), (87), (88), (89), % 188.54/30.13 | | | (91), (92), (96) are inconsistent by sub-proof #77. % 188.54/30.13 | | | % 188.54/30.13 | | Case 2: % 188.54/30.13 | | | % 188.54/30.13 | | | (97) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_18 = e2 & op(e2, % 188.54/30.13 | | | e0) = e2) % 188.54/30.13 | | | % 188.54/30.13 | | | BETA: splitting (97) gives: % 188.54/30.13 | | | % 188.54/30.13 | | | Case 1: % 188.54/30.13 | | | | % 188.54/30.13 | | | | (98) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.13 | | | | % 188.54/30.13 | | | | ALPHA: (98) implies: % 188.54/30.13 | | | | (99) all_252_11 = e2 % 188.54/30.13 | | | | (100) op(e2, e1) = e2 % 188.54/30.13 | | | | % 188.54/30.14 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 188.54/30.14 | | | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), % 188.54/30.14 | | | | (26), (27), (29), (31), (32), (33), (34), (35), (36), (37), % 188.54/30.14 | | | | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), % 188.54/30.14 | | | | (48), (49), (51), (52), (53), (54), (55), (56), (58), (59), % 188.54/30.14 | | | | (60), (61), (62), (63), (64), (65), (66), (67), (68), (69), % 188.54/30.14 | | | | (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 188.54/30.14 | | | | (80), (81), (83), (84), (85), (86), (87), (88), (89), (90), % 188.54/30.14 | | | | (91), (92), (99), (100) are inconsistent by sub-proof #115. % 188.54/30.14 | | | | % 188.54/30.14 | | | Case 2: % 188.54/30.14 | | | | % 188.54/30.14 | | | | (101) all_252_18 = e2 & op(e2, e0) = e2 % 188.54/30.14 | | | | % 188.54/30.14 | | | | REF_CLOSE: (6), (12), (67), (101) are inconsistent by sub-proof #76. % 188.54/30.14 | | | | % 188.54/30.14 | | | End of split % 188.54/30.14 | | | % 188.54/30.14 | | End of split % 188.54/30.14 | | % 188.54/30.14 | End of split % 188.54/30.14 | % 188.54/30.14 End of proof % 188.54/30.14 % 188.54/30.14 Sub-proof #76 shows that the following formulas are inconsistent: % 188.54/30.14 ---------------------------------------------------------------- % 188.54/30.14 (1) all_252_18 = e2 & op(e2, e0) = e2 % 188.54/30.14 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.14 (3) op(e2, e0) = all_40_2 % 188.54/30.14 (4) ~ (all_40_2 = e2) % 188.54/30.14 % 188.54/30.14 Begin of proof % 188.54/30.14 | % 188.54/30.14 | ALPHA: (1) implies: % 188.54/30.14 | (5) op(e2, e0) = e2 % 188.54/30.14 | % 188.54/30.14 | GROUND_INST: instantiating (2) with all_40_2, e2, e0, e2, simplifying with % 188.54/30.14 | (3), (5) gives: % 188.54/30.14 | (6) all_40_2 = e2 % 188.54/30.14 | % 188.54/30.14 | REDUCE: (4), (6) imply: % 188.54/30.14 | (7) $false % 188.54/30.14 | % 188.54/30.14 | CLOSE: (7) is inconsistent. % 188.54/30.14 | % 188.54/30.14 End of proof % 188.54/30.14 % 188.54/30.14 Sub-proof #77 shows that the following formulas are inconsistent: % 188.54/30.14 ---------------------------------------------------------------- % 188.54/30.14 (1) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = e1 & op(e4, e3) = e1) | % 188.54/30.14 (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = e1 & op(e4, e1) = e1) | % 188.54/30.14 (all_252_16 = e1 & op(e4, e0) = e1) % 188.54/30.14 (2) all_252_20 = e2 % 188.54/30.14 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 188.54/30.14 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 188.54/30.14 | (all_252_20 = e3 & op(e0, e4) = e3) % 188.54/30.14 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 188.54/30.14 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 188.54/30.14 | (all_252_20 = e4 & op(e0, e4) = e4) % 188.54/30.14 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 188.54/30.14 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 188.54/30.14 | (all_252_18 = e3 & op(e2, e0) = e3) % 188.54/30.14 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 188.54/30.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 188.54/30.14 (7) ~ (all_20_2 = e4) % 188.54/30.14 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 188.54/30.14 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 188.54/30.14 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 188.54/30.14 (9) op(e0, e2) = e4 % 188.54/30.14 (10) op(e0, e2) = all_28_2 % 188.54/30.14 (11) op(e3, e1) = all_36_2 % 188.54/30.14 (12) all_252_12 = e0 % 188.54/30.14 (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 188.54/30.14 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 188.54/30.14 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 188.54/30.14 (14) op(e1, e3) = all_62_2 % 188.54/30.14 (15) op(e2, e1) = e0 % 188.54/30.14 (16) all_252_7 = e0 % 188.54/30.14 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 188.54/30.14 all_250_23 = e0 % 188.54/30.14 (18) ~ (e4 = e0) % 188.54/30.14 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 188.54/30.14 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 188.54/30.14 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 188.54/30.14 (20) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 188.54/30.14 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 188.54/30.14 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.14 (21) ~ (e4 = e3) % 188.54/30.14 (22) ~ (all_36_2 = e2) % 188.54/30.14 (23) all_252_9 = e0 % 188.54/30.14 (24) ~ (all_40_2 = all_34_2) % 188.54/30.14 (25) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 188.54/30.14 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 188.54/30.14 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 188.54/30.14 (26) ~ (all_244_24 = all_20_2) % 188.54/30.14 (27) all_252_8 = e2 % 188.54/30.14 (28) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 188.54/30.14 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 188.54/30.14 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 188.54/30.14 (29) op(e1, e4) = e0 % 188.54/30.14 (30) ~ (all_6_2 = e4) % 188.54/30.14 (31) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 188.54/30.14 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 188.54/30.14 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 188.54/30.14 (32) ~ (all_20_2 = e3) % 188.54/30.14 (33) op(all_20_2, e4) = e1 % 188.54/30.14 (34) op(e0, e0) = all_244_24 % 188.54/30.14 (35) op(e0, e1) = all_20_2 % 188.54/30.14 (36) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.14 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 188.54/30.14 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 188.54/30.14 (37) all_252_19 = e4 % 188.54/30.14 (38) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 188.54/30.14 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.14 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 188.54/30.14 (39) ~ (all_8_1 = e2) % 188.54/30.14 (40) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 188.54/30.14 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 188.54/30.14 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.14 (41) ~ (all_20_2 = e0) % 188.54/30.14 (42) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.14 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 188.54/30.14 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 188.54/30.14 (43) all_252_17 = e2 % 188.54/30.14 (44) ~ (all_20_2 = e2) % 188.54/30.14 (45) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 188.54/30.14 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 188.54/30.14 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.14 (46) op(e4, e4) = all_244_0 % 188.54/30.14 (47) op(e0, e4) = e2 % 188.54/30.14 (48) ~ (e3 = e0) % 188.54/30.14 (49) ~ (all_20_2 = all_8_1) % 188.54/30.14 (50) ~ (all_28_2 = e0) % 188.54/30.14 (51) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.14 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 188.54/30.14 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 188.54/30.14 (52) ~ (all_244_0 = e2) % 188.54/30.14 (53) op(e2, all_40_2) = e0 % 188.54/30.14 (54) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 188.54/30.14 | (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.14 e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 188.54/30.14 (55) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 188.54/30.14 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 188.54/30.14 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 188.54/30.14 (56) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 188.54/30.14 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 188.54/30.14 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 188.54/30.14 (57) ~ (e3 = e2) % 188.54/30.14 (58) all_252_22 = e4 % 188.54/30.14 (59) op(e4, all_20_2) = e0 % 188.54/30.14 (60) op(e0, e3) = all_8_1 % 188.54/30.14 (61) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 188.54/30.14 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 188.54/30.14 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 188.54/30.14 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 188.54/30.14 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 188.54/30.14 op(e0, e1) = e0))) % 188.54/30.14 (62) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 188.54/30.14 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 188.54/30.14 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 188.54/30.14 (63) ~ (e4 = e2) % 188.54/30.14 (64) op(e2, e0) = all_40_2 % 188.54/30.14 (65) op(all_28_2, all_40_2) = e2 % 188.54/30.14 (66) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 188.54/30.14 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 188.54/30.14 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 188.54/30.14 (67) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.14 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 188.54/30.14 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 188.54/30.14 (68) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 188.54/30.14 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 188.54/30.14 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 188.54/30.14 (69) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.14 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 188.54/30.14 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 188.54/30.14 (70) op(e0, e4) = all_12_2 % 188.54/30.14 (71) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 188.54/30.14 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 188.54/30.14 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 188.54/30.14 (72) all_250_23 = all_20_2 % 188.54/30.14 (73) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 188.54/30.14 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 188.54/30.14 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 188.54/30.14 (74) ~ (e2 = e0) % 188.54/30.14 (75) op(e1, e0) = all_34_2 % 188.54/30.14 (76) ~ (all_12_2 = e3) % 188.54/30.14 (77) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 188.54/30.14 | (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = e3 & op(e1, e3) = % 188.54/30.14 e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 188.54/30.14 (78) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 188.54/30.14 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 188.54/30.14 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 188.54/30.14 (79) ~ (all_34_2 = e2) % 188.54/30.14 (80) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 188.54/30.14 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.14 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 188.54/30.14 (81) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 188.54/30.14 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 188.54/30.14 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 188.54/30.14 (82) op(e4, e2) = all_6_2 % 188.54/30.14 (83) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 188.54/30.14 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 188.54/30.14 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 188.54/30.14 (84) all_252_5 = e0 % 188.54/30.14 (85) op(e2, e0) = e1 % 188.54/30.14 % 188.54/30.14 Begin of proof % 188.54/30.14 | % 188.54/30.14 | BETA: splitting (17) gives: % 188.54/30.14 | % 188.54/30.14 | Case 1: % 188.54/30.14 | | % 188.54/30.14 | | (86) all_250_23 = e4 % 188.54/30.14 | | % 188.54/30.14 | | REF_CLOSE: (7), (72), (86) are inconsistent by sub-proof #489. % 188.54/30.14 | | % 188.54/30.14 | Case 2: % 188.54/30.14 | | % 188.54/30.14 | | (87) ~ (all_250_23 = e4) % 188.54/30.14 | | (88) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 188.54/30.14 | | e0 % 188.54/30.14 | | % 188.54/30.14 | | BETA: splitting (88) gives: % 188.54/30.14 | | % 188.54/30.14 | | Case 1: % 188.54/30.14 | | | % 188.54/30.14 | | | (89) all_250_23 = e3 % 188.54/30.14 | | | % 188.54/30.14 | | | REF_CLOSE: (32), (72), (89) are inconsistent by sub-proof #488. % 188.54/30.14 | | | % 188.54/30.14 | | Case 2: % 188.54/30.14 | | | % 188.54/30.14 | | | (90) ~ (all_250_23 = e3) % 188.54/30.14 | | | (91) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 188.54/30.14 | | | % 188.54/30.14 | | | BETA: splitting (91) gives: % 188.54/30.14 | | | % 188.54/30.14 | | | Case 1: % 188.54/30.14 | | | | % 188.54/30.14 | | | | (92) all_250_23 = e2 % 188.54/30.14 | | | | % 188.54/30.14 | | | | REF_CLOSE: (44), (72), (92) are inconsistent by sub-proof #487. % 188.54/30.14 | | | | % 188.54/30.14 | | | Case 2: % 188.54/30.14 | | | | % 188.54/30.14 | | | | (93) ~ (all_250_23 = e2) % 188.54/30.14 | | | | (94) all_250_23 = e1 | all_250_23 = e0 % 188.54/30.14 | | | | % 188.54/30.14 | | | | BETA: splitting (94) gives: % 188.54/30.14 | | | | % 188.54/30.14 | | | | Case 1: % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | (95) all_250_23 = e1 % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | COMBINE_EQS: (72), (95) imply: % 188.54/30.14 | | | | | (96) all_20_2 = e1 % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | SIMP: (96) implies: % 188.54/30.14 | | | | | (97) all_20_2 = e1 % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (26), (97) imply: % 188.54/30.14 | | | | | (98) ~ (all_244_24 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (49), (97) imply: % 188.54/30.14 | | | | | (99) ~ (all_8_1 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | SIMP: (99) implies: % 188.54/30.14 | | | | | (100) ~ (all_8_1 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (7), (97) imply: % 188.54/30.14 | | | | | (101) ~ (e4 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | SIMP: (101) implies: % 188.54/30.14 | | | | | (102) ~ (e4 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (32), (97) imply: % 188.54/30.14 | | | | | (103) ~ (e3 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | SIMP: (103) implies: % 188.54/30.14 | | | | | (104) ~ (e3 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (44), (97) imply: % 188.54/30.14 | | | | | (105) ~ (e2 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | SIMP: (105) implies: % 188.54/30.14 | | | | | (106) ~ (e2 = e1) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (41), (97) imply: % 188.54/30.14 | | | | | (107) ~ (e1 = e0) % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (33), (97) imply: % 188.54/30.14 | | | | | (108) op(e1, e4) = e1 % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (59), (97) imply: % 188.54/30.14 | | | | | (109) op(e4, e1) = e0 % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | REDUCE: (35), (97) imply: % 188.54/30.14 | | | | | (110) op(e0, e1) = e1 % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | BETA: splitting (45) gives: % 188.54/30.14 | | | | | % 188.54/30.14 | | | | | Case 1: % 188.54/30.14 | | | | | | % 188.54/30.14 | | | | | | (111) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & % 188.54/30.14 | | | | | | op(e3, e1) = e4) % 188.54/30.14 | | | | | | % 188.54/30.14 | | | | | | BETA: splitting (111) gives: % 188.54/30.14 | | | | | | % 188.54/30.14 | | | | | | Case 1: % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | | (112) all_252_9 = e4 & op(e4, e1) = e4 % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | | REF_CLOSE: (18), (23), (112) are inconsistent by sub-proof #220. % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | Case 2: % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | | (113) all_252_10 = e4 & op(e3, e1) = e4 % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | | ALPHA: (113) implies: % 188.54/30.14 | | | | | | | (114) all_252_10 = e4 % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | | BETA: splitting (56) gives: % 188.54/30.14 | | | | | | | % 188.54/30.14 | | | | | | | Case 1: % 188.54/30.14 | | | | | | | | % 188.54/30.14 | | | | | | | | (115) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & % 188.54/30.14 | | | | | | | | op(e3, e3) = e2) % 188.54/30.14 | | | | | | | | % 188.54/30.14 | | | | | | | | BETA: splitting (115) gives: % 188.54/30.14 | | | | | | | | % 188.54/30.14 | | | | | | | | Case 1: % 188.54/30.14 | | | | | | | | | % 188.54/30.14 | | | | | | | | | (116) all_252_1 = e2 & op(e4, e3) = e2 % 188.54/30.14 | | | | | | | | | % 188.54/30.14 | | | | | | | | | ALPHA: (116) implies: % 188.54/30.14 | | | | | | | | | (117) all_252_1 = e2 % 188.54/30.14 | | | | | | | | | % 188.54/30.14 | | | | | | | | | BETA: splitting (13) gives: % 188.54/30.14 | | | | | | | | | % 188.54/30.14 | | | | | | | | | Case 1: % 188.54/30.14 | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | (118) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 188.54/30.14 | | | | | | | | | | e3 & op(e3, e1) = e3) % 188.54/30.14 | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | REF_CLOSE: (6), (21), (48), (109), (114), (118) are % 188.54/30.14 | | | | | | | | | | inconsistent by sub-proof #218. % 188.54/30.14 | | | | | | | | | | % 188.54/30.14 | | | | | | | | | Case 2: % 188.54/30.14 | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | (119) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = % 188.54/30.14 | | | | | | | | | | e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, % 188.54/30.14 | | | | | | | | | | e1) = e3) % 188.54/30.14 | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | BETA: splitting (119) gives: % 188.54/30.14 | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | Case 1: % 188.54/30.14 | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | (120) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.14 | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | ALPHA: (120) implies: % 188.54/30.14 | | | | | | | | | | | (121) all_252_11 = e3 % 188.54/30.14 | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | BETA: splitting (68) gives: % 188.54/30.14 | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | Case 1: % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | (122) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 188.54/30.14 | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), % 188.54/30.14 | | | | | | | | | | | | (13), (15), (16), (17), (18), (19), (20), (21), % 188.54/30.14 | | | | | | | | | | | | (22), (23), (24), (26), (29), (30), (32), (33), % 188.54/30.14 | | | | | | | | | | | | (34), (35), (37), (38), (40), (41), (42), (43), % 188.54/30.14 | | | | | | | | | | | | (44), (45), (47), (48), (49), (51), (55), (57), % 188.54/30.14 | | | | | | | | | | | | (58), (59), (60), (61), (62), (63), (64), (66), % 188.54/30.14 | | | | | | | | | | | | (67), (70), (72), (74), (75), (76), (78), (79), % 188.54/30.14 | | | | | | | | | | | | (82), (84), (85), (98), (102), (104), (106), % 188.54/30.14 | | | | | | | | | | | | (107), (114), (117), (122) are inconsistent by % 188.54/30.14 | | | | | | | | | | | | sub-proof #164. % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | Case 2: % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | (123) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 188.54/30.14 | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 188.54/30.14 | | | | | | | | | | | | op(e2, e0) = e4) % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | BETA: splitting (123) gives: % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | Case 1: % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | | (124) all_252_8 = e4 & op(e2, e2) = e4 % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | | ALPHA: (124) implies: % 188.54/30.14 | | | | | | | | | | | | | (125) all_252_8 = e4 % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | | REF_CLOSE: (27), (63), (125) are inconsistent by sub-proof % 188.54/30.14 | | | | | | | | | | | | | #163. % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | Case 2: % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | | (126) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 188.54/30.14 | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (12), (13), (15), % 188.54/30.14 | | | | | | | | | | | | | (17), (18), (20), (21), (22), (23), (24), (26), % 188.54/30.14 | | | | | | | | | | | | | (29), (32), (33), (34), (35), (37), (38), (40), % 188.54/30.14 | | | | | | | | | | | | | (41), (42), (43), (44), (45), (47), (48), (49), % 188.54/30.14 | | | | | | | | | | | | | (51), (55), (57), (58), (59), (60), (61), (63), % 188.54/30.14 | | | | | | | | | | | | | (64), (66), (72), (74), (75), (79), (85), (102), % 188.54/30.14 | | | | | | | | | | | | | (104), (106), (107), (121), (126) are inconsistent % 188.54/30.14 | | | | | | | | | | | | | by sub-proof #157. % 188.54/30.14 | | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | | End of split % 188.54/30.14 | | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | End of split % 188.54/30.14 | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | Case 2: % 188.54/30.14 | | | | | | | | | | | % 188.54/30.14 | | | | | | | | | | | (127) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 188.54/30.14 | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 188.54/30.14 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.15 | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.15 | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.15 | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.15 | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.15 | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.15 | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.15 | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.15 | | | | | | | | | | | (107), (109), (127) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | #112. % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | (128) all_252_3 = e2 & op(e3, e3) = e2 % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | ALPHA: (128) implies: % 188.54/30.15 | | | | | | | | | (129) all_252_3 = e2 % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | REF_CLOSE: (18), (21), (36), (43), (48), (57), (63), (67), % 188.54/30.15 | | | | | | | | | (81), (84), (102), (104), (106), (107), (114), % 188.54/30.15 | | | | | | | | | (129) are inconsistent by sub-proof #127. % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | End of split % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | | (130) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 188.54/30.15 | | | | | | | | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = % 188.54/30.15 | | | | | | | | e2) % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | | BETA: splitting (130) gives: % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | (131) all_252_7 = e2 & op(e2, e3) = e2 % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | REF_CLOSE: (16), (74), (131) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | #222. % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | (132) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = % 188.54/30.15 | | | | | | | | | e2 & op(e0, e3) = e2) % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | BETA: splitting (132) gives: % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | (133) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | ALPHA: (133) implies: % 188.54/30.15 | | | | | | | | | | (134) all_252_13 = e2 % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.15 | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.15 | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.15 | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.15 | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.15 | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.15 | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.15 | | | | | | | | | | (81), (82), (83), (84), (85), (91), (94), (98), % 188.54/30.15 | | | | | | | | | | (100), (102), (104), (106), (107), (108), (109), % 188.54/30.15 | | | | | | | | | | (114), (134) are inconsistent by sub-proof #106. % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | (135) all_252_21 = e2 & op(e0, e3) = e2 % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | REF_CLOSE: (6), (39), (60), (135) are inconsistent by % 188.54/30.15 | | | | | | | | | | sub-proof #289. % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | End of split % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | End of split % 188.54/30.15 | | | | | | | % 188.54/30.15 | | | | | | End of split % 188.54/30.15 | | | | | | % 188.54/30.15 | | | | | Case 2: % 188.54/30.15 | | | | | | % 188.54/30.15 | | | | | | (136) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & % 188.54/30.15 | | | | | | op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 188.54/30.15 | | | | | | % 188.54/30.15 | | | | | | BETA: splitting (136) gives: % 188.54/30.15 | | | | | | % 188.54/30.15 | | | | | | Case 1: % 188.54/30.15 | | | | | | | % 188.54/30.15 | | | | | | | (137) all_252_11 = e4 & op(e2, e1) = e4 % 188.54/30.15 | | | | | | | % 188.54/30.15 | | | | | | | ALPHA: (137) implies: % 188.54/30.15 | | | | | | | (138) all_252_11 = e4 % 188.54/30.15 | | | | | | | % 188.54/30.15 | | | | | | | BETA: splitting (56) gives: % 188.54/30.15 | | | | | | | % 188.54/30.15 | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | | (139) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & % 188.54/30.15 | | | | | | | | op(e3, e3) = e2) % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | | BETA: splitting (139) gives: % 188.54/30.15 | | | | | | | | % 188.54/30.15 | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | (140) all_252_1 = e2 & op(e4, e3) = e2 % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | ALPHA: (140) implies: % 188.54/30.15 | | | | | | | | | (141) all_252_1 = e2 % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | BETA: splitting (55) gives: % 188.54/30.15 | | | | | | | | | % 188.54/30.15 | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | (142) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 188.54/30.15 | | | | | | | | | | e1 & op(e3, e1) = e1) % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.15 | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.15 | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.15 | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.15 | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.15 | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.15 | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.15 | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.15 | | | | | | | | | | (107), (109), (138), (142) are inconsistent by % 188.54/30.15 | | | | | | | | | | sub-proof #103. % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | (143) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = % 188.54/30.15 | | | | | | | | | | e1 & op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.15 | | | | | | | | | | e1) = e1) % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | BETA: splitting (143) gives: % 188.54/30.15 | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | (144) all_252_11 = e1 & op(e2, e1) = e1 % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | ALPHA: (144) implies: % 188.54/30.15 | | | | | | | | | | | (145) all_252_11 = e1 % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | REF_CLOSE: (102), (138), (145) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | #461. % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | (146) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 188.54/30.15 | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | BETA: splitting (146) gives: % 188.54/30.15 | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | (147) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | ALPHA: (147) implies: % 188.54/30.15 | | | | | | | | | | | | (148) all_252_15 = e1 % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.15 | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.15 | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.15 | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.15 | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.15 | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.15 | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.15 | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.15 | | | | | | | | | | | | (107), (109), (148) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | #102. % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | (149) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | ALPHA: (149) implies: % 188.54/30.15 | | | | | | | | | | | | (150) all_252_23 = e1 % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | BETA: splitting (19) gives: % 188.54/30.15 | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | (151) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = % 188.54/30.15 | | | | | | | | | | | | | e4 & op(e4, e3) = e4) % 188.54/30.15 | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | BETA: splitting (151) gives: % 188.54/30.15 | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | (152) all_252_0 = e4 & op(e4, e4) = e4 % 188.54/30.15 | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | ALPHA: (152) implies: % 188.54/30.15 | | | | | | | | | | | | | | (153) all_252_0 = e4 % 188.54/30.15 | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | BETA: splitting (69) gives: % 188.54/30.15 | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | (154) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 188.54/30.15 | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 188.54/30.15 | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | BETA: splitting (154) gives: % 188.54/30.15 | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | (155) all_252_1 = e4 & op(e4, e3) = e4 % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | REF_CLOSE: (63), (141), (155) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | #152. % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | (156) all_252_3 = e4 & op(e3, e3) = e4 % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | ALPHA: (156) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | (157) all_252_3 = e4 % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | (158) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 188.54/30.15 | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (57), (141), (153), (158) are inconsistent % 188.54/30.15 | | | | | | | | | | | | | | | | | by sub-proof #156. % 188.54/30.15 | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | (159) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 188.54/30.15 | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 188.54/30.15 | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | BETA: splitting (159) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | (160) all_252_4 = e3 & op(e4, e2) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | ALPHA: (160) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | (161) all_252_4 = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | (162) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (106), (141), (157), (162) are inconsistent % 188.54/30.15 | | | | | | | | | | | | | | | | | | | by sub-proof #101. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | (163) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 188.54/30.15 | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (164) all_252_7 = e1 & op(e2, e3) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (165) all_252_7 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (165) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (166) e1 = e0 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | SIMP: (166) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (167) e1 = e0 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (167) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (168) all_252_23 = e0 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (26), (34), (38), (41), (44), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (49), (60), (72), (94), (168) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | sub-proof #192. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (169) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | (170) all_252_13 = e1 & op(e1, e3) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | (171) all_252_13 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | (172) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (22), (23), (74), (172) are % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #207. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | (173) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_11 = e2 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (176) op(e2, e1) = e2 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (107), (109), (175), (176) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (177) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | (179) all_252_15 = e2 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (180) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_4 = e1 & op(e4, e2) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (161), (181) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | #348. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_252_5 = e1 & op(e3, e2) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_252_5 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (84), (183) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (184) e1 = e0 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (184) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_252_23 = e0 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (26), (34), (38), (41), (44), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (60), (72), (94), (185) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #192. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (186) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_8 = e1 & op(e2, e2) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_252_8 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (188) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (189) e2 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (189) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_15 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (109), (190) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | #102. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (191) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_252_14 = e1 & op(e1, e2) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_252_14 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_252_12 = e3 & op(e1, e4) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (48), (195) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #216. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_13 = e3 & op(e1, e3) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_13 = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (197) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) e3 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (198) imply: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_252_4 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (21), (27), (28), (48), (57), (84), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (193), (199) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #97. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (27), (28), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (53), (55), (56), (57), (58), (59), (60), (61), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (78), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (102), % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (106), (107), (109), (161), (193), (200) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #95. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) all_252_22 = e1 & op(e0, e2) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) op(e0, e2) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (102), (202) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #256. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | (203) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (35), (44), (203) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #540. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | (204) all_252_21 = e1 & op(e0, e3) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (60), (100), (204) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | sub-proof #281. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | (205) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | (206) all_252_9 = e3 & op(e4, e1) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (48), (109), (206) are inconsistent by % 188.54/30.15 | | | | | | | | | | | | | | | | | | | sub-proof #275. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | (207) all_252_16 = e3 & op(e4, e0) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | (208) op(e4, e0) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | (209) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | (210) all_252_2 = e1 & op(e3, e4) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | (211) all_252_2 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | (212) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (43), (104), (106), (208), (212) are % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | (213) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (214) all_252_18 = e1 & op(e2, e0) = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_18 = e1 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | (216) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e4) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_252_0 = e3 & op(e4, e4) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (153), (217) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | #235. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_2 = e3 & op(e3, e4) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (211), (218) are inconsistent by sub-proof % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | #234. % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e3) % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_252_6 = e3 & op(e2, e4) = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_252_6 = e3 % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (54) gives: % 188.54/30.15 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (106), (141), (157), (222) are inconsistent % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #101. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (223) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e3) = e1) | (all_252_21 = e1 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_252_7 = e1 & op(e2, e3) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (224) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_252_7 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (225) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) e1 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (215), (226) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_252_18 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (17), (20), (24), (26), (32), (34), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (41), (43), (44), (64), (72), (75), (85), (104), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (107), (208), (227) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #141. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_252_13 = e1 & op(e1, e3) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_13 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_252_2 = e3 & op(e3, e4) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (211), (232) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #234. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_3 = e3 & op(e3, e3) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (157), (233) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_5 = e3 & op(e3, e2) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (84), (235) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #217. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_10 = e3 & op(e3, e1) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_252_10 = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_252_1 = e3 & op(e4, e3) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (240) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_252_1 = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (241) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) e3 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (242) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) e3 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (243) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_252_6 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (12), (18), (21), (47), (48), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (62), (63), (70), (74), (76), (78), (102), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (106), (107), (211), (244) are inconsistent % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #225. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_252_3 = e3 & op(e3, e3) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (157), (245) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_252_7 = e3 & op(e2, e3) = e3) | (all_252_13 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e3) = e3) | (all_252_21 = e3 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_252_7 = e3 & op(e2, e3) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_252_7 = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (248) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) e3 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (249) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_252_10 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (21), (36), (43), (48), (57), (63), (67), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (81), (84), (102), (104), (106), (107), (211), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) are inconsistent by sub-proof #88. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) (all_252_13 = e3 & op(e1, e3) = e3) | (all_252_21 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e3) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_252_13 = e3 & op(e1, e3) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (230), (252) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #87. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_252_21 = e3 & op(e0, e3) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_252_21 = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (18), (21), (29), (36), (43), (48), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (61), (63), (74), (81), (84), (102), (104), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (106), (107), (108), (150), (211), (238), (254) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #85. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_252_17 = e3 & op(e3, e0) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_252_17 = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (256) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) e3 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (257) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_252_6 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (12), (18), (21), (47), (48), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (57), (62), (63), (70), (74), (76), (78), (102), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (106), (107), (211), (258) are inconsistent % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #225. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_252_21 = e1 & op(e0, e3) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (60), (100), (259) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #281. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (260) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e0, e4) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (48), (70), (76), (260) are % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | (261) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (24), (34), (64), (75), (85), (98), (261) are % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #166. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (262) all_252_3 = e1 & op(e3, e3) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (262) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (263) all_252_3 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (263) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (264) e4 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | SIMP: (264) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (265) e4 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | REDUCE: (102), (265) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (266) $false % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | CLOSE: (266) is inconsistent. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (267) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (94), (102), (104), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (106), (107), (109), (138), (150), (267) are % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #84. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | (268) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 188.54/30.16 | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 188.54/30.16 | | | | | | | | | | | | | | | op(e0, e3) = e4) % 188.54/30.16 | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | BETA: splitting (268) gives: % 188.54/30.16 | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | (269) all_252_7 = e4 & op(e2, e3) = e4 % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | ALPHA: (269) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | (270) all_252_7 = e4 % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (270) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | (271) e4 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | SIMP: (271) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | (272) e4 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (272) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | (273) all_252_11 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (13), (18), (21), % 188.54/30.16 | | | | | | | | | | | | | | | | (22), (26), (29), (32), (34), (35), (38), (41), % 188.54/30.16 | | | | | | | | | | | | | | | | (44), (45), (48), (49), (55), (57), (60), (63), % 188.54/30.16 | | | | | | | | | | | | | | | | (72), (74), (94), (102), (104), (106), (107), % 188.54/30.16 | | | | | | | | | | | | | | | | (108), (109), (110), (273) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | sub-proof #191. % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | (274) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 188.54/30.16 | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | BETA: splitting (274) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | (275) all_252_13 = e4 & op(e1, e3) = e4 % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | ALPHA: (275) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | (276) op(e1, e3) = e4 % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | (277) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 188.54/30.16 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (278) all_252_12 = e1 & op(e1, e4) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (12), (26), (34), (38), (41), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (44), (49), (60), (72), (94), (150), (278) are % 188.54/30.16 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #181. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (279) all_252_13 = e1 & op(e1, e3) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (102), (276), (279) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | sub-proof #423. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | (280) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 188.54/30.16 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | op(e1, e0) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (281) all_252_14 = e1 & op(e1, e2) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (282) all_252_14 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (283) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (22), (23), (74), (283) are % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #111. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | (284) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (285) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (286) all_252_11 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (287) op(e2, e1) = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (107), (109), (286), (287) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | sub-proof #115. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | (288) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | (289) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | (290) all_252_15 = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | (291) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (57), (141), (153), (291) are inconsistent % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #156. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | (292) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | (293) all_252_4 = e3 & op(e4, e2) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | (294) all_252_4 = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e3) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (14), (18), (21), (25), (37), (42), (48), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (57), (63), (66), (74), (75), (79), (102), (104), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (106), (107), (276), (295) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #83. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (296) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (27), (28), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (53), (55), (56), (57), (58), (59), (60), (61), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (62), (63), (64), (65), (66), (67), (68), (69), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (70), (71), (72), (73), (74), (75), (76), (78), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (79), (80), (81), (82), (83), (84), (85), (102), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (104), (106), (107), (109), (282), (294), (296) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #95. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | (297) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (297) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_252_9 = e3 & op(e4, e1) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (48), (109), (298) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #275. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_252_16 = e3 & op(e4, e0) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | (300) op(e4, e0) = e3 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (301) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_1 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e3) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_252_0 = e1 & op(e4, e4) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (153), (302) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | #231. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_252_1 = e1 & op(e4, e3) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_252_1 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (141), (304) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e2 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (305) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_252_15 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (107), (109), (306) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | #102. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (307) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_9 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e1) = e1) | (all_252_16 = e1 & % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (307) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) all_252_4 = e1 & op(e4, e2) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_252_4 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (21), (27), (28), (48), (57), (84), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (282), (309) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | #97. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (310) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_16 = % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e4, e0) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (310) gives: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (311) all_252_9 = e1 & op(e4, e1) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (311) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (312) all_252_9 = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (312) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (313) e1 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (313) imply: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (314) all_252_23 = e0 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (9), (26), (34), (38), (41), (44), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (49), (60), (72), (94), (314) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #192. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_252_16 = e1 & op(e4, e0) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (316) op(e4, e0) = e1 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (104), (300), (316) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #387. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | (317) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (35), (44), (317) are inconsistent by % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | sub-proof #540. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (318) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 188.54/30.16 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.16 | | | | | | | | | | | | | | | | | | | (107), (109), (318) are inconsistent by sub-proof % 188.54/30.16 | | | | | | | | | | | | | | | | | | | #82. % 188.54/30.16 | | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | End of split % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.16 | | | | | | | | | | | | | | | | | (319) all_252_21 = e4 & op(e0, e3) = e4 % 188.54/30.16 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (12), (13), (15), % 188.54/30.17 | | | | | | | | | | | | | | | | | (17), (18), (21), (22), (23), (24), (26), (29), % 188.54/30.17 | | | | | | | | | | | | | | | | | (32), (33), (34), (35), (37), (38), (41), (42), % 188.54/30.17 | | | | | | | | | | | | | | | | | (44), (45), (47), (48), (49), (51), (55), (57), % 188.54/30.17 | | | | | | | | | | | | | | | | | (58), (59), (60), (61), (63), (64), (66), (70), % 188.54/30.17 | | | | | | | | | | | | | | | | | (72), (74), (75), (76), (79), (80), (85), (319) % 188.54/30.17 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137. % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (320) all_252_1 = e4 & op(e4, e3) = e4 % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | REF_CLOSE: (63), (141), (320) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | #152. % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | (321) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = % 188.54/30.17 | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 & % 188.54/30.17 | | | | | | | | | | | | | op(e4, e0) = e4) % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | BETA: splitting (321) gives: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (322) all_252_4 = e4 & op(e4, e2) = e4 % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | REF_CLOSE: (6), (30), (82), (322) are inconsistent by % 188.54/30.17 | | | | | | | | | | | | | | sub-proof #388. % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (323) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = % 188.54/30.17 | | | | | | | | | | | | | | e4 & op(e4, e0) = e4) % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | BETA: splitting (323) gives: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | (324) all_252_9 = e4 & op(e4, e1) = e4 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | ALPHA: (324) implies: % 188.54/30.17 | | | | | | | | | | | | | | | (325) all_252_9 = e4 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | COMBINE_EQS: (23), (325) imply: % 188.54/30.17 | | | | | | | | | | | | | | | (326) e4 = e0 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | COMBINE_EQS: (138), (326) imply: % 188.54/30.17 | | | | | | | | | | | | | | | (327) all_252_11 = e0 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (13), (18), (21), % 188.54/30.17 | | | | | | | | | | | | | | | (22), (26), (29), (32), (34), (35), (38), (41), % 188.54/30.17 | | | | | | | | | | | | | | | (44), (45), (48), (49), (55), (57), (60), (63), % 188.54/30.17 | | | | | | | | | | | | | | | (72), (74), (94), (102), (104), (106), (107), % 188.54/30.17 | | | | | | | | | | | | | | | (108), (109), (110), (327) are inconsistent by % 188.54/30.17 | | | | | | | | | | | | | | | sub-proof #191. % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | (328) all_252_16 = e4 & op(e4, e0) = e4 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | ALPHA: (328) implies: % 188.54/30.17 | | | | | | | | | | | | | | | (329) all_252_16 = e4 % 188.54/30.17 | | | | | | | | | | | | | | | (330) op(e4, e0) = e4 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | BETA: splitting (8) gives: % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | (331) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 188.54/30.17 | | | | | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11), (22), (23), (74), (331) are % 188.54/30.17 | | | | | | | | | | | | | | | | inconsistent by sub-proof #207. % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | (332) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 188.54/30.17 | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 188.54/30.17 | | | | | | | | | | | | | | | | op(e0, e1) = e2) % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | BETA: splitting (332) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | (333) all_252_11 = e2 & op(e2, e1) = e2 % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | ALPHA: (333) implies: % 188.54/30.17 | | | | | | | | | | | | | | | | | (334) all_252_11 = e2 % 188.54/30.17 | | | | | | | | | | | | | | | | | (335) op(e2, e1) = e2 % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.17 | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.17 | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.17 | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.17 | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.17 | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.17 | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.17 | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.17 | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.17 | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.17 | | | | | | | | | | | | | | | | | (107), (109), (334), (335) are inconsistent by % 188.54/30.17 | | | | | | | | | | | | | | | | | sub-proof #115. % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | (336) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 188.54/30.17 | | | | | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | BETA: splitting (336) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | (337) all_252_15 = e2 & op(e1, e1) = e2 % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | ALPHA: (337) implies: % 188.54/30.17 | | | | | | | | | | | | | | | | | | (338) all_252_15 = e2 % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | (339) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | BETA: splitting (339) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (340) all_252_16 = e1 & op(e4, e0) = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (329), (340) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | #538. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (341) all_252_17 = e1 & op(e3, e0) = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (342) all_252_17 = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (43), (342) imply: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (343) e2 = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | SIMP: (343) implies: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (344) e2 = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (338), (344) imply: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (345) all_252_15 = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (107), (109), (345) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | #102. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | (346) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 188.54/30.17 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | BETA: splitting (346) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (347) all_252_18 = e1 & op(e2, e0) = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | ALPHA: (347) implies: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (348) all_252_18 = e1 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | (349) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = e3) % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (349) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (350) all_252_6 = e3 & op(e2, e4) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (350) implies: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (351) all_252_6 = e3 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (13), (15), (17), (18), (21), (22), (23), (24), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (26), (29), (32), (33), (34), (35), (37), (38), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (40), (41), (42), (43), (44), (45), (47), (48), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (49), (51), (55), (57), (58), (59), (60), (61), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (62), (63), (64), (66), (70), (72), (74), (75), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (76), (78), (79), (85), (102), (104), (106), % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (107), (330), (348), (351) are inconsistent by % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | sub-proof #168. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (352) all_252_7 = e3 & op(e2, e3) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (48), (352) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | #358. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | (353) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 & % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e3) % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (353) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (354) all_252_8 = e3 & op(e2, e2) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (57), (354) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | #100. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | (355) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3) % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | (356) all_252_11 = e3 & op(e2, e1) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (138), (356) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | #105. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | (357) all_252_18 = e3 & op(e2, e0) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (104), (348), (357) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | #209. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | (358) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (24), (34), (64), (75), (85), (98), (358) are % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #166. % 188.54/30.17 | | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | (359) all_252_23 = e2 & op(e0, e1) = e2 % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (35), (44), (359) are inconsistent by % 188.54/30.17 | | | | | | | | | | | | | | | | | | sub-proof #540. % 188.54/30.17 | | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | (360) all_252_3 = e2 & op(e3, e3) = e2 % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | ALPHA: (360) implies: % 188.54/30.17 | | | | | | | | | (361) all_252_3 = e2 % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | BETA: splitting (55) gives: % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | (362) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = % 188.54/30.17 | | | | | | | | | | e1 & op(e3, e1) = e1) % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.17 | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.17 | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.17 | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.17 | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.17 | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.17 | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.17 | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.17 | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.17 | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.17 | | | | | | | | | | (107), (109), (138), (362) are inconsistent by % 188.54/30.17 | | | | | | | | | | sub-proof #103. % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | (363) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = % 188.54/30.17 | | | | | | | | | | e1 & op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, % 188.54/30.17 | | | | | | | | | | e1) = e1) % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | BETA: splitting (363) gives: % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | (364) all_252_11 = e1 & op(e2, e1) = e1 % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | ALPHA: (364) implies: % 188.54/30.17 | | | | | | | | | | | (365) all_252_11 = e1 % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | REF_CLOSE: (102), (138), (365) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | #461. % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | (366) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 % 188.54/30.17 | | | | | | | | | | | = e1 & op(e0, e1) = e1) % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | BETA: splitting (366) gives: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | (367) all_252_15 = e1 & op(e1, e1) = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | ALPHA: (367) implies: % 188.54/30.17 | | | | | | | | | | | | (368) all_252_15 = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.17 | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.17 | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.17 | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.17 | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.17 | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.17 | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.17 | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.17 | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.17 | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.17 | | | | | | | | | | | | (107), (109), (368) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | #102. % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | (369) all_252_23 = e1 & op(e0, e1) = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | ALPHA: (369) implies: % 188.54/30.17 | | | | | | | | | | | | (370) all_252_23 = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | BETA: splitting (36) gives: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | (371) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = % 188.54/30.17 | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | REF_CLOSE: (18), (21), (36), (43), (48), (57), (63), (67), % 188.54/30.17 | | | | | | | | | | | | | (81), (84), (102), (104), (106), (107), (361), % 188.54/30.17 | | | | | | | | | | | | | (371) are inconsistent by sub-proof #129. % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | (372) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = % 188.54/30.17 | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 188.54/30.17 | | | | | | | | | | | | | op(e3, e0) = e1) % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.17 | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.17 | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.17 | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.17 | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.17 | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.17 | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.17 | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.17 | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.17 | | | | | | | | | | | | | (81), (82), (83), (84), (85), (94), (102), (104), % 188.54/30.17 | | | | | | | | | | | | | (106), (107), (109), (138), (370), (372) are % 188.54/30.17 | | | | | | | | | | | | | inconsistent by sub-proof #84. % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | End of split % 188.54/30.17 | | | | | | | | % 188.54/30.17 | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | % 188.54/30.17 | | | | | | | | (373) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 188.54/30.17 | | | | | | | | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = % 188.54/30.17 | | | | | | | | e2) % 188.54/30.17 | | | | | | | | % 188.54/30.17 | | | | | | | | BETA: splitting (373) gives: % 188.54/30.17 | | | | | | | | % 188.54/30.17 | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | (374) all_252_7 = e2 & op(e2, e3) = e2 % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | REF_CLOSE: (16), (74), (374) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | #222. % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | (375) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = % 188.54/30.17 | | | | | | | | | e2 & op(e0, e3) = e2) % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | BETA: splitting (375) gives: % 188.54/30.17 | | | | | | | | | % 188.54/30.17 | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | (376) all_252_13 = e2 & op(e1, e3) = e2 % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | ALPHA: (376) implies: % 188.54/30.17 | | | | | | | | | | (377) all_252_13 = e2 % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | BETA: splitting (66) gives: % 188.54/30.17 | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | (378) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 % 188.54/30.17 | | | | | | | | | | | = e1 & op(e1, e3) = e1) % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | BETA: splitting (378) gives: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | (379) all_252_12 = e1 & op(e1, e4) = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | REF_CLOSE: (12), (107), (379) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | #224. % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | (380) all_252_13 = e1 & op(e1, e3) = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | REF_CLOSE: (106), (377), (380) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | #180. % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | (381) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 % 188.54/30.17 | | | | | | | | | | | = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 188.54/30.17 | | | | | | | | | | | op(e1, e0) = e1) % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | BETA: splitting (381) gives: % 188.54/30.17 | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | (382) all_252_14 = e1 & op(e1, e2) = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | ALPHA: (382) implies: % 188.54/30.17 | | | | | | | | | | | | (383) all_252_14 = e1 % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | BETA: splitting (51) gives: % 188.54/30.17 | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | (384) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 % 188.54/30.17 | | | | | | | | | | | | | = e3 & op(e1, e3) = e3) % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | BETA: splitting (384) gives: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (385) all_252_12 = e3 & op(e1, e4) = e3 % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | REF_CLOSE: (12), (48), (385) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | #216. % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (386) all_252_13 = e3 & op(e1, e3) = e3 % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | REF_CLOSE: (57), (377), (386) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | #182. % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | End of split % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | (387) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 % 188.54/30.17 | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & % 188.54/30.17 | | | | | | | | | | | | | op(e1, e0) = e3) % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | BETA: splitting (387) gives: % 188.54/30.17 | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (388) all_252_14 = e3 & op(e1, e2) = e3 % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | ALPHA: (388) implies: % 188.54/30.17 | | | | | | | | | | | | | | (389) all_252_14 = e3 % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | REF_CLOSE: (104), (383), (389) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | #179. % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | (390) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 % 188.54/30.17 | | | | | | | | | | | | | | = e3 & op(e1, e0) = e3) % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | BETA: splitting (390) gives: % 188.54/30.17 | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | Case 1: % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | (391) all_252_15 = e3 & op(e1, e1) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | ALPHA: (391) implies: % 188.54/30.17 | | | | | | | | | | | | | | | (392) all_252_15 = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 188.54/30.17 | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 188.54/30.17 | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 188.54/30.17 | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 188.54/30.17 | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 188.54/30.17 | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 188.54/30.17 | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 188.54/30.17 | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 188.54/30.17 | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 188.54/30.17 | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 188.54/30.17 | | | | | | | | | | | | | | | (107), (109), (392) are inconsistent by sub-proof % 188.54/30.17 | | | | | | | | | | | | | | | #113. % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | Case 2: % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | (393) all_252_19 = e3 & op(e1, e0) = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | ALPHA: (393) implies: % 188.54/30.17 | | | | | | | | | | | | | | | (394) all_252_19 = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | COMBINE_EQS: (37), (394) imply: % 188.54/30.17 | | | | | | | | | | | | | | | (395) e4 = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | SIMP: (395) implies: % 188.54/30.17 | | | | | | | | | | | | | | | (396) e4 = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 188.54/30.17 | | | | | | | | | | | | | | | COMBINE_EQS: (138), (396) imply: % 188.54/30.17 | | | | | | | | | | | | | | | (397) all_252_11 = e3 % 188.54/30.17 | | | | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 189.00/30.17 | | | | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 189.00/30.17 | | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 189.00/30.17 | | | | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 189.00/30.17 | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 189.00/30.17 | | | | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 189.00/30.17 | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 189.00/30.17 | | | | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 189.00/30.17 | | | | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 189.00/30.17 | | | | | | | | | | | | | | | (81), (82), (83), (84), (85), (94), (102), (104), % 189.00/30.17 | | | | | | | | | | | | | | | (106), (107), (108), (109), (110), (377), (383), % 189.00/30.17 | | | | | | | | | | | | | | | (397) are inconsistent by sub-proof #107. % 189.00/30.17 | | | | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | | | | End of split % 189.00/30.17 | | | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | | | End of split % 189.00/30.17 | | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | | End of split % 189.00/30.17 | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | Case 2: % 189.00/30.17 | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | | (398) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 189.00/30.17 | | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 189.00/30.17 | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), % 189.00/30.17 | | | | | | | | | | | | (11), (12), (13), (15), (16), (17), (18), (19), % 189.00/30.17 | | | | | | | | | | | | (20), (21), (22), (23), (24), (26), (29), (30), % 189.00/30.17 | | | | | | | | | | | | (31), (32), (33), (34), (35), (36), (37), (38), % 189.00/30.17 | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), % 189.00/30.17 | | | | | | | | | | | | (47), (48), (49), (50), (51), (52), (53), (55), % 189.00/30.17 | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (63), % 189.00/30.17 | | | | | | | | | | | | (64), (65), (66), (67), (68), (69), (70), (71), % 189.00/30.17 | | | | | | | | | | | | (72), (73), (74), (75), (76), (78), (79), (80), % 189.00/30.17 | | | | | | | | | | | | (81), (82), (83), (84), (85), (102), (104), (106), % 189.00/30.17 | | | | | | | | | | | | (107), (109), (398) are inconsistent by sub-proof % 189.00/30.17 | | | | | | | | | | | | #82. % 189.00/30.17 | | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | | End of split % 189.00/30.17 | | | | | | | | | | | % 189.00/30.17 | | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | (399) all_252_21 = e2 & op(e0, e3) = e2 % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | REF_CLOSE: (6), (39), (60), (399) are inconsistent by % 189.00/30.18 | | | | | | | | | | sub-proof #289. % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | End of split % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | End of split % 189.00/30.18 | | | | | | | % 189.00/30.18 | | | | | | Case 2: % 189.00/30.18 | | | | | | | % 189.00/30.18 | | | | | | | (400) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 189.00/30.18 | | | | | | | op(e0, e1) = e4) % 189.00/30.18 | | | | | | | % 189.00/30.18 | | | | | | | BETA: splitting (400) gives: % 189.00/30.18 | | | | | | | % 189.00/30.18 | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | (401) all_252_15 = e4 & op(e1, e1) = e4 % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | ALPHA: (401) implies: % 189.00/30.18 | | | | | | | | (402) all_252_15 = e4 % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | BETA: splitting (68) gives: % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | | (403) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 % 189.00/30.18 | | | | | | | | | & op(e2, e3) = e4) % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | | BETA: splitting (403) gives: % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | (404) all_252_6 = e4 & op(e2, e4) = e4 % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | ALPHA: (404) implies: % 189.00/30.18 | | | | | | | | | | (405) all_252_6 = e4 % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (12), (18), (21), % 189.00/30.18 | | | | | | | | | | (24), (26), (34), (37), (38), (41), (42), (44), % 189.00/30.18 | | | | | | | | | | (47), (48), (49), (51), (57), (60), (62), (63), % 189.00/30.18 | | | | | | | | | | (64), (66), (70), (72), (74), (75), (76), (78), % 189.00/30.18 | | | | | | | | | | (79), (85), (94), (98), (100), (102), (104), % 189.00/30.18 | | | | | | | | | | (106), (107), (402), (405) are inconsistent by % 189.00/30.18 | | | | | | | | | | sub-proof #79. % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | (406) all_252_7 = e4 & op(e2, e3) = e4 % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | REF_CLOSE: (16), (18), (406) are inconsistent by sub-proof % 189.00/30.18 | | | | | | | | | | #165. % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | | (407) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 % 189.00/30.18 | | | | | | | | | & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) % 189.00/30.18 | | | | | | | | | = e4) % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | | BETA: splitting (407) gives: % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | (408) all_252_8 = e4 & op(e2, e2) = e4 % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | ALPHA: (408) implies: % 189.00/30.18 | | | | | | | | | | (409) all_252_8 = e4 % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | REF_CLOSE: (27), (63), (409) are inconsistent by sub-proof % 189.00/30.18 | | | | | | | | | | #163. % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | (410) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = % 189.00/30.18 | | | | | | | | | | e4 & op(e2, e0) = e4) % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | BETA: splitting (410) gives: % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | (411) all_252_11 = e4 & op(e2, e1) = e4 % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | ALPHA: (411) implies: % 189.00/30.18 | | | | | | | | | | | (412) all_252_11 = e4 % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | BETA: splitting (38) gives: % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | (413) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 189.00/30.18 | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | REF_CLOSE: (6), (47), (60), (100), (106), (413) are % 189.00/30.18 | | | | | | | | | | | | inconsistent by sub-proof #244. % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | (414) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 189.00/30.18 | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 189.00/30.18 | | | | | | | | | | | | op(e0, e0) = e1) % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | BETA: splitting (414) gives: % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | (415) all_252_22 = e1 & op(e0, e2) = e1 % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | ALPHA: (415) implies: % 189.00/30.18 | | | | | | | | | | | | | (416) op(e0, e2) = e1 % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | REF_CLOSE: (6), (9), (102), (416) are inconsistent by % 189.00/30.18 | | | | | | | | | | | | | sub-proof #256. % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | (417) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 189.00/30.18 | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | BETA: splitting (417) gives: % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | Case 1: % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | | (418) all_252_23 = e1 & op(e0, e1) = e1 % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | | ALPHA: (418) implies: % 189.00/30.18 | | | | | | | | | | | | | | (419) all_252_23 = e1 % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (12), (13), (18), % 189.00/30.18 | | | | | | | | | | | | | | (21), (22), (23), (24), (26), (29), (32), (34), % 189.00/30.18 | | | | | | | | | | | | | | (35), (37), (38), (41), (42), (44), (45), (48), % 189.00/30.18 | | | | | | | | | | | | | | (49), (51), (55), (57), (60), (63), (64), (66), % 189.00/30.18 | | | | | | | | | | | | | | (72), (74), (75), (79), (85), (94), (102), (104), % 189.00/30.18 | | | | | | | | | | | | | | (106), (107), (108), (109), (110), (402), (412), % 189.00/30.18 | | | | | | | | | | | | | | (419) are inconsistent by sub-proof #78. % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | | (420) all_252_24 = e1 & op(e0, e0) = e1 % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | | ALPHA: (420) implies: % 189.00/30.18 | | | | | | | | | | | | | | (421) op(e0, e0) = e1 % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | | REF_CLOSE: (6), (34), (98), (421) are inconsistent by % 189.00/30.18 | | | | | | | | | | | | | | sub-proof #474. % 189.00/30.18 | | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | (422) all_252_18 = e4 & op(e2, e0) = e4 % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | ALPHA: (422) implies: % 189.00/30.18 | | | | | | | | | | | (423) all_252_18 = e4 % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (12), (13), (15), % 189.00/30.18 | | | | | | | | | | | (17), (18), (20), (21), (22), (23), (24), (26), % 189.00/30.18 | | | | | | | | | | | (29), (32), (33), (34), (35), (37), (38), (40), % 189.00/30.18 | | | | | | | | | | | (41), (42), (43), (44), (45), (47), (48), (49), % 189.00/30.18 | | | | | | | | | | | (51), (55), (57), (58), (59), (60), (61), (63), % 189.00/30.18 | | | | | | | | | | | (64), (66), (72), (74), (75), (79), (85), (102), % 189.00/30.18 | | | | | | | | | | | (104), (106), (107), (423) are inconsistent by % 189.00/30.18 | | | | | | | | | | | sub-proof #158. % 189.00/30.18 | | | | | | | | | | | % 189.00/30.18 | | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | | % 189.00/30.18 | | | | | | | | | End of split % 189.00/30.18 | | | | | | | | | % 189.00/30.18 | | | | | | | | End of split % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | Case 2: % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | (424) all_252_23 = e4 & op(e0, e1) = e4 % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | ALPHA: (424) implies: % 189.00/30.18 | | | | | | | | (425) op(e0, e1) = e4 % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | | REF_CLOSE: (6), (35), (102), (110), (425) are inconsistent by % 189.00/30.18 | | | | | | | | sub-proof #401. % 189.00/30.18 | | | | | | | | % 189.00/30.18 | | | | | | | End of split % 189.00/30.18 | | | | | | | % 189.00/30.18 | | | | | | End of split % 189.00/30.18 | | | | | | % 189.00/30.18 | | | | | End of split % 189.00/30.18 | | | | | % 189.00/30.18 | | | | Case 2: % 189.00/30.18 | | | | | % 189.00/30.18 | | | | | (426) all_250_23 = e0 % 189.00/30.18 | | | | | % 189.00/30.18 | | | | | REF_CLOSE: (41), (72), (426) are inconsistent by sub-proof #486. % 189.00/30.18 | | | | | % 189.00/30.18 | | | | End of split % 189.00/30.18 | | | | % 189.00/30.18 | | | End of split % 189.00/30.18 | | | % 189.00/30.18 | | End of split % 189.00/30.18 | | % 189.00/30.18 | End of split % 189.00/30.18 | % 189.00/30.18 End of proof % 189.00/30.18 % 189.00/30.18 Sub-proof #78 shows that the following formulas are inconsistent: % 189.00/30.18 ---------------------------------------------------------------- % 189.00/30.18 (1) all_252_20 = e2 % 189.00/30.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.18 (3) ~ (all_20_2 = e4) % 189.00/30.18 (4) all_252_15 = e4 % 189.00/30.18 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.18 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.18 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.18 (6) op(e0, e2) = e4 % 189.00/30.18 (7) op(e3, e1) = all_36_2 % 189.00/30.18 (8) ~ (e2 = e1) % 189.00/30.18 (9) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.18 (10) all_252_12 = e0 % 189.00/30.18 (11) op(e4, e1) = e0 % 189.00/30.18 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.18 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.18 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.18 (13) all_252_11 = e4 % 189.00/30.18 (14) ~ (e4 = e0) % 189.00/30.18 (15) ~ (e4 = e3) % 189.00/30.18 (16) ~ (all_36_2 = e2) % 189.00/30.18 (17) all_252_9 = e0 % 189.00/30.18 (18) ~ (all_40_2 = all_34_2) % 189.00/30.18 (19) ~ (all_244_24 = all_20_2) % 189.00/30.18 (20) op(e1, e4) = e0 % 189.00/30.18 (21) all_252_23 = e1 % 189.00/30.18 (22) ~ (all_20_2 = e3) % 189.00/30.18 (23) op(e0, e0) = all_244_24 % 189.00/30.18 (24) op(e0, e1) = all_20_2 % 189.00/30.18 (25) all_252_19 = e4 % 189.00/30.18 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.18 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.18 (27) ~ (all_20_2 = e0) % 189.00/30.18 (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.18 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.18 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.18 (29) ~ (all_20_2 = e2) % 189.00/30.18 (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.18 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.18 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.18 (31) ~ (e3 = e0) % 189.00/30.18 (32) ~ (all_20_2 = all_8_1) % 189.00/30.18 (33) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.18 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.18 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.18 (34) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.18 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.18 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.18 (35) ~ (e3 = e2) % 189.00/30.18 (36) op(e0, e3) = all_8_1 % 189.00/30.18 (37) op(e1, e4) = e1 % 189.00/30.18 (38) ~ (e4 = e2) % 189.00/30.18 (39) op(e2, e0) = all_40_2 % 189.00/30.18 (40) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.18 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.18 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.18 (41) ~ (e1 = e0) % 189.00/30.18 (42) all_250_23 = all_20_2 % 189.00/30.18 (43) ~ (e3 = e1) % 189.00/30.18 (44) ~ (e2 = e0) % 189.00/30.18 (45) op(e0, e1) = e1 % 189.00/30.18 (46) op(e1, e0) = all_34_2 % 189.00/30.18 (47) ~ (all_34_2 = e2) % 189.00/30.18 (48) ~ (e4 = e1) % 189.00/30.18 (49) op(e2, e0) = e1 % 189.00/30.18 % 189.00/30.18 Begin of proof % 189.00/30.18 | % 189.00/30.18 | BETA: splitting (5) gives: % 189.00/30.18 | % 189.00/30.18 | Case 1: % 189.00/30.18 | | % 189.00/30.18 | | (50) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 189.00/30.18 | | e2) % 189.00/30.18 | | % 189.00/30.18 | | REF_CLOSE: (2), (7), (16), (17), (44), (50) are inconsistent by sub-proof % 189.00/30.18 | | #111. % 189.00/30.18 | | % 189.00/30.18 | Case 2: % 189.00/30.18 | | % 189.00/30.18 | | (51) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) % 189.00/30.18 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.18 | | % 189.00/30.18 | | BETA: splitting (51) gives: % 189.00/30.18 | | % 189.00/30.18 | | Case 1: % 189.00/30.18 | | | % 189.00/30.18 | | | (52) all_252_11 = e2 & op(e2, e1) = e2 % 189.00/30.18 | | | % 189.00/30.18 | | | ALPHA: (52) implies: % 189.00/30.18 | | | (53) all_252_11 = e2 % 189.00/30.18 | | | % 189.00/30.18 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.18 | | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24), % 189.00/30.18 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 189.00/30.18 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), % 189.00/30.18 | | | (45), (46), (47), (48), (49), (53) are inconsistent by % 189.00/30.18 | | | sub-proof #173. % 189.00/30.18 | | | % 189.00/30.18 | | Case 2: % 189.00/30.18 | | | % 189.00/30.18 | | | (54) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, % 189.00/30.18 | | | e1) = e2) % 189.00/30.18 | | | % 189.00/30.18 | | | BETA: splitting (54) gives: % 189.00/30.18 | | | % 189.00/30.18 | | | Case 1: % 189.00/30.18 | | | | % 189.00/30.18 | | | | (55) all_252_15 = e2 & op(e1, e1) = e2 % 189.00/30.18 | | | | % 189.00/30.18 | | | | ALPHA: (55) implies: % 189.00/30.18 | | | | (56) all_252_15 = e2 % 189.00/30.18 | | | | % 189.00/30.18 | | | | COMBINE_EQS: (4), (56) imply: % 189.00/30.18 | | | | (57) e4 = e2 % 189.00/30.18 | | | | % 189.00/30.18 | | | | COMBINE_EQS: (13), (57) imply: % 189.00/30.18 | | | | (58) all_252_11 = e2 % 189.00/30.18 | | | | % 189.00/30.18 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 189.00/30.18 | | | | (12), (14), (15), (16), (18), (19), (20), (21), (22), (23), % 189.00/30.18 | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 189.00/30.18 | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 189.00/30.18 | | | | (44), (45), (46), (47), (48), (49), (58) are inconsistent by % 189.00/30.18 | | | | sub-proof #173. % 189.00/30.18 | | | | % 189.00/30.18 | | | Case 2: % 189.00/30.18 | | | | % 189.00/30.18 | | | | (59) all_252_23 = e2 & op(e0, e1) = e2 % 189.00/30.18 | | | | % 189.00/30.18 | | | | REF_CLOSE: (2), (24), (29), (59) are inconsistent by sub-proof #540. % 189.00/30.18 | | | | % 189.00/30.18 | | | End of split % 189.00/30.18 | | | % 189.00/30.18 | | End of split % 189.00/30.18 | | % 189.00/30.18 | End of split % 189.00/30.18 | % 189.00/30.18 End of proof % 189.00/30.18 % 189.00/30.18 Sub-proof #79 shows that the following formulas are inconsistent: % 189.00/30.18 ---------------------------------------------------------------- % 189.00/30.18 (1) all_252_20 = e2 % 189.00/30.18 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.18 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.18 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.18 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.18 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.18 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.18 (5) ~ (all_20_2 = e4) % 189.00/30.18 (6) all_252_15 = e4 % 189.00/30.18 (7) op(e0, e2) = e4 % 189.00/30.18 (8) ~ (e2 = e1) % 189.00/30.18 (9) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.18 (10) all_252_12 = e0 % 189.00/30.18 (11) ~ (e4 = e0) % 189.00/30.18 (12) ~ (e4 = e3) % 189.00/30.18 (13) ~ (all_40_2 = all_34_2) % 189.00/30.18 (14) ~ (all_244_24 = all_20_2) % 189.00/30.18 (15) op(e0, e0) = all_244_24 % 189.00/30.18 (16) all_252_19 = e4 % 189.00/30.18 (17) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.18 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.18 (18) ~ (all_20_2 = e0) % 189.00/30.18 (19) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.18 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.18 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.18 (20) ~ (all_20_2 = e2) % 189.00/30.18 (21) op(e0, e4) = e2 % 189.00/30.18 (22) ~ (e3 = e0) % 189.00/30.18 (23) ~ (all_20_2 = all_8_1) % 189.00/30.18 (24) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.18 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.18 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.18 (25) all_252_6 = e4 % 189.00/30.18 (26) ~ (e3 = e2) % 189.00/30.18 (27) op(e0, e3) = all_8_1 % 189.00/30.18 (28) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.18 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.18 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.18 (29) ~ (e4 = e2) % 189.00/30.18 (30) op(e2, e0) = all_40_2 % 189.00/30.18 (31) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.18 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.18 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.18 (32) ~ (e1 = e0) % 189.00/30.18 (33) op(e0, e4) = all_12_2 % 189.00/30.18 (34) all_250_23 = all_20_2 % 189.00/30.18 (35) ~ (e3 = e1) % 189.00/30.18 (36) ~ (e2 = e0) % 189.00/30.18 (37) op(e1, e0) = all_34_2 % 189.00/30.18 (38) ~ (all_244_24 = e1) % 189.00/30.18 (39) ~ (all_8_1 = e1) % 189.00/30.18 (40) ~ (all_12_2 = e3) % 189.00/30.18 (41) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.18 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.18 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.18 (42) ~ (all_34_2 = e2) % 189.00/30.18 (43) ~ (e4 = e1) % 189.00/30.18 (44) op(e2, e0) = e1 % 189.00/30.18 % 189.00/30.18 Begin of proof % 189.00/30.18 | % 189.00/30.18 | BETA: splitting (17) gives: % 189.00/30.18 | % 189.00/30.18 | Case 1: % 189.00/30.18 | | % 189.00/30.18 | | (45) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.00/30.18 | | = e1) % 189.00/30.18 | | % 189.00/30.18 | | REF_CLOSE: (4), (8), (21), (27), (39), (45) are inconsistent by sub-proof % 189.00/30.18 | | #244. % 189.00/30.18 | | % 189.00/30.18 | Case 2: % 189.00/30.18 | | % 189.00/30.18 | | (46) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.00/30.18 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.18 | | % 189.00/30.18 | | BETA: splitting (46) gives: % 189.00/30.18 | | % 189.00/30.18 | | Case 1: % 189.00/30.18 | | | % 189.00/30.18 | | | (47) all_252_22 = e1 & op(e0, e2) = e1 % 189.00/30.18 | | | % 189.00/30.18 | | | ALPHA: (47) implies: % 189.00/30.18 | | | (48) op(e0, e2) = e1 % 189.00/30.18 | | | % 189.00/30.18 | | | REF_CLOSE: (4), (7), (43), (48) are inconsistent by sub-proof #256. % 189.00/30.18 | | | % 189.00/30.18 | | Case 2: % 189.00/30.18 | | | % 189.00/30.18 | | | (49) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.00/30.18 | | | e0) = e1) % 189.00/30.18 | | | % 189.00/30.18 | | | BETA: splitting (49) gives: % 189.00/30.18 | | | % 189.00/30.18 | | | Case 1: % 189.00/30.18 | | | | % 189.00/30.18 | | | | (50) all_252_23 = e1 & op(e0, e1) = e1 % 189.00/30.18 | | | | % 189.00/30.18 | | | | ALPHA: (50) implies: % 189.00/30.18 | | | | (51) all_252_23 = e1 % 189.00/30.18 | | | | % 189.00/30.18 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 189.00/30.18 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 189.00/30.18 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), % 189.00/30.18 | | | | (32), (33), (34), (35), (36), (37), (40), (41), (42), (43), % 189.00/30.18 | | | | (44), (51) are inconsistent by sub-proof #80. % 189.00/30.18 | | | | % 189.00/30.18 | | | Case 2: % 189.00/30.18 | | | | % 189.00/30.18 | | | | (52) all_252_24 = e1 & op(e0, e0) = e1 % 189.00/30.18 | | | | % 189.00/30.18 | | | | ALPHA: (52) implies: % 189.00/30.18 | | | | (53) op(e0, e0) = e1 % 189.00/30.18 | | | | % 189.00/30.18 | | | | REF_CLOSE: (4), (15), (38), (53) are inconsistent by sub-proof #474. % 189.00/30.18 | | | | % 189.00/30.18 | | | End of split % 189.00/30.18 | | | % 189.00/30.18 | | End of split % 189.00/30.18 | | % 189.00/30.18 | End of split % 189.00/30.18 | % 189.00/30.18 End of proof % 189.00/30.18 % 189.00/30.18 Sub-proof #80 shows that the following formulas are inconsistent: % 189.00/30.18 ---------------------------------------------------------------- % 189.00/30.18 (1) all_252_20 = e2 % 189.00/30.18 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.18 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.18 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.18 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.18 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.18 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.18 (5) ~ (all_20_2 = e4) % 189.00/30.18 (6) all_252_15 = e4 % 189.00/30.18 (7) op(e0, e2) = e4 % 189.00/30.18 (8) ~ (e2 = e1) % 189.00/30.18 (9) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.18 (10) all_252_12 = e0 % 189.00/30.18 (11) ~ (e4 = e0) % 189.00/30.18 (12) ~ (e4 = e3) % 189.00/30.18 (13) ~ (all_40_2 = all_34_2) % 189.00/30.18 (14) ~ (all_244_24 = all_20_2) % 189.00/30.18 (15) all_252_23 = e1 % 189.00/30.18 (16) op(e0, e0) = all_244_24 % 189.00/30.18 (17) all_252_19 = e4 % 189.00/30.18 (18) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.18 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.18 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.18 (19) ~ (all_20_2 = e0) % 189.00/30.18 (20) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.18 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.18 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.19 (21) ~ (all_20_2 = e2) % 189.00/30.19 (22) op(e0, e4) = e2 % 189.00/30.19 (23) ~ (e3 = e0) % 189.00/30.19 (24) ~ (all_20_2 = all_8_1) % 189.00/30.19 (25) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.19 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.19 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.19 (26) all_252_6 = e4 % 189.00/30.19 (27) ~ (e3 = e2) % 189.00/30.19 (28) op(e0, e3) = all_8_1 % 189.00/30.19 (29) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.19 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.19 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.19 (30) ~ (e4 = e2) % 189.00/30.19 (31) op(e2, e0) = all_40_2 % 189.00/30.19 (32) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.19 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.19 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.19 (33) ~ (e1 = e0) % 189.00/30.19 (34) op(e0, e4) = all_12_2 % 189.00/30.19 (35) all_250_23 = all_20_2 % 189.00/30.19 (36) ~ (e3 = e1) % 189.00/30.19 (37) ~ (e2 = e0) % 189.00/30.19 (38) op(e1, e0) = all_34_2 % 189.00/30.19 (39) ~ (all_12_2 = e3) % 189.00/30.19 (40) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.19 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.19 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.19 (41) ~ (all_34_2 = e2) % 189.00/30.19 (42) ~ (e4 = e1) % 189.00/30.19 (43) op(e2, e0) = e1 % 189.00/30.19 % 189.00/30.19 Begin of proof % 189.00/30.19 | % 189.00/30.19 | BETA: splitting (20) gives: % 189.00/30.19 | % 189.00/30.19 | Case 1: % 189.00/30.19 | | % 189.00/30.19 | | (44) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 189.00/30.19 | | = e2) % 189.00/30.19 | | % 189.00/30.19 | | BETA: splitting (44) gives: % 189.00/30.19 | | % 189.00/30.19 | | Case 1: % 189.00/30.19 | | | % 189.00/30.19 | | | (45) all_252_12 = e2 & op(e1, e4) = e2 % 189.00/30.19 | | | % 189.00/30.19 | | | ALPHA: (45) implies: % 189.00/30.19 | | | (46) all_252_12 = e2 % 189.00/30.19 | | | % 189.00/30.19 | | | REF_CLOSE: (10), (37), (46) are inconsistent by sub-proof #81. % 189.00/30.19 | | | % 189.00/30.19 | | Case 2: % 189.00/30.19 | | | % 189.00/30.19 | | | (47) all_252_13 = e2 & op(e1, e3) = e2 % 189.00/30.19 | | | % 189.00/30.19 | | | ALPHA: (47) implies: % 189.00/30.19 | | | (48) all_252_13 = e2 % 189.00/30.19 | | | % 189.00/30.19 | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), % 189.00/30.19 | | | (15), (16), (17), (18), (19), (21), (23), (24), (25), (27), % 189.00/30.19 | | | (28), (31), (32), (35), (36), (38), (42), (43), (48) are % 189.00/30.19 | | | inconsistent by sub-proof #176. % 189.00/30.19 | | | % 189.00/30.19 | | End of split % 189.00/30.19 | | % 189.00/30.19 | Case 2: % 189.00/30.19 | | % 189.00/30.19 | | (49) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) % 189.00/30.19 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.19 | | % 189.00/30.19 | | BETA: splitting (49) gives: % 189.00/30.19 | | % 189.00/30.19 | | Case 1: % 189.00/30.19 | | | % 189.00/30.19 | | | (50) all_252_14 = e2 & op(e1, e2) = e2 % 189.00/30.19 | | | % 189.00/30.19 | | | ALPHA: (50) implies: % 189.00/30.19 | | | (51) all_252_14 = e2 % 189.00/30.19 | | | % 189.00/30.19 | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14), % 189.00/30.19 | | | (15), (16), (17), (18), (19), (21), (23), (24), (25), (27), % 189.00/30.19 | | | (28), (31), (32), (35), (36), (38), (42), (43), (51) are % 189.00/30.19 | | | inconsistent by sub-proof #174. % 189.00/30.19 | | | % 189.00/30.19 | | Case 2: % 189.00/30.19 | | | % 189.00/30.19 | | | (52) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, % 189.00/30.19 | | | e0) = e2) % 189.00/30.19 | | | % 189.00/30.19 | | | BETA: splitting (52) gives: % 189.00/30.19 | | | % 189.00/30.19 | | | Case 1: % 189.00/30.19 | | | | % 189.00/30.19 | | | | (53) all_252_15 = e2 & op(e1, e1) = e2 % 189.00/30.19 | | | | % 189.00/30.19 | | | | ALPHA: (53) implies: % 189.00/30.19 | | | | (54) all_252_15 = e2 % 189.00/30.19 | | | | % 189.00/30.19 | | | | COMBINE_EQS: (6), (54) imply: % 189.00/30.19 | | | | (55) e4 = e2 % 189.00/30.19 | | | | % 189.00/30.19 | | | | SIMP: (55) implies: % 189.00/30.19 | | | | (56) e4 = e2 % 189.00/30.19 | | | | % 189.00/30.19 | | | | COMBINE_EQS: (26), (56) imply: % 189.00/30.19 | | | | (57) all_252_6 = e2 % 189.00/30.19 | | | | % 189.00/30.19 | | | | REF_CLOSE: (1), (2), (3), (4), (8), (10), (11), (12), (22), (23), (27), % 189.00/30.19 | | | | (29), (30), (33), (34), (36), (37), (39), (40), (42), (57) % 189.00/30.19 | | | | are inconsistent by sub-proof #223. % 189.00/30.19 | | | | % 189.00/30.19 | | | Case 2: % 189.00/30.19 | | | | % 189.00/30.19 | | | | (58) all_252_19 = e2 & op(e1, e0) = e2 % 189.00/30.19 | | | | % 189.00/30.19 | | | | REF_CLOSE: (4), (38), (41), (58) are inconsistent by sub-proof #438. % 189.00/30.19 | | | | % 189.00/30.19 | | | End of split % 189.00/30.19 | | | % 189.00/30.19 | | End of split % 189.00/30.19 | | % 189.00/30.19 | End of split % 189.00/30.19 | % 189.00/30.19 End of proof % 189.00/30.19 % 189.00/30.19 Sub-proof #81 shows that the following formulas are inconsistent: % 189.00/30.19 ---------------------------------------------------------------- % 189.00/30.19 (1) all_252_12 = e2 % 189.00/30.19 (2) all_252_12 = e0 % 189.00/30.19 (3) ~ (e2 = e0) % 189.00/30.19 % 189.00/30.19 Begin of proof % 189.00/30.19 | % 189.00/30.19 | COMBINE_EQS: (1), (2) imply: % 189.00/30.19 | (4) e2 = e0 % 189.00/30.19 | % 189.00/30.19 | SIMP: (4) implies: % 189.00/30.19 | (5) e2 = e0 % 189.00/30.19 | % 189.00/30.19 | REDUCE: (3), (5) imply: % 189.00/30.19 | (6) $false % 189.00/30.19 | % 189.00/30.19 | CLOSE: (6) is inconsistent. % 189.00/30.19 | % 189.00/30.19 End of proof % 189.00/30.19 % 189.00/30.19 Sub-proof #82 shows that the following formulas are inconsistent: % 189.00/30.19 ---------------------------------------------------------------- % 189.00/30.19 (1) all_252_20 = e2 % 189.00/30.19 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.19 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.19 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.19 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.19 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.19 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.19 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.19 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.19 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.19 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.19 (6) ~ (all_20_2 = e4) % 189.00/30.19 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.19 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.19 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.19 (8) op(e0, e2) = e4 % 189.00/30.19 (9) op(e0, e2) = all_28_2 % 189.00/30.19 (10) op(e3, e1) = all_36_2 % 189.00/30.19 (11) ~ (e2 = e1) % 189.00/30.19 (12) all_252_12 = e0 % 189.00/30.19 (13) op(e4, e1) = e0 % 189.00/30.19 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.19 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.19 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.19 (15) op(e2, e1) = e0 % 189.00/30.19 (16) all_252_7 = e0 % 189.00/30.19 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.19 all_250_23 = e0 % 189.00/30.19 (18) ~ (e4 = e0) % 189.00/30.19 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.19 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.19 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.19 (20) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.19 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.19 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.19 (21) ~ (e4 = e3) % 189.00/30.19 (22) ~ (all_36_2 = e2) % 189.00/30.19 (23) all_252_9 = e0 % 189.00/30.19 (24) ~ (all_40_2 = all_34_2) % 189.00/30.19 (25) ~ (all_244_24 = all_20_2) % 189.00/30.19 (26) op(e1, e4) = e0 % 189.00/30.19 (27) ~ (all_6_2 = e4) % 189.00/30.19 (28) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.19 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.19 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.19 (29) ~ (all_20_2 = e3) % 189.00/30.19 (30) op(all_20_2, e4) = e1 % 189.00/30.19 (31) op(e0, e0) = all_244_24 % 189.00/30.19 (32) op(e0, e1) = all_20_2 % 189.00/30.19 (33) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.19 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.19 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.19 (34) all_252_19 = e4 % 189.00/30.19 (35) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.19 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.19 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.19 (36) ~ (all_8_1 = e2) % 189.00/30.19 (37) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.19 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.19 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.19 (38) ~ (all_20_2 = e0) % 189.00/30.19 (39) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.19 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.19 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.19 (40) all_252_17 = e2 % 189.00/30.19 (41) ~ (all_20_2 = e2) % 189.00/30.19 (42) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.19 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.19 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.19 (43) op(e4, e4) = all_244_0 % 189.00/30.19 (44) op(e0, e4) = e2 % 189.00/30.19 (45) ~ (e3 = e0) % 189.00/30.19 (46) ~ (all_20_2 = all_8_1) % 189.00/30.19 (47) ~ (all_28_2 = e0) % 189.00/30.19 (48) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.19 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.19 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.19 (49) ~ (all_244_0 = e2) % 189.00/30.19 (50) op(e2, all_40_2) = e0 % 189.00/30.19 (51) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.19 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.19 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.19 (52) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.19 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.19 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.19 (53) ~ (e3 = e2) % 189.00/30.19 (54) all_252_22 = e4 % 189.00/30.19 (55) op(e4, all_20_2) = e0 % 189.00/30.19 (56) op(e0, e3) = all_8_1 % 189.00/30.19 (57) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.19 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.19 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.19 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.19 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.19 op(e0, e1) = e0))) % 189.00/30.19 (58) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = % 189.00/30.19 e1) % 189.00/30.19 (59) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.19 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.19 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.19 (60) ~ (e4 = e2) % 189.00/30.19 (61) op(e2, e0) = all_40_2 % 189.00/30.19 (62) op(all_28_2, all_40_2) = e2 % 189.00/30.19 (63) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.19 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.19 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.19 (64) ~ (e1 = e0) % 189.00/30.19 (65) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.19 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.19 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.19 (66) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.19 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.19 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.19 (67) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.19 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.19 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.19 (68) op(e0, e4) = all_12_2 % 189.00/30.19 (69) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.19 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.19 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.19 (70) all_250_23 = all_20_2 % 189.00/30.19 (71) ~ (e3 = e1) % 189.00/30.19 (72) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.19 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.19 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.19 (73) ~ (e2 = e0) % 189.00/30.19 (74) op(e1, e0) = all_34_2 % 189.00/30.19 (75) ~ (all_12_2 = e3) % 189.00/30.19 (76) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.19 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.19 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.19 (77) ~ (all_34_2 = e2) % 189.00/30.19 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.19 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.19 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.19 (79) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.19 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.19 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.19 (80) op(e4, e2) = all_6_2 % 189.00/30.19 (81) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.19 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.19 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.19 (82) all_252_5 = e0 % 189.00/30.19 (83) ~ (e4 = e1) % 189.00/30.19 (84) op(e2, e0) = e1 % 189.00/30.19 % 189.00/30.19 Begin of proof % 189.00/30.19 | % 189.00/30.19 | BETA: splitting (58) gives: % 189.00/30.19 | % 189.00/30.19 | Case 1: % 189.00/30.19 | | % 189.00/30.19 | | (85) all_252_15 = e1 & op(e1, e1) = e1 % 189.00/30.19 | | % 189.00/30.19 | | ALPHA: (85) implies: % 189.00/30.19 | | (86) all_252_15 = e1 % 189.00/30.19 | | % 189.00/30.19 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.19 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.19 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 189.00/30.19 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 189.00/30.19 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 189.00/30.19 | | (57), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 189.00/30.19 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 189.00/30.19 | | (80), (81), (82), (83), (84), (86) are inconsistent by sub-proof % 189.00/30.19 | | #102. % 189.00/30.19 | | % 189.00/30.19 | Case 2: % 189.00/30.19 | | % 189.00/30.19 | | (87) all_252_19 = e1 & op(e1, e0) = e1 % 189.00/30.19 | | % 189.00/30.19 | | ALPHA: (87) implies: % 189.00/30.19 | | (88) op(e1, e0) = e1 % 189.00/30.19 | | % 189.00/30.19 | | REF_CLOSE: (5), (24), (61), (74), (84), (88) are inconsistent by sub-proof % 189.00/30.19 | | #352. % 189.00/30.19 | | % 189.00/30.19 | End of split % 189.00/30.19 | % 189.00/30.19 End of proof % 189.00/30.19 % 189.00/30.19 Sub-proof #83 shows that the following formulas are inconsistent: % 189.00/30.19 ---------------------------------------------------------------- % 189.00/30.19 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.19 (2) ~ (e2 = e1) % 189.00/30.19 (3) op(e1, e3) = all_62_2 % 189.00/30.19 (4) ~ (e4 = e0) % 189.00/30.19 (5) ~ (e4 = e3) % 189.00/30.19 (6) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 189.00/30.19 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) = % 189.00/30.19 e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 189.00/30.19 (7) all_252_19 = e4 % 189.00/30.19 (8) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 189.00/30.19 | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.19 e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.19 (9) op(e1, e3) = e4 % 189.00/30.19 (10) ~ (e3 = e0) % 189.00/30.19 (11) ~ (e3 = e2) % 189.00/30.19 (12) ~ (e4 = e2) % 189.00/30.19 (13) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.19 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.19 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.19 (14) ~ (e1 = e0) % 189.00/30.19 (15) ~ (e3 = e1) % 189.00/30.19 (16) ~ (e2 = e0) % 189.00/30.19 (17) op(e1, e0) = all_34_2 % 189.00/30.19 (18) ~ (all_34_2 = e2) % 189.00/30.19 (19) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.19 e3) % 189.00/30.19 (20) ~ (e4 = e1) % 189.00/30.19 % 189.00/30.19 Begin of proof % 189.00/30.19 | % 189.00/30.19 | BETA: splitting (19) gives: % 189.00/30.19 | % 189.00/30.19 | Case 1: % 189.00/30.19 | | % 189.00/30.19 | | (21) all_252_12 = e3 & op(e1, e4) = e3 % 189.00/30.19 | | % 189.00/30.19 | | ALPHA: (21) implies: % 189.00/30.19 | | (22) all_252_12 = e3 % 189.00/30.19 | | % 189.00/30.19 | | BETA: splitting (6) gives: % 189.00/30.19 | | % 189.00/30.19 | | Case 1: % 189.00/30.19 | | | % 189.00/30.19 | | | (23) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, % 189.00/30.19 | | | e3) = e0) % 189.00/30.19 | | | % 189.00/30.19 | | | BETA: splitting (23) gives: % 189.00/30.19 | | | % 189.00/30.19 | | | Case 1: % 189.00/30.19 | | | | % 189.00/30.19 | | | | (24) all_252_12 = e0 & op(e1, e4) = e0 % 189.00/30.19 | | | | % 189.00/30.19 | | | | REF_CLOSE: (10), (22), (24) are inconsistent by sub-proof #417. % 189.00/30.19 | | | | % 189.00/30.19 | | | Case 2: % 189.00/30.19 | | | | % 189.00/30.19 | | | | (25) all_252_13 = e0 & op(e1, e3) = e0 % 189.00/30.19 | | | | % 189.00/30.19 | | | | REF_CLOSE: (1), (4), (9), (25) are inconsistent by sub-proof #428. % 189.00/30.19 | | | | % 189.00/30.19 | | | End of split % 189.00/30.19 | | | % 189.00/30.19 | | Case 2: % 189.00/30.19 | | | % 189.00/30.19 | | | (26) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 189.00/30.19 | | | e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 189.00/30.19 | | | % 189.00/30.19 | | | BETA: splitting (26) gives: % 189.00/30.19 | | | % 189.00/30.19 | | | Case 1: % 189.00/30.19 | | | | % 189.00/30.19 | | | | (27) all_252_14 = e0 & op(e1, e2) = e0 % 189.00/30.19 | | | | % 189.00/30.19 | | | | ALPHA: (27) implies: % 189.00/30.19 | | | | (28) all_252_14 = e0 % 189.00/30.19 | | | | % 189.00/30.19 | | | | BETA: splitting (8) gives: % 189.00/30.19 | | | | % 189.00/30.19 | | | | Case 1: % 189.00/30.19 | | | | | % 189.00/30.19 | | | | | (29) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & % 189.00/30.19 | | | | | op(e1, e3) = e2) % 189.00/30.19 | | | | | % 189.00/30.19 | | | | | REF_CLOSE: (1), (9), (11), (12), (22), (29) are inconsistent by % 189.00/30.19 | | | | | sub-proof #425. % 189.00/30.19 | | | | | % 189.00/30.19 | | | | Case 2: % 189.00/30.19 | | | | | % 189.00/30.19 | | | | | (30) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & % 189.00/30.19 | | | | | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.19 | | | | | % 189.00/30.19 | | | | | BETA: splitting (30) gives: % 189.00/30.19 | | | | | % 189.00/30.19 | | | | | Case 1: % 189.00/30.19 | | | | | | % 189.00/30.19 | | | | | | (31) all_252_14 = e2 & op(e1, e2) = e2 % 189.00/30.19 | | | | | | % 189.00/30.19 | | | | | | REF_CLOSE: (16), (28), (31) are inconsistent by sub-proof #397. % 189.00/30.19 | | | | | | % 189.00/30.19 | | | | | Case 2: % 189.00/30.19 | | | | | | % 189.00/30.19 | | | | | | (32) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 189.00/30.19 | | | | | | op(e1, e0) = e2) % 189.00/30.19 | | | | | | % 189.00/30.19 | | | | | | BETA: splitting (32) gives: % 189.00/30.19 | | | | | | % 189.00/30.19 | | | | | | Case 1: % 189.00/30.19 | | | | | | | % 189.00/30.19 | | | | | | | (33) all_252_15 = e2 & op(e1, e1) = e2 % 189.00/30.19 | | | | | | | % 189.00/30.20 | | | | | | | ALPHA: (33) implies: % 189.00/30.20 | | | | | | | (34) all_252_15 = e2 % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | BETA: splitting (13) gives: % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | Case 1: % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | | (35) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & % 189.00/30.20 | | | | | | | | op(e1, e3) = e1) % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | | BETA: splitting (35) gives: % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | | Case 1: % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | (36) all_252_12 = e1 & op(e1, e4) = e1 % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | REF_CLOSE: (15), (22), (36) are inconsistent by sub-proof % 189.00/30.20 | | | | | | | | | #424. % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | Case 2: % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | (37) all_252_13 = e1 & op(e1, e3) = e1 % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | REF_CLOSE: (1), (9), (20), (37) are inconsistent by sub-proof % 189.00/30.20 | | | | | | | | | #423. % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | End of split % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | Case 2: % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | | (38) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & % 189.00/30.20 | | | | | | | | op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | | BETA: splitting (38) gives: % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | | Case 1: % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | (39) all_252_14 = e1 & op(e1, e2) = e1 % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | ALPHA: (39) implies: % 189.00/30.20 | | | | | | | | | (40) all_252_14 = e1 % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | COMBINE_EQS: (28), (40) imply: % 189.00/30.20 | | | | | | | | | (41) e1 = e0 % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | SIMP: (41) implies: % 189.00/30.20 | | | | | | | | | (42) e1 = e0 % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | REDUCE: (14), (42) imply: % 189.00/30.20 | | | | | | | | | (43) $false % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | CLOSE: (43) is inconsistent. % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | Case 2: % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | (44) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 % 189.00/30.20 | | | | | | | | | & op(e1, e0) = e1) % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | BETA: splitting (44) gives: % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | | Case 1: % 189.00/30.20 | | | | | | | | | | % 189.00/30.20 | | | | | | | | | | (45) all_252_15 = e1 & op(e1, e1) = e1 % 189.00/30.20 | | | | | | | | | | % 189.00/30.20 | | | | | | | | | | REF_CLOSE: (2), (34), (45) are inconsistent by sub-proof % 189.00/30.20 | | | | | | | | | | #415. % 189.00/30.20 | | | | | | | | | | % 189.00/30.20 | | | | | | | | | Case 2: % 189.00/30.20 | | | | | | | | | | % 189.00/30.20 | | | | | | | | | | (46) all_252_19 = e1 & op(e1, e0) = e1 % 189.00/30.20 | | | | | | | | | | % 189.00/30.20 | | | | | | | | | | REF_CLOSE: (7), (20), (46) are inconsistent by sub-proof % 189.00/30.20 | | | | | | | | | | #354. % 189.00/30.20 | | | | | | | | | | % 189.00/30.20 | | | | | | | | | End of split % 189.00/30.20 | | | | | | | | | % 189.00/30.20 | | | | | | | | End of split % 189.00/30.20 | | | | | | | | % 189.00/30.20 | | | | | | | End of split % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | Case 2: % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | (47) all_252_19 = e2 & op(e1, e0) = e2 % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | REF_CLOSE: (1), (17), (18), (47) are inconsistent by sub-proof % 189.00/30.20 | | | | | | | #438. % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | End of split % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | End of split % 189.00/30.20 | | | | | % 189.00/30.20 | | | | End of split % 189.00/30.20 | | | | % 189.00/30.20 | | | Case 2: % 189.00/30.20 | | | | % 189.00/30.20 | | | | (48) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, % 189.00/30.20 | | | | e0) = e0) % 189.00/30.20 | | | | % 189.00/30.20 | | | | BETA: splitting (48) gives: % 189.00/30.20 | | | | % 189.00/30.20 | | | | Case 1: % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | (49) all_252_15 = e0 & op(e1, e1) = e0 % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | ALPHA: (49) implies: % 189.00/30.20 | | | | | (50) all_252_15 = e0 % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | BETA: splitting (8) gives: % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | Case 1: % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | | (51) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & % 189.00/30.20 | | | | | | op(e1, e3) = e2) % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | | REF_CLOSE: (1), (9), (11), (12), (22), (51) are inconsistent by % 189.00/30.20 | | | | | | sub-proof #425. % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | Case 2: % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | | (52) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & % 189.00/30.20 | | | | | | op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | | BETA: splitting (52) gives: % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | | Case 1: % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | (53) all_252_14 = e2 & op(e1, e2) = e2 % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | ALPHA: (53) implies: % 189.00/30.20 | | | | | | | (54) all_252_14 = e2 % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | REF_CLOSE: (1), (2), (7), (9), (13), (14), (15), (20), (22), (50), % 189.00/30.20 | | | | | | | (54) are inconsistent by sub-proof #353. % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | Case 2: % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | (55) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 189.00/30.20 | | | | | | | op(e1, e0) = e2) % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | | REF_CLOSE: (1), (16), (17), (18), (50), (55) are inconsistent by % 189.00/30.20 | | | | | | | sub-proof #404. % 189.00/30.20 | | | | | | | % 189.00/30.20 | | | | | | End of split % 189.00/30.20 | | | | | | % 189.00/30.20 | | | | | End of split % 189.00/30.20 | | | | | % 189.00/30.20 | | | | Case 2: % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | (56) all_252_19 = e0 & op(e1, e0) = e0 % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | ALPHA: (56) implies: % 189.00/30.20 | | | | | (57) all_252_19 = e0 % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | COMBINE_EQS: (7), (57) imply: % 189.00/30.20 | | | | | (58) e4 = e0 % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | REDUCE: (4), (58) imply: % 189.00/30.20 | | | | | (59) $false % 189.00/30.20 | | | | | % 189.00/30.20 | | | | | CLOSE: (59) is inconsistent. % 189.00/30.20 | | | | | % 189.00/30.20 | | | | End of split % 189.00/30.20 | | | | % 189.00/30.20 | | | End of split % 189.00/30.20 | | | % 189.00/30.20 | | End of split % 189.00/30.20 | | % 189.00/30.20 | Case 2: % 189.00/30.20 | | % 189.00/30.20 | | (60) all_252_13 = e3 & op(e1, e3) = e3 % 189.00/30.20 | | % 189.00/30.20 | | REF_CLOSE: (1), (3), (5), (9), (60) are inconsistent by sub-proof #336. % 189.00/30.20 | | % 189.00/30.20 | End of split % 189.00/30.20 | % 189.00/30.20 End of proof % 189.00/30.20 % 189.00/30.20 Sub-proof #84 shows that the following formulas are inconsistent: % 189.00/30.20 ---------------------------------------------------------------- % 189.00/30.20 (1) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.20 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.20 (2) all_252_20 = e2 % 189.00/30.20 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.20 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.20 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.20 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.20 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.20 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.20 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.20 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.20 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.20 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.20 (7) ~ (all_20_2 = e4) % 189.00/30.20 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.20 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.20 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.20 (9) op(e0, e2) = e4 % 189.00/30.20 (10) op(e0, e2) = all_28_2 % 189.00/30.20 (11) op(e3, e1) = all_36_2 % 189.00/30.20 (12) ~ (e2 = e1) % 189.00/30.20 (13) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.20 (14) all_252_12 = e0 % 189.00/30.20 (15) op(e4, e1) = e0 % 189.00/30.20 (16) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.20 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.20 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.20 (17) op(e2, e1) = e0 % 189.00/30.20 (18) all_252_7 = e0 % 189.00/30.20 (19) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.20 all_250_23 = e0 % 189.00/30.20 (20) all_252_11 = e4 % 189.00/30.20 (21) ~ (e4 = e0) % 189.00/30.20 (22) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.20 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.20 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.20 (23) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.20 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.20 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.20 (24) ~ (e4 = e3) % 189.00/30.20 (25) ~ (all_36_2 = e2) % 189.00/30.20 (26) all_252_9 = e0 % 189.00/30.20 (27) ~ (all_40_2 = all_34_2) % 189.00/30.20 (28) ~ (all_244_24 = all_20_2) % 189.00/30.20 (29) op(e1, e4) = e0 % 189.00/30.20 (30) ~ (all_6_2 = e4) % 189.00/30.20 (31) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.20 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.20 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.20 (32) all_252_23 = e1 % 189.00/30.20 (33) ~ (all_20_2 = e3) % 189.00/30.20 (34) op(all_20_2, e4) = e1 % 189.00/30.20 (35) op(e0, e0) = all_244_24 % 189.00/30.20 (36) op(e0, e1) = all_20_2 % 189.00/30.20 (37) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.20 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.20 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.20 (38) all_252_19 = e4 % 189.00/30.20 (39) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.20 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.20 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.20 (40) ~ (all_8_1 = e2) % 189.00/30.20 (41) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.20 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.20 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.20 (42) ~ (all_20_2 = e0) % 189.00/30.20 (43) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.20 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.20 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.20 (44) all_252_17 = e2 % 189.00/30.20 (45) ~ (all_20_2 = e2) % 189.00/30.20 (46) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.20 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.20 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.20 (47) op(e4, e4) = all_244_0 % 189.00/30.20 (48) op(e0, e4) = e2 % 189.00/30.20 (49) ~ (e3 = e0) % 189.00/30.20 (50) ~ (all_20_2 = all_8_1) % 189.00/30.20 (51) ~ (all_28_2 = e0) % 189.00/30.20 (52) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.20 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.20 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.20 (53) ~ (all_244_0 = e2) % 189.00/30.20 (54) op(e2, all_40_2) = e0 % 189.00/30.20 (55) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.20 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.20 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.20 (56) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.20 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.20 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.20 (57) ~ (e3 = e2) % 189.00/30.20 (58) all_252_22 = e4 % 189.00/30.20 (59) op(e4, all_20_2) = e0 % 189.00/30.20 (60) op(e0, e3) = all_8_1 % 189.00/30.20 (61) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.20 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.20 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.20 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.20 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.20 op(e0, e1) = e0))) % 189.00/30.20 (62) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.20 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.20 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.20 (63) ~ (e4 = e2) % 189.00/30.20 (64) op(e2, e0) = all_40_2 % 189.00/30.20 (65) op(all_28_2, all_40_2) = e2 % 189.00/30.20 (66) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.20 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.20 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.20 (67) ~ (e1 = e0) % 189.00/30.20 (68) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.20 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.20 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.20 (69) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.20 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.20 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.20 (70) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.20 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.20 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.20 (71) op(e0, e4) = all_12_2 % 189.00/30.20 (72) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.20 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.20 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.20 (73) all_250_23 = all_20_2 % 189.00/30.20 (74) ~ (e3 = e1) % 189.00/30.20 (75) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.20 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.20 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.20 (76) ~ (e2 = e0) % 189.00/30.20 (77) op(e1, e0) = all_34_2 % 189.00/30.20 (78) ~ (all_12_2 = e3) % 189.00/30.20 (79) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.20 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.20 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.20 (80) ~ (all_34_2 = e2) % 189.00/30.20 (81) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.20 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.20 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.20 (82) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.20 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.20 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.20 (83) op(e4, e2) = all_6_2 % 189.00/30.20 (84) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.20 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.20 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.20 (85) all_252_5 = e0 % 189.00/30.20 (86) ~ (e4 = e1) % 189.00/30.20 (87) op(e2, e0) = e1 % 189.00/30.20 % 189.00/30.20 Begin of proof % 189.00/30.20 | % 189.00/30.20 | BETA: splitting (1) gives: % 189.00/30.20 | % 189.00/30.20 | Case 1: % 189.00/30.20 | | % 189.00/30.20 | | (88) all_252_5 = e1 & op(e3, e2) = e1 % 189.00/30.20 | | % 189.00/30.20 | | ALPHA: (88) implies: % 189.00/30.20 | | (89) all_252_5 = e1 % 189.00/30.20 | | % 189.00/30.20 | | COMBINE_EQS: (85), (89) imply: % 189.00/30.20 | | (90) e1 = e0 % 189.00/30.20 | | % 189.00/30.20 | | SIMP: (90) implies: % 189.00/30.20 | | (91) e1 = e0 % 189.00/30.20 | | % 189.00/30.20 | | COMBINE_EQS: (32), (91) imply: % 189.00/30.20 | | (92) all_252_23 = e0 % 189.00/30.20 | | % 189.00/30.20 | | REF_CLOSE: (2), (6), (7), (9), (13), (28), (35), (39), (42), (45), (50), % 189.00/30.20 | | (60), (73), (92) are inconsistent by sub-proof #192. % 189.00/30.20 | | % 189.00/30.20 | Case 2: % 189.00/30.20 | | % 189.00/30.20 | | (93) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) % 189.00/30.20 | | = e1) % 189.00/30.20 | | % 189.00/30.20 | | BETA: splitting (93) gives: % 189.00/30.20 | | % 189.00/30.20 | | Case 1: % 189.00/30.20 | | | % 189.00/30.20 | | | (94) all_252_10 = e1 & op(e3, e1) = e1 % 189.00/30.20 | | | % 189.00/30.20 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), % 189.00/30.20 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 189.00/30.20 | | | (25), (26), (27), (28), (29), (30), (31), (33), (34), (35), % 189.00/30.20 | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 189.00/30.20 | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), % 189.00/30.20 | | | (56), (57), (58), (59), (60), (61), (62), (63), (64), (65), % 189.00/30.20 | | | (66), (67), (68), (69), (70), (71), (72), (73), (74), (75), % 189.00/30.20 | | | (76), (77), (78), (79), (80), (81), (82), (83), (84), (85), % 189.00/30.20 | | | (86), (87), (94) are inconsistent by sub-proof #104. % 189.00/30.20 | | | % 189.00/30.20 | | Case 2: % 189.00/30.20 | | | % 189.00/30.20 | | | (95) all_252_17 = e1 & op(e3, e0) = e1 % 189.00/30.20 | | | % 189.00/30.20 | | | REF_CLOSE: (12), (44), (95) are inconsistent by sub-proof #247. % 189.00/30.20 | | | % 189.00/30.20 | | End of split % 189.00/30.20 | | % 189.00/30.20 | End of split % 189.00/30.20 | % 189.00/30.20 End of proof % 189.00/30.20 % 189.00/30.20 Sub-proof #85 shows that the following formulas are inconsistent: % 189.00/30.20 ---------------------------------------------------------------- % 189.00/30.20 (1) all_252_20 = e2 % 189.00/30.20 (2) all_252_21 = e3 % 189.00/30.20 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.20 (4) ~ (e2 = e1) % 189.00/30.20 (5) ~ (e4 = e0) % 189.00/30.20 (6) ~ (e4 = e3) % 189.00/30.20 (7) op(e1, e4) = e0 % 189.00/30.20 (8) all_252_23 = e1 % 189.00/30.20 (9) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.00/30.20 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.20 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.20 (10) all_252_10 = e3 % 189.00/30.20 (11) all_252_17 = e2 % 189.00/30.20 (12) all_252_2 = e1 % 189.00/30.20 (13) ~ (e3 = e0) % 189.00/30.20 (14) all_252_22 = e4 % 189.00/30.20 (15) op(e1, e4) = e1 % 189.00/30.20 (16) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.20 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.20 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.20 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.20 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.20 op(e0, e1) = e0))) % 189.00/30.20 (17) ~ (e4 = e2) % 189.00/30.20 (18) ~ (e1 = e0) % 189.00/30.20 (19) ~ (e3 = e1) % 189.00/30.20 (20) ~ (e2 = e0) % 189.00/30.20 (21) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.20 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.20 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.20 (22) all_252_5 = e0 % 189.00/30.20 (23) ~ (e4 = e1) % 189.00/30.20 % 189.00/30.20 Begin of proof % 189.00/30.20 | % 189.00/30.20 | BETA: splitting (16) gives: % 189.00/30.20 | % 189.00/30.20 | Case 1: % 189.00/30.20 | | % 189.00/30.20 | | % 189.00/30.20 | | GROUND_INST: instantiating (3) with e0, e1, e4, e1, simplifying with (7), % 189.00/30.20 | | (15) gives: % 189.00/30.20 | | (24) e1 = e0 % 189.00/30.20 | | % 189.00/30.20 | | COMBINE_EQS: (12), (24) imply: % 189.00/30.20 | | (25) all_252_2 = e0 % 189.00/30.20 | | % 189.00/30.20 | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (17), (18), (19), (21), (22), % 189.00/30.20 | | (23), (25) are inconsistent by sub-proof #86. % 189.00/30.20 | | % 189.00/30.20 | Case 2: % 189.00/30.20 | | % 189.00/30.20 | | (26) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) % 189.00/30.20 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & % 189.00/30.20 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) | % 189.00/30.20 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, % 189.00/30.20 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)) % 189.00/30.20 | | % 189.00/30.20 | | ALPHA: (26) implies: % 189.00/30.20 | | (27) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 189.00/30.20 | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.20 | | op(e0, e1) = e0) % 189.00/30.20 | | % 189.00/30.20 | | REF_CLOSE: (1), (2), (5), (8), (13), (14), (18), (20), (27) are inconsistent % 189.00/30.20 | | by sub-proof #238. % 189.00/30.20 | | % 189.00/30.20 | End of split % 189.00/30.20 | % 189.00/30.20 End of proof % 189.00/30.20 % 189.00/30.20 Sub-proof #86 shows that the following formulas are inconsistent: % 189.00/30.20 ---------------------------------------------------------------- % 189.00/30.20 (1) ~ (e2 = e1) % 189.00/30.20 (2) all_252_2 = e0 % 189.00/30.20 (3) ~ (e4 = e0) % 189.00/30.20 (4) ~ (e4 = e3) % 189.00/30.20 (5) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.00/30.20 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.20 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.20 (6) all_252_10 = e3 % 189.00/30.20 (7) all_252_17 = e2 % 189.00/30.20 (8) ~ (e4 = e2) % 189.00/30.20 (9) ~ (e1 = e0) % 189.00/30.20 (10) ~ (e3 = e1) % 189.00/30.20 (11) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.20 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.20 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.20 (12) all_252_5 = e0 % 189.00/30.20 (13) ~ (e4 = e1) % 189.00/30.20 % 189.00/30.20 Begin of proof % 189.00/30.20 | % 189.00/30.20 | BETA: splitting (11) gives: % 189.00/30.20 | % 189.00/30.20 | Case 1: % 189.00/30.20 | | % 189.00/30.21 | | (14) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = % 189.00/30.21 | | e4) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (14) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (15) all_252_2 = e4 & op(e3, e4) = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | ALPHA: (15) implies: % 189.00/30.21 | | | (16) all_252_2 = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | COMBINE_EQS: (2), (16) imply: % 189.00/30.21 | | | (17) e4 = e0 % 189.00/30.21 | | | % 189.00/30.21 | | | REDUCE: (3), (17) imply: % 189.00/30.21 | | | (18) $false % 189.00/30.21 | | | % 189.00/30.21 | | | CLOSE: (18) is inconsistent. % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (19) all_252_3 = e4 & op(e3, e3) = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | ALPHA: (19) implies: % 189.00/30.21 | | | (20) all_252_3 = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | BETA: splitting (5) gives: % 189.00/30.21 | | | % 189.00/30.21 | | | Case 1: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (21) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, % 189.00/30.21 | | | | e3) = e1) % 189.00/30.21 | | | | % 189.00/30.21 | | | | BETA: splitting (21) gives: % 189.00/30.21 | | | | % 189.00/30.21 | | | | Case 1: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | (22) all_252_2 = e1 & op(e3, e4) = e1 % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | REF_CLOSE: (2), (9), (22) are inconsistent by sub-proof #230. % 189.00/30.21 | | | | | % 189.00/30.21 | | | | Case 2: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | (23) all_252_3 = e1 & op(e3, e3) = e1 % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | REF_CLOSE: (13), (20), (23) are inconsistent by sub-proof #149. % 189.00/30.21 | | | | | % 189.00/30.21 | | | | End of split % 189.00/30.21 | | | | % 189.00/30.21 | | | Case 2: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (24) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, % 189.00/30.21 | | | | e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.21 | | | | % 189.00/30.21 | | | | BETA: splitting (24) gives: % 189.00/30.21 | | | | % 189.00/30.21 | | | | Case 1: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | (25) all_252_5 = e1 & op(e3, e2) = e1 % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | REF_CLOSE: (9), (12), (25) are inconsistent by sub-proof #155. % 189.00/30.21 | | | | | % 189.00/30.21 | | | | Case 2: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | (26) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 189.00/30.21 | | | | | op(e3, e0) = e1) % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | BETA: splitting (26) gives: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | Case 1: % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | (27) all_252_10 = e1 & op(e3, e1) = e1 % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | ALPHA: (27) implies: % 189.00/30.21 | | | | | | (28) all_252_10 = e1 % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | COMBINE_EQS: (6), (28) imply: % 189.00/30.21 | | | | | | (29) e3 = e1 % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | REDUCE: (10), (29) imply: % 189.00/30.21 | | | | | | (30) $false % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | CLOSE: (30) is inconsistent. % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | Case 2: % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | (31) all_252_17 = e1 & op(e3, e0) = e1 % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | | REF_CLOSE: (1), (7), (31) are inconsistent by sub-proof #247. % 189.00/30.21 | | | | | | % 189.00/30.21 | | | | | End of split % 189.00/30.21 | | | | | % 189.00/30.21 | | | | End of split % 189.00/30.21 | | | | % 189.00/30.21 | | | End of split % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | Case 2: % 189.00/30.21 | | % 189.00/30.21 | | (32) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.21 | | e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (32) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (33) all_252_5 = e4 & op(e3, e2) = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (3), (12), (33) are inconsistent by sub-proof #132. % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (34) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, % 189.00/30.21 | | | e0) = e4) % 189.00/30.21 | | | % 189.00/30.21 | | | BETA: splitting (34) gives: % 189.00/30.21 | | | % 189.00/30.21 | | | Case 1: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (35) all_252_10 = e4 & op(e3, e1) = e4 % 189.00/30.21 | | | | % 189.00/30.21 | | | | ALPHA: (35) implies: % 189.00/30.21 | | | | (36) all_252_10 = e4 % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (4), (6), (36) are inconsistent by sub-proof #219. % 189.00/30.21 | | | | % 189.00/30.21 | | | Case 2: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (37) all_252_17 = e4 & op(e3, e0) = e4 % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (7), (8), (37) are inconsistent by sub-proof #131. % 189.00/30.21 | | | | % 189.00/30.21 | | | End of split % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | End of split % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #87 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) all_252_13 = e3 & op(e1, e3) = e3 % 189.00/30.21 (2) all_252_13 = e1 % 189.00/30.21 (3) ~ (e3 = e1) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | ALPHA: (1) implies: % 189.00/30.21 | (4) all_252_13 = e3 % 189.00/30.21 | % 189.00/30.21 | COMBINE_EQS: (2), (4) imply: % 189.00/30.21 | (5) e3 = e1 % 189.00/30.21 | % 189.00/30.21 | REDUCE: (3), (5) imply: % 189.00/30.21 | (6) $false % 189.00/30.21 | % 189.00/30.21 | CLOSE: (6) is inconsistent. % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #88 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) ~ (e2 = e1) % 189.00/30.21 (2) ~ (e4 = e0) % 189.00/30.21 (3) ~ (e4 = e3) % 189.00/30.21 (4) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.00/30.21 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.21 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.21 (5) all_252_17 = e2 % 189.00/30.21 (6) all_252_2 = e1 % 189.00/30.21 (7) ~ (e3 = e0) % 189.00/30.21 (8) all_252_10 = e0 % 189.00/30.21 (9) ~ (e3 = e2) % 189.00/30.21 (10) ~ (e4 = e2) % 189.00/30.21 (11) ~ (e1 = e0) % 189.00/30.21 (12) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.21 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.21 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.21 (13) ~ (e3 = e1) % 189.00/30.21 (14) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.21 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.21 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.21 (15) all_252_5 = e0 % 189.00/30.21 (16) ~ (e4 = e1) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | BETA: splitting (12) gives: % 189.00/30.21 | % 189.00/30.21 | Case 1: % 189.00/30.21 | | % 189.00/30.21 | | (17) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = % 189.00/30.21 | | e3) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (17) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (18) all_252_2 = e3 & op(e3, e4) = e3 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (6), (13), (18) are inconsistent by sub-proof #151. % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (19) all_252_3 = e3 & op(e3, e3) = e3 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (13), (14), (15), % 189.00/30.21 | | | (16), (19) are inconsistent by sub-proof #90. % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | Case 2: % 189.00/30.21 | | % 189.00/30.21 | | (20) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.21 | | e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (20) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (21) all_252_5 = e3 & op(e3, e2) = e3 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (7), (15), (21) are inconsistent by sub-proof #217. % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (22) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, % 189.00/30.21 | | | e0) = e3) % 189.00/30.21 | | | % 189.00/30.21 | | | BETA: splitting (22) gives: % 189.00/30.21 | | | % 189.00/30.21 | | | Case 1: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (23) all_252_10 = e3 & op(e3, e1) = e3 % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (7), (8), (23) are inconsistent by sub-proof #89. % 189.00/30.21 | | | | % 189.00/30.21 | | | Case 2: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (24) all_252_17 = e3 & op(e3, e0) = e3 % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (5), (9), (24) are inconsistent by sub-proof #159. % 189.00/30.21 | | | | % 189.00/30.21 | | | End of split % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | End of split % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #89 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) all_252_10 = e3 & op(e3, e1) = e3 % 189.00/30.21 (2) all_252_10 = e0 % 189.00/30.21 (3) ~ (e3 = e0) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | ALPHA: (1) implies: % 189.00/30.21 | (4) all_252_10 = e3 % 189.00/30.21 | % 189.00/30.21 | COMBINE_EQS: (2), (4) imply: % 189.00/30.21 | (5) e3 = e0 % 189.00/30.21 | % 189.00/30.21 | SIMP: (5) implies: % 189.00/30.21 | (6) e3 = e0 % 189.00/30.21 | % 189.00/30.21 | REDUCE: (3), (6) imply: % 189.00/30.21 | (7) $false % 189.00/30.21 | % 189.00/30.21 | CLOSE: (7) is inconsistent. % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #90 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) ~ (e2 = e1) % 189.00/30.21 (2) ~ (e4 = e0) % 189.00/30.21 (3) ~ (e4 = e3) % 189.00/30.21 (4) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.00/30.21 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.21 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.21 (5) all_252_17 = e2 % 189.00/30.21 (6) all_252_3 = e3 & op(e3, e3) = e3 % 189.00/30.21 (7) all_252_10 = e0 % 189.00/30.21 (8) ~ (e4 = e2) % 189.00/30.21 (9) ~ (e1 = e0) % 189.00/30.21 (10) ~ (e3 = e1) % 189.00/30.21 (11) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.21 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.21 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.21 (12) all_252_5 = e0 % 189.00/30.21 (13) ~ (e4 = e1) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | ALPHA: (6) implies: % 189.00/30.21 | (14) all_252_3 = e3 % 189.00/30.21 | % 189.00/30.21 | BETA: splitting (11) gives: % 189.00/30.21 | % 189.00/30.21 | Case 1: % 189.00/30.21 | | % 189.00/30.21 | | (15) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = % 189.00/30.21 | | e4) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (15) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (16) all_252_2 = e4 & op(e3, e4) = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | ALPHA: (16) implies: % 189.00/30.21 | | | (17) all_252_2 = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | BETA: splitting (4) gives: % 189.00/30.21 | | | % 189.00/30.21 | | | Case 1: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (18) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, % 189.00/30.21 | | | | e3) = e1) % 189.00/30.21 | | | | % 189.00/30.21 | | | | BETA: splitting (18) gives: % 189.00/30.21 | | | | % 189.00/30.21 | | | | Case 1: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | (19) all_252_2 = e1 & op(e3, e4) = e1 % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | REF_CLOSE: (13), (17), (19) are inconsistent by sub-proof #232. % 189.00/30.21 | | | | | % 189.00/30.21 | | | | Case 2: % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | (20) all_252_3 = e1 & op(e3, e3) = e1 % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | ALPHA: (20) implies: % 189.00/30.21 | | | | | (21) all_252_3 = e1 % 189.00/30.21 | | | | | % 189.00/30.21 | | | | | REF_CLOSE: (10), (14), (21) are inconsistent by sub-proof #366. % 189.00/30.21 | | | | | % 189.00/30.21 | | | | End of split % 189.00/30.21 | | | | % 189.00/30.21 | | | Case 2: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (22) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, % 189.00/30.21 | | | | e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (1), (5), (7), (9), (12), (22) are inconsistent by sub-proof % 189.00/30.21 | | | | #93. % 189.00/30.21 | | | | % 189.00/30.21 | | | End of split % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (23) all_252_3 = e4 & op(e3, e3) = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (3), (14), (23) are inconsistent by sub-proof #92. % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | Case 2: % 189.00/30.21 | | % 189.00/30.21 | | (24) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.21 | | e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (24) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (25) all_252_5 = e4 & op(e3, e2) = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | ALPHA: (25) implies: % 189.00/30.21 | | | (26) all_252_5 = e4 % 189.00/30.21 | | | % 189.00/30.21 | | | COMBINE_EQS: (12), (26) imply: % 189.00/30.21 | | | (27) e4 = e0 % 189.00/30.21 | | | % 189.00/30.21 | | | SIMP: (27) implies: % 189.00/30.21 | | | (28) e4 = e0 % 189.00/30.21 | | | % 189.00/30.21 | | | REDUCE: (2), (28) imply: % 189.00/30.21 | | | (29) $false % 189.00/30.21 | | | % 189.00/30.21 | | | CLOSE: (29) is inconsistent. % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (30) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, % 189.00/30.21 | | | e0) = e4) % 189.00/30.21 | | | % 189.00/30.21 | | | BETA: splitting (30) gives: % 189.00/30.21 | | | % 189.00/30.21 | | | Case 1: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (31) all_252_10 = e4 & op(e3, e1) = e4 % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (2), (7), (31) are inconsistent by sub-proof #91. % 189.00/30.21 | | | | % 189.00/30.21 | | | Case 2: % 189.00/30.21 | | | | % 189.00/30.21 | | | | (32) all_252_17 = e4 & op(e3, e0) = e4 % 189.00/30.21 | | | | % 189.00/30.21 | | | | REF_CLOSE: (5), (8), (32) are inconsistent by sub-proof #131. % 189.00/30.21 | | | | % 189.00/30.21 | | | End of split % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | End of split % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #91 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) all_252_10 = e4 & op(e3, e1) = e4 % 189.00/30.21 (2) all_252_10 = e0 % 189.00/30.21 (3) ~ (e4 = e0) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | ALPHA: (1) implies: % 189.00/30.21 | (4) all_252_10 = e4 % 189.00/30.21 | % 189.00/30.21 | COMBINE_EQS: (2), (4) imply: % 189.00/30.21 | (5) e4 = e0 % 189.00/30.21 | % 189.00/30.21 | REDUCE: (3), (5) imply: % 189.00/30.21 | (6) $false % 189.00/30.21 | % 189.00/30.21 | CLOSE: (6) is inconsistent. % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #92 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) all_252_3 = e4 & op(e3, e3) = e4 % 189.00/30.21 (2) all_252_3 = e3 % 189.00/30.21 (3) ~ (e4 = e3) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | ALPHA: (1) implies: % 189.00/30.21 | (4) all_252_3 = e4 % 189.00/30.21 | % 189.00/30.21 | COMBINE_EQS: (2), (4) imply: % 189.00/30.21 | (5) e4 = e3 % 189.00/30.21 | % 189.00/30.21 | SIMP: (5) implies: % 189.00/30.21 | (6) e4 = e3 % 189.00/30.21 | % 189.00/30.21 | REDUCE: (3), (6) imply: % 189.00/30.21 | (7) $false % 189.00/30.21 | % 189.00/30.21 | CLOSE: (7) is inconsistent. % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #93 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.21 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.21 (2) ~ (e2 = e1) % 189.00/30.21 (3) all_252_17 = e2 % 189.00/30.21 (4) all_252_10 = e0 % 189.00/30.21 (5) ~ (e1 = e0) % 189.00/30.21 (6) all_252_5 = e0 % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | BETA: splitting (1) gives: % 189.00/30.21 | % 189.00/30.21 | Case 1: % 189.00/30.21 | | % 189.00/30.21 | | (7) all_252_5 = e1 & op(e3, e2) = e1 % 189.00/30.21 | | % 189.00/30.21 | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #155. % 189.00/30.21 | | % 189.00/30.21 | Case 2: % 189.00/30.21 | | % 189.00/30.21 | | (8) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.21 | | e1) % 189.00/30.21 | | % 189.00/30.21 | | BETA: splitting (8) gives: % 189.00/30.21 | | % 189.00/30.21 | | Case 1: % 189.00/30.21 | | | % 189.00/30.21 | | | (9) all_252_10 = e1 & op(e3, e1) = e1 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #94. % 189.00/30.21 | | | % 189.00/30.21 | | Case 2: % 189.00/30.21 | | | % 189.00/30.21 | | | (10) all_252_17 = e1 & op(e3, e0) = e1 % 189.00/30.21 | | | % 189.00/30.21 | | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #247. % 189.00/30.21 | | | % 189.00/30.21 | | End of split % 189.00/30.21 | | % 189.00/30.21 | End of split % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #94 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) all_252_10 = e1 & op(e3, e1) = e1 % 189.00/30.21 (2) all_252_10 = e0 % 189.00/30.21 (3) ~ (e1 = e0) % 189.00/30.21 % 189.00/30.21 Begin of proof % 189.00/30.21 | % 189.00/30.21 | ALPHA: (1) implies: % 189.00/30.21 | (4) all_252_10 = e1 % 189.00/30.21 | % 189.00/30.21 | COMBINE_EQS: (2), (4) imply: % 189.00/30.21 | (5) e1 = e0 % 189.00/30.21 | % 189.00/30.21 | SIMP: (5) implies: % 189.00/30.21 | (6) e1 = e0 % 189.00/30.21 | % 189.00/30.21 | REDUCE: (3), (6) imply: % 189.00/30.21 | (7) $false % 189.00/30.21 | % 189.00/30.21 | CLOSE: (7) is inconsistent. % 189.00/30.21 | % 189.00/30.21 End of proof % 189.00/30.21 % 189.00/30.21 Sub-proof #95 shows that the following formulas are inconsistent: % 189.00/30.21 ---------------------------------------------------------------- % 189.00/30.21 (1) all_252_20 = e2 % 189.00/30.21 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.21 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.21 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.21 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.21 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.21 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.21 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.21 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.21 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.21 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.21 (6) ~ (all_20_2 = e4) % 189.00/30.21 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.21 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.21 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.21 (8) op(e0, e2) = e4 % 189.00/30.21 (9) op(e0, e2) = all_28_2 % 189.00/30.21 (10) op(e3, e1) = all_36_2 % 189.00/30.21 (11) ~ (e2 = e1) % 189.00/30.21 (12) all_252_12 = e0 % 189.00/30.21 (13) op(e4, e1) = e0 % 189.00/30.21 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.21 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.21 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.21 (15) op(e2, e1) = e0 % 189.00/30.21 (16) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.21 e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.21 (17) all_252_7 = e0 % 189.00/30.21 (18) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.21 all_250_23 = e0 % 189.00/30.21 (19) ~ (e4 = e0) % 189.00/30.21 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.21 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.21 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.21 (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.21 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.21 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.21 (22) ~ (e4 = e3) % 189.00/30.21 (23) ~ (all_36_2 = e2) % 189.00/30.21 (24) all_252_9 = e0 % 189.00/30.21 (25) ~ (all_40_2 = all_34_2) % 189.00/30.21 (26) ~ (all_244_24 = all_20_2) % 189.00/30.21 (27) all_252_8 = e2 % 189.00/30.21 (28) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) % 189.00/30.21 | (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 189.00/30.21 e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 189.00/30.21 (29) op(e1, e4) = e0 % 189.00/30.21 (30) ~ (all_6_2 = e4) % 189.00/30.21 (31) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.21 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.21 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.21 (32) all_252_4 = e3 % 189.00/30.21 (33) ~ (all_20_2 = e3) % 189.00/30.21 (34) op(all_20_2, e4) = e1 % 189.00/30.21 (35) op(e0, e0) = all_244_24 % 189.00/30.21 (36) op(e0, e1) = all_20_2 % 189.00/30.21 (37) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.21 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.21 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.21 (38) all_252_19 = e4 % 189.00/30.21 (39) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.21 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.21 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.21 (40) ~ (all_8_1 = e2) % 189.00/30.21 (41) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.21 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.21 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.21 (42) ~ (all_20_2 = e0) % 189.00/30.21 (43) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.21 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.21 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.21 (44) all_252_17 = e2 % 189.00/30.21 (45) ~ (all_20_2 = e2) % 189.00/30.21 (46) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.21 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.21 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.21 (47) all_252_14 = e1 % 189.00/30.21 (48) op(e4, e4) = all_244_0 % 189.00/30.21 (49) op(e0, e4) = e2 % 189.00/30.21 (50) ~ (e3 = e0) % 189.00/30.21 (51) ~ (all_20_2 = all_8_1) % 189.00/30.21 (52) ~ (all_28_2 = e0) % 189.00/30.21 (53) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.21 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.21 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.21 (54) ~ (all_244_0 = e2) % 189.00/30.21 (55) op(e2, all_40_2) = e0 % 189.00/30.21 (56) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.21 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.21 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.21 (57) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.21 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.21 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.21 (58) ~ (e3 = e2) % 189.00/30.21 (59) all_252_22 = e4 % 189.00/30.21 (60) op(e4, all_20_2) = e0 % 189.00/30.21 (61) op(e0, e3) = all_8_1 % 189.00/30.21 (62) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.21 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.21 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.21 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.21 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.21 op(e0, e1) = e0))) % 189.00/30.21 (63) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.22 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.22 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.22 (64) ~ (e4 = e2) % 189.00/30.22 (65) op(e2, e0) = all_40_2 % 189.00/30.22 (66) op(all_28_2, all_40_2) = e2 % 189.00/30.22 (67) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.22 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.22 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.22 (68) ~ (e1 = e0) % 189.00/30.22 (69) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.22 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.22 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.22 (70) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.22 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.22 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.22 (71) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.22 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.22 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.22 (72) op(e0, e4) = all_12_2 % 189.00/30.22 (73) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.22 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.22 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.22 (74) all_250_23 = all_20_2 % 189.00/30.22 (75) ~ (e3 = e1) % 189.00/30.22 (76) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.22 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.22 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.22 (77) ~ (e2 = e0) % 189.00/30.22 (78) op(e1, e0) = all_34_2 % 189.00/30.22 (79) ~ (all_12_2 = e3) % 189.00/30.22 (80) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.22 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.22 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.22 (81) ~ (all_34_2 = e2) % 189.00/30.22 (82) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.22 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.22 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.22 (83) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.22 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.22 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.22 (84) op(e4, e2) = all_6_2 % 189.00/30.22 (85) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.22 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.22 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.22 (86) all_252_5 = e0 % 189.00/30.22 (87) ~ (e4 = e1) % 189.00/30.22 (88) op(e2, e0) = e1 % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | BETA: splitting (16) gives: % 189.00/30.22 | % 189.00/30.22 | Case 1: % 189.00/30.22 | | % 189.00/30.22 | | (89) all_252_14 = e3 & op(e1, e2) = e3 % 189.00/30.22 | | % 189.00/30.22 | | REF_CLOSE: (5), (8), (22), (27), (28), (32), (47), (50), (58), (75), (86), % 189.00/30.22 | | (89) are inconsistent by sub-proof #96. % 189.00/30.22 | | % 189.00/30.22 | Case 2: % 189.00/30.22 | | % 189.00/30.22 | | (90) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, e0) % 189.00/30.22 | | = e3) % 189.00/30.22 | | % 189.00/30.22 | | BETA: splitting (90) gives: % 189.00/30.22 | | % 189.00/30.22 | | Case 1: % 189.00/30.22 | | | % 189.00/30.22 | | | (91) all_252_15 = e3 & op(e1, e1) = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | ALPHA: (91) implies: % 189.00/30.22 | | | (92) all_252_15 = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.22 | | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.22 | | | (24), (25), (26), (29), (30), (31), (33), (34), (35), (36), % 189.00/30.22 | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 189.00/30.22 | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 189.00/30.22 | | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), % 189.00/30.22 | | | (68), (69), (70), (71), (72), (73), (74), (75), (76), (77), % 189.00/30.22 | | | (78), (79), (80), (81), (82), (83), (84), (85), (86), (87), % 189.00/30.22 | | | (88), (92) are inconsistent by sub-proof #113. % 189.00/30.22 | | | % 189.00/30.22 | | Case 2: % 189.00/30.22 | | | % 189.00/30.22 | | | (93) all_252_19 = e3 & op(e1, e0) = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | REF_CLOSE: (22), (38), (93) are inconsistent by sub-proof #243. % 189.00/30.22 | | | % 189.00/30.22 | | End of split % 189.00/30.22 | | % 189.00/30.22 | End of split % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #96 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.22 (2) op(e0, e2) = e4 % 189.00/30.22 (3) ~ (e4 = e3) % 189.00/30.22 (4) all_252_8 = e2 % 189.00/30.22 (5) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) | % 189.00/30.22 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = e3) % 189.00/30.22 | (all_252_22 = e3 & op(e0, e2) = e3) % 189.00/30.22 (6) all_252_4 = e3 % 189.00/30.22 (7) all_252_14 = e1 % 189.00/30.22 (8) ~ (e3 = e0) % 189.00/30.22 (9) all_252_14 = e3 & op(e1, e2) = e3 % 189.00/30.22 (10) ~ (e3 = e2) % 189.00/30.22 (11) ~ (e3 = e1) % 189.00/30.22 (12) all_252_5 = e0 % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | ALPHA: (9) implies: % 189.00/30.22 | (13) all_252_14 = e3 % 189.00/30.22 | % 189.00/30.22 | COMBINE_EQS: (7), (13) imply: % 189.00/30.22 | (14) e3 = e1 % 189.00/30.22 | % 189.00/30.22 | COMBINE_EQS: (6), (14) imply: % 189.00/30.22 | (15) all_252_4 = e1 % 189.00/30.22 | % 189.00/30.22 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (15) are % 189.00/30.22 | inconsistent by sub-proof #97. % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #97 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.22 (2) op(e0, e2) = e4 % 189.00/30.22 (3) ~ (e4 = e3) % 189.00/30.22 (4) all_252_4 = e1 % 189.00/30.22 (5) all_252_8 = e2 % 189.00/30.22 (6) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) | % 189.00/30.22 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = e3) % 189.00/30.22 | (all_252_22 = e3 & op(e0, e2) = e3) % 189.00/30.22 (7) all_252_14 = e1 % 189.00/30.22 (8) ~ (e3 = e0) % 189.00/30.22 (9) ~ (e3 = e2) % 189.00/30.22 (10) ~ (e3 = e1) % 189.00/30.22 (11) all_252_5 = e0 % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | BETA: splitting (6) gives: % 189.00/30.22 | % 189.00/30.22 | Case 1: % 189.00/30.22 | | % 189.00/30.22 | | (12) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = % 189.00/30.22 | | e3) % 189.00/30.22 | | % 189.00/30.22 | | BETA: splitting (12) gives: % 189.00/30.22 | | % 189.00/30.22 | | Case 1: % 189.00/30.22 | | | % 189.00/30.22 | | | (13) all_252_4 = e3 & op(e4, e2) = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | ALPHA: (13) implies: % 189.00/30.22 | | | (14) all_252_4 = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | COMBINE_EQS: (4), (14) imply: % 189.00/30.22 | | | (15) e3 = e1 % 189.00/30.22 | | | % 189.00/30.22 | | | SIMP: (15) implies: % 189.00/30.22 | | | (16) e3 = e1 % 189.00/30.22 | | | % 189.00/30.22 | | | REDUCE: (10), (16) imply: % 189.00/30.22 | | | (17) $false % 189.00/30.22 | | | % 189.00/30.22 | | | CLOSE: (17) is inconsistent. % 189.00/30.22 | | | % 189.00/30.22 | | Case 2: % 189.00/30.22 | | | % 189.00/30.22 | | | (18) all_252_5 = e3 & op(e3, e2) = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | REF_CLOSE: (8), (11), (18) are inconsistent by sub-proof #134. % 189.00/30.22 | | | % 189.00/30.22 | | End of split % 189.00/30.22 | | % 189.00/30.22 | Case 2: % 189.00/30.22 | | % 189.00/30.22 | | (19) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 189.00/30.22 | | e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 189.00/30.22 | | % 189.00/30.22 | | BETA: splitting (19) gives: % 189.00/30.22 | | % 189.00/30.22 | | Case 1: % 189.00/30.22 | | | % 189.00/30.22 | | | (20) all_252_8 = e3 & op(e2, e2) = e3 % 189.00/30.22 | | | % 189.00/30.22 | | | REF_CLOSE: (5), (9), (20) are inconsistent by sub-proof #100. % 189.00/30.22 | | | % 189.00/30.22 | | Case 2: % 189.00/30.22 | | | % 189.00/30.22 | | | (21) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, % 189.00/30.22 | | | e2) = e3) % 189.00/30.22 | | | % 189.00/30.22 | | | REF_CLOSE: (1), (2), (3), (7), (10), (21) are inconsistent by sub-proof % 189.00/30.22 | | | #98. % 189.00/30.22 | | | % 189.00/30.22 | | End of split % 189.00/30.22 | | % 189.00/30.22 | End of split % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #98 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.22 (2) op(e0, e2) = e4 % 189.00/30.22 (3) ~ (e4 = e3) % 189.00/30.22 (4) all_252_14 = e1 % 189.00/30.22 (5) ~ (e3 = e1) % 189.00/30.22 (6) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | BETA: splitting (6) gives: % 189.00/30.22 | % 189.00/30.22 | Case 1: % 189.00/30.22 | | % 189.00/30.22 | | (7) all_252_14 = e3 & op(e1, e2) = e3 % 189.00/30.22 | | % 189.00/30.22 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #99. % 189.00/30.22 | | % 189.00/30.22 | Case 2: % 189.00/30.22 | | % 189.00/30.22 | | (8) all_252_22 = e3 & op(e0, e2) = e3 % 189.00/30.22 | | % 189.00/30.22 | | ALPHA: (8) implies: % 189.00/30.22 | | (9) op(e0, e2) = e3 % 189.00/30.22 | | % 189.00/30.22 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #328. % 189.00/30.22 | | % 189.00/30.22 | End of split % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #99 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) all_252_14 = e3 & op(e1, e2) = e3 % 189.00/30.22 (2) all_252_14 = e1 % 189.00/30.22 (3) ~ (e3 = e1) % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | ALPHA: (1) implies: % 189.00/30.22 | (4) all_252_14 = e3 % 189.00/30.22 | % 189.00/30.22 | COMBINE_EQS: (2), (4) imply: % 189.00/30.22 | (5) e3 = e1 % 189.00/30.22 | % 189.00/30.22 | REDUCE: (3), (5) imply: % 189.00/30.22 | (6) $false % 189.00/30.22 | % 189.00/30.22 | CLOSE: (6) is inconsistent. % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #100 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) all_252_8 = e3 & op(e2, e2) = e3 % 189.00/30.22 (2) all_252_8 = e2 % 189.00/30.22 (3) ~ (e3 = e2) % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | ALPHA: (1) implies: % 189.00/30.22 | (4) all_252_8 = e3 % 189.00/30.22 | % 189.00/30.22 | COMBINE_EQS: (2), (4) imply: % 189.00/30.22 | (5) e3 = e2 % 189.00/30.22 | % 189.00/30.22 | SIMP: (5) implies: % 189.00/30.22 | (6) e3 = e2 % 189.00/30.22 | % 189.00/30.22 | REDUCE: (3), (6) imply: % 189.00/30.22 | (7) $false % 189.00/30.22 | % 189.00/30.22 | CLOSE: (7) is inconsistent. % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #101 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) ~ (e2 = e1) % 189.00/30.22 (2) (all_252_1 = e1 & op(e4, e3) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.22 (3) all_252_1 = e2 % 189.00/30.22 (4) all_252_3 = e4 % 189.00/30.22 (5) ~ (e4 = e1) % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | BETA: splitting (2) gives: % 189.00/30.22 | % 189.00/30.22 | Case 1: % 189.00/30.22 | | % 189.00/30.22 | | (6) all_252_1 = e1 & op(e4, e3) = e1 % 189.00/30.22 | | % 189.00/30.22 | | ALPHA: (6) implies: % 189.00/30.22 | | (7) all_252_1 = e1 % 189.00/30.22 | | % 189.00/30.22 | | COMBINE_EQS: (3), (7) imply: % 189.00/30.22 | | (8) e2 = e1 % 189.00/30.22 | | % 189.00/30.22 | | REDUCE: (1), (8) imply: % 189.00/30.22 | | (9) $false % 189.00/30.22 | | % 189.00/30.22 | | CLOSE: (9) is inconsistent. % 189.00/30.22 | | % 189.00/30.22 | Case 2: % 189.00/30.22 | | % 189.00/30.22 | | (10) all_252_3 = e1 & op(e3, e3) = e1 % 189.00/30.22 | | % 189.00/30.22 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #149. % 189.00/30.22 | | % 189.00/30.22 | End of split % 189.00/30.22 | % 189.00/30.22 End of proof % 189.00/30.22 % 189.00/30.22 Sub-proof #102 shows that the following formulas are inconsistent: % 189.00/30.22 ---------------------------------------------------------------- % 189.00/30.22 (1) all_252_20 = e2 % 189.00/30.22 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.22 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.22 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.22 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.22 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.22 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.22 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.22 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.22 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.22 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.22 (6) ~ (all_20_2 = e4) % 189.00/30.22 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.22 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.22 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.22 (8) op(e0, e2) = e4 % 189.00/30.22 (9) op(e0, e2) = all_28_2 % 189.00/30.22 (10) op(e3, e1) = all_36_2 % 189.00/30.22 (11) ~ (e2 = e1) % 189.00/30.22 (12) all_252_12 = e0 % 189.00/30.22 (13) op(e4, e1) = e0 % 189.00/30.22 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.22 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.22 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.22 (15) all_252_15 = e1 % 189.00/30.22 (16) op(e2, e1) = e0 % 189.00/30.22 (17) all_252_7 = e0 % 189.00/30.22 (18) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.22 all_250_23 = e0 % 189.00/30.22 (19) ~ (e4 = e0) % 189.00/30.22 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.22 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.22 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.22 (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.22 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.22 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.22 (22) ~ (e4 = e3) % 189.00/30.22 (23) ~ (all_36_2 = e2) % 189.00/30.22 (24) all_252_9 = e0 % 189.00/30.22 (25) ~ (all_40_2 = all_34_2) % 189.00/30.22 (26) ~ (all_244_24 = all_20_2) % 189.00/30.22 (27) op(e1, e4) = e0 % 189.00/30.22 (28) ~ (all_6_2 = e4) % 189.00/30.22 (29) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.22 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.22 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.22 (30) ~ (all_20_2 = e3) % 189.00/30.22 (31) op(all_20_2, e4) = e1 % 189.00/30.22 (32) op(e0, e0) = all_244_24 % 189.00/30.22 (33) op(e0, e1) = all_20_2 % 189.00/30.22 (34) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.22 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.22 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.22 (35) all_252_19 = e4 % 189.00/30.22 (36) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.22 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.22 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.22 (37) ~ (all_8_1 = e2) % 189.00/30.22 (38) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.22 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.22 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.22 (39) ~ (all_20_2 = e0) % 189.00/30.22 (40) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.22 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.22 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.22 (41) all_252_17 = e2 % 189.00/30.22 (42) ~ (all_20_2 = e2) % 189.00/30.22 (43) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.22 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.22 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.22 (44) op(e4, e4) = all_244_0 % 189.00/30.22 (45) op(e0, e4) = e2 % 189.00/30.22 (46) ~ (e3 = e0) % 189.00/30.22 (47) ~ (all_20_2 = all_8_1) % 189.00/30.22 (48) ~ (all_28_2 = e0) % 189.00/30.22 (49) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.22 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.22 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.22 (50) ~ (all_244_0 = e2) % 189.00/30.22 (51) op(e2, all_40_2) = e0 % 189.00/30.22 (52) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.22 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.22 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.22 (53) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.22 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.22 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.22 (54) ~ (e3 = e2) % 189.00/30.22 (55) all_252_22 = e4 % 189.00/30.22 (56) op(e4, all_20_2) = e0 % 189.00/30.22 (57) op(e0, e3) = all_8_1 % 189.00/30.22 (58) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.22 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.22 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.22 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.22 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.22 op(e0, e1) = e0))) % 189.00/30.22 (59) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.22 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.22 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.22 (60) ~ (e4 = e2) % 189.00/30.22 (61) op(e2, e0) = all_40_2 % 189.00/30.22 (62) op(all_28_2, all_40_2) = e2 % 189.00/30.22 (63) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.22 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.22 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.22 (64) ~ (e1 = e0) % 189.00/30.22 (65) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.22 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.22 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.22 (66) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.22 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.22 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.22 (67) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.22 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.22 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.22 (68) op(e0, e4) = all_12_2 % 189.00/30.22 (69) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.22 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.22 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.22 (70) all_250_23 = all_20_2 % 189.00/30.22 (71) ~ (e3 = e1) % 189.00/30.22 (72) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.22 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.22 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.22 (73) ~ (e2 = e0) % 189.00/30.22 (74) op(e1, e0) = all_34_2 % 189.00/30.22 (75) ~ (all_12_2 = e3) % 189.00/30.22 (76) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.22 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.22 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.22 (77) ~ (all_34_2 = e2) % 189.00/30.22 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.22 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.22 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.22 (79) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.22 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.22 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.22 (80) op(e4, e2) = all_6_2 % 189.00/30.22 (81) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.22 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.22 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.22 (82) all_252_5 = e0 % 189.00/30.22 (83) ~ (e4 = e1) % 189.00/30.22 (84) op(e2, e0) = e1 % 189.00/30.22 % 189.00/30.22 Begin of proof % 189.00/30.22 | % 189.00/30.22 | BETA: splitting (7) gives: % 189.00/30.22 | % 189.00/30.22 | Case 1: % 189.00/30.23 | | % 189.00/30.23 | | (85) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 189.00/30.23 | | e2) % 189.00/30.23 | | % 189.00/30.23 | | REF_CLOSE: (5), (10), (23), (24), (73), (85) are inconsistent by sub-proof % 189.00/30.23 | | #111. % 189.00/30.23 | | % 189.00/30.23 | Case 2: % 189.00/30.23 | | % 189.00/30.23 | | (86) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) % 189.00/30.23 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.23 | | % 189.00/30.23 | | BETA: splitting (86) gives: % 189.00/30.23 | | % 189.00/30.23 | | Case 1: % 189.00/30.23 | | | % 189.00/30.23 | | | (87) all_252_11 = e2 & op(e2, e1) = e2 % 189.00/30.23 | | | % 189.00/30.23 | | | ALPHA: (87) implies: % 189.00/30.23 | | | (88) all_252_11 = e2 % 189.00/30.23 | | | (89) op(e2, e1) = e2 % 189.00/30.23 | | | % 189.00/30.23 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.23 | | | (13), (14), (16), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.23 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 189.00/30.23 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 189.00/30.23 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), % 189.00/30.23 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), % 189.00/30.23 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 189.00/30.23 | | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), % 189.00/30.23 | | | (84), (88), (89) are inconsistent by sub-proof #115. % 189.00/30.23 | | | % 189.00/30.23 | | Case 2: % 189.00/30.23 | | | % 189.00/30.23 | | | (90) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, % 189.00/30.23 | | | e1) = e2) % 189.00/30.23 | | | % 189.00/30.23 | | | REF_CLOSE: (5), (11), (15), (33), (42), (90) are inconsistent by sub-proof % 189.00/30.23 | | | #194. % 189.00/30.23 | | | % 189.00/30.23 | | End of split % 189.00/30.23 | | % 189.00/30.23 | End of split % 189.00/30.23 | % 189.00/30.23 End of proof % 189.00/30.23 % 189.00/30.23 Sub-proof #103 shows that the following formulas are inconsistent: % 189.00/30.23 ---------------------------------------------------------------- % 189.00/30.23 (1) all_252_20 = e2 % 189.00/30.23 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.23 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.23 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.23 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.23 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.23 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.23 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.23 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.23 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.23 (6) ~ (all_20_2 = e4) % 189.00/30.23 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.23 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.23 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.23 (8) op(e0, e2) = e4 % 189.00/30.23 (9) op(e0, e2) = all_28_2 % 189.00/30.23 (10) op(e3, e1) = all_36_2 % 189.00/30.23 (11) ~ (e2 = e1) % 189.00/30.23 (12) all_252_12 = e0 % 189.00/30.23 (13) op(e4, e1) = e0 % 189.00/30.23 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.23 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.23 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.23 (15) op(e2, e1) = e0 % 189.00/30.23 (16) all_252_7 = e0 % 189.00/30.23 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.23 all_250_23 = e0 % 189.00/30.23 (18) all_252_11 = e4 % 189.00/30.23 (19) ~ (e4 = e0) % 189.00/30.23 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.23 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.23 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.23 (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.23 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.23 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.23 (22) ~ (e4 = e3) % 189.00/30.23 (23) ~ (all_36_2 = e2) % 189.00/30.23 (24) all_252_9 = e0 % 189.00/30.23 (25) ~ (all_40_2 = all_34_2) % 189.00/30.23 (26) ~ (all_244_24 = all_20_2) % 189.00/30.23 (27) op(e1, e4) = e0 % 189.00/30.23 (28) ~ (all_6_2 = e4) % 189.00/30.23 (29) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.23 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.23 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.23 (30) ~ (all_20_2 = e3) % 189.00/30.23 (31) op(all_20_2, e4) = e1 % 189.00/30.23 (32) op(e0, e0) = all_244_24 % 189.00/30.23 (33) op(e0, e1) = all_20_2 % 189.00/30.23 (34) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.23 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.23 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.23 (35) all_252_19 = e4 % 189.00/30.23 (36) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.23 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.23 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.23 (37) ~ (all_8_1 = e2) % 189.00/30.23 (38) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.23 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.23 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.23 (39) ~ (all_20_2 = e0) % 189.00/30.23 (40) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.23 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.23 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.23 (41) all_252_17 = e2 % 189.00/30.23 (42) ~ (all_20_2 = e2) % 189.00/30.23 (43) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.23 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.23 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.23 (44) op(e4, e4) = all_244_0 % 189.00/30.23 (45) op(e0, e4) = e2 % 189.00/30.23 (46) ~ (e3 = e0) % 189.00/30.23 (47) ~ (all_20_2 = all_8_1) % 189.00/30.23 (48) ~ (all_28_2 = e0) % 189.00/30.23 (49) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.23 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.23 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.23 (50) ~ (all_244_0 = e2) % 189.00/30.23 (51) op(e2, all_40_2) = e0 % 189.00/30.23 (52) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.23 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.23 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.23 (53) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.23 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.23 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.23 (54) ~ (e3 = e2) % 189.00/30.23 (55) all_252_22 = e4 % 189.00/30.23 (56) op(e4, all_20_2) = e0 % 189.00/30.23 (57) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.23 (58) op(e0, e3) = all_8_1 % 189.00/30.23 (59) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.23 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.23 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.23 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.23 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.23 op(e0, e1) = e0))) % 189.00/30.23 (60) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.23 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.23 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.23 (61) ~ (e4 = e2) % 189.00/30.23 (62) op(e2, e0) = all_40_2 % 189.00/30.23 (63) op(all_28_2, all_40_2) = e2 % 189.00/30.23 (64) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.23 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.23 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.23 (65) ~ (e1 = e0) % 189.00/30.23 (66) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.23 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.23 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.23 (67) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.23 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.23 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.23 (68) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.23 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.23 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.23 (69) op(e0, e4) = all_12_2 % 189.00/30.23 (70) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.23 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.23 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.23 (71) all_250_23 = all_20_2 % 189.00/30.23 (72) ~ (e3 = e1) % 189.00/30.23 (73) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.23 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.23 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.23 (74) ~ (e2 = e0) % 189.00/30.23 (75) op(e1, e0) = all_34_2 % 189.00/30.23 (76) ~ (all_12_2 = e3) % 189.00/30.23 (77) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.23 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.23 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.23 (78) ~ (all_34_2 = e2) % 189.00/30.23 (79) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.23 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.23 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.23 (80) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.23 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.23 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.23 (81) op(e4, e2) = all_6_2 % 189.00/30.23 (82) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.23 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.23 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.23 (83) all_252_5 = e0 % 189.00/30.23 (84) ~ (e4 = e1) % 189.00/30.23 (85) op(e2, e0) = e1 % 189.00/30.23 % 189.00/30.23 Begin of proof % 189.00/30.23 | % 189.00/30.23 | BETA: splitting (57) gives: % 189.00/30.23 | % 189.00/30.23 | Case 1: % 189.00/30.23 | | % 189.00/30.23 | | (86) all_252_9 = e1 & op(e4, e1) = e1 % 189.00/30.23 | | % 189.00/30.23 | | ALPHA: (86) implies: % 189.00/30.23 | | (87) all_252_9 = e1 % 189.00/30.23 | | % 189.00/30.23 | | COMBINE_EQS: (24), (87) imply: % 189.00/30.23 | | (88) e1 = e0 % 189.00/30.23 | | % 189.00/30.23 | | REDUCE: (65), (88) imply: % 189.00/30.23 | | (89) $false % 189.00/30.23 | | % 189.00/30.23 | | CLOSE: (89) is inconsistent. % 189.00/30.23 | | % 189.00/30.23 | Case 2: % 189.00/30.23 | | % 189.00/30.23 | | (90) all_252_10 = e1 & op(e3, e1) = e1 % 189.00/30.23 | | % 189.00/30.23 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.23 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.23 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 189.00/30.23 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 189.00/30.23 | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 189.00/30.23 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 189.00/30.23 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 189.00/30.23 | | (80), (81), (82), (83), (84), (85), (90) are inconsistent by % 189.00/30.23 | | sub-proof #104. % 189.00/30.23 | | % 189.00/30.23 | End of split % 189.00/30.23 | % 189.00/30.23 End of proof % 189.00/30.23 % 189.00/30.23 Sub-proof #104 shows that the following formulas are inconsistent: % 189.00/30.23 ---------------------------------------------------------------- % 189.00/30.23 (1) all_252_20 = e2 % 189.00/30.23 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.23 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.23 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.23 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.23 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.23 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.23 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.23 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.23 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.23 (6) ~ (all_20_2 = e4) % 189.00/30.23 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.23 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.23 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.23 (8) op(e0, e2) = e4 % 189.00/30.23 (9) op(e0, e2) = all_28_2 % 189.00/30.23 (10) op(e3, e1) = all_36_2 % 189.00/30.23 (11) all_252_10 = e1 & op(e3, e1) = e1 % 189.00/30.23 (12) ~ (e2 = e1) % 189.00/30.23 (13) all_252_12 = e0 % 189.00/30.23 (14) op(e4, e1) = e0 % 189.00/30.23 (15) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.23 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.23 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.23 (16) op(e2, e1) = e0 % 189.00/30.23 (17) all_252_7 = e0 % 189.00/30.23 (18) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.23 all_250_23 = e0 % 189.00/30.23 (19) all_252_11 = e4 % 189.00/30.23 (20) ~ (e4 = e0) % 189.00/30.23 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.23 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.23 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.23 (22) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.23 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.23 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.23 (23) ~ (e4 = e3) % 189.00/30.23 (24) ~ (all_36_2 = e2) % 189.00/30.23 (25) all_252_9 = e0 % 189.00/30.23 (26) ~ (all_40_2 = all_34_2) % 189.00/30.23 (27) ~ (all_244_24 = all_20_2) % 189.00/30.23 (28) op(e1, e4) = e0 % 189.00/30.23 (29) ~ (all_6_2 = e4) % 189.00/30.23 (30) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.23 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.23 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.23 (31) ~ (all_20_2 = e3) % 189.00/30.23 (32) op(all_20_2, e4) = e1 % 189.00/30.23 (33) op(e0, e0) = all_244_24 % 189.00/30.23 (34) op(e0, e1) = all_20_2 % 189.00/30.23 (35) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.23 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.23 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.23 (36) all_252_19 = e4 % 189.00/30.23 (37) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.23 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.23 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.23 (38) ~ (all_8_1 = e2) % 189.00/30.23 (39) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.23 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.23 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.23 (40) ~ (all_20_2 = e0) % 189.00/30.23 (41) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.23 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.23 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.23 (42) all_252_17 = e2 % 189.00/30.23 (43) ~ (all_20_2 = e2) % 189.00/30.23 (44) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.23 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.23 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.23 (45) op(e4, e4) = all_244_0 % 189.00/30.23 (46) op(e0, e4) = e2 % 189.00/30.23 (47) ~ (e3 = e0) % 189.00/30.23 (48) ~ (all_20_2 = all_8_1) % 189.00/30.23 (49) ~ (all_28_2 = e0) % 189.00/30.23 (50) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.23 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.23 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.23 (51) ~ (all_244_0 = e2) % 189.00/30.23 (52) op(e2, all_40_2) = e0 % 189.00/30.23 (53) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.23 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.23 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.23 (54) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.23 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.23 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.23 (55) ~ (e3 = e2) % 189.00/30.23 (56) all_252_22 = e4 % 189.00/30.23 (57) op(e4, all_20_2) = e0 % 189.00/30.23 (58) op(e0, e3) = all_8_1 % 189.00/30.23 (59) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.23 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.23 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.23 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.23 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.23 op(e0, e1) = e0))) % 189.00/30.23 (60) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.23 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.23 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.23 (61) ~ (e4 = e2) % 189.00/30.23 (62) op(e2, e0) = all_40_2 % 189.00/30.23 (63) op(all_28_2, all_40_2) = e2 % 189.00/30.23 (64) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.23 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.23 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.23 (65) ~ (e1 = e0) % 189.00/30.23 (66) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.23 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.23 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.23 (67) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.23 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.23 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.23 (68) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.23 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.23 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.23 (69) op(e0, e4) = all_12_2 % 189.00/30.23 (70) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.23 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.23 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.23 (71) all_250_23 = all_20_2 % 189.00/30.23 (72) ~ (e3 = e1) % 189.00/30.24 (73) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.24 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.24 (74) ~ (e2 = e0) % 189.00/30.24 (75) op(e1, e0) = all_34_2 % 189.00/30.24 (76) ~ (all_12_2 = e3) % 189.00/30.24 (77) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.24 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.24 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.24 (78) ~ (all_34_2 = e2) % 189.00/30.24 (79) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.24 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.24 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.24 (80) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.24 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.24 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.24 (81) op(e4, e2) = all_6_2 % 189.00/30.24 (82) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.24 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.24 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.24 (83) all_252_5 = e0 % 189.00/30.24 (84) ~ (e4 = e1) % 189.00/30.24 (85) op(e2, e0) = e1 % 189.00/30.24 % 189.00/30.24 Begin of proof % 189.00/30.24 | % 189.00/30.24 | ALPHA: (11) implies: % 189.00/30.24 | (86) all_252_10 = e1 % 189.00/30.24 | % 189.00/30.24 | BETA: splitting (15) gives: % 189.00/30.24 | % 189.00/30.24 | Case 1: % 189.00/30.24 | | % 189.00/30.24 | | (87) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.24 | | e3) % 189.00/30.24 | | % 189.00/30.24 | | REF_CLOSE: (5), (14), (47), (72), (86), (87) are inconsistent by sub-proof % 189.00/30.24 | | #266. % 189.00/30.24 | | % 189.00/30.24 | Case 2: % 189.00/30.24 | | % 189.00/30.24 | | (88) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) % 189.00/30.24 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.24 | | % 189.00/30.24 | | BETA: splitting (88) gives: % 189.00/30.24 | | % 189.00/30.24 | | Case 1: % 189.00/30.24 | | | % 189.00/30.24 | | | (89) all_252_11 = e3 & op(e2, e1) = e3 % 189.00/30.24 | | | % 189.00/30.24 | | | REF_CLOSE: (19), (23), (89) are inconsistent by sub-proof #105. % 189.00/30.24 | | | % 189.00/30.24 | | Case 2: % 189.00/30.24 | | | % 189.00/30.24 | | | (90) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.24 | | | e1) = e3) % 189.00/30.24 | | | % 189.00/30.24 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), % 189.00/30.24 | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), % 189.00/30.24 | | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 189.00/30.24 | | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), % 189.00/30.24 | | | (45), (46), (47), (48), (49), (50), (51), (52), (53), (54), % 189.00/30.24 | | | (55), (56), (57), (58), (59), (60), (61), (62), (63), (64), % 189.00/30.24 | | | (65), (66), (67), (68), (69), (70), (71), (72), (73), (74), % 189.00/30.24 | | | (75), (76), (77), (78), (79), (80), (81), (82), (83), (84), % 189.00/30.24 | | | (85), (90) are inconsistent by sub-proof #112. % 189.00/30.24 | | | % 189.00/30.24 | | End of split % 189.00/30.24 | | % 189.00/30.24 | End of split % 189.00/30.24 | % 189.00/30.24 End of proof % 189.00/30.24 % 189.00/30.24 Sub-proof #105 shows that the following formulas are inconsistent: % 189.00/30.24 ---------------------------------------------------------------- % 189.00/30.24 (1) all_252_11 = e3 & op(e2, e1) = e3 % 189.00/30.24 (2) all_252_11 = e4 % 189.00/30.24 (3) ~ (e4 = e3) % 189.00/30.24 % 189.00/30.24 Begin of proof % 189.00/30.24 | % 189.00/30.24 | ALPHA: (1) implies: % 189.00/30.24 | (4) all_252_11 = e3 % 189.00/30.24 | % 189.00/30.24 | COMBINE_EQS: (2), (4) imply: % 189.00/30.24 | (5) e4 = e3 % 189.00/30.24 | % 189.00/30.24 | REDUCE: (3), (5) imply: % 189.00/30.24 | (6) $false % 189.00/30.24 | % 189.00/30.24 | CLOSE: (6) is inconsistent. % 189.00/30.24 | % 189.00/30.24 End of proof % 189.00/30.24 % 189.00/30.24 Sub-proof #106 shows that the following formulas are inconsistent: % 189.00/30.24 ---------------------------------------------------------------- % 189.00/30.24 (1) all_252_13 = e2 % 189.00/30.24 (2) all_252_20 = e2 % 189.00/30.24 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.24 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.24 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.24 (4) all_252_10 = e4 % 189.00/30.24 (5) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.00/30.24 (6) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.24 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.24 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.24 (7) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.24 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.24 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.24 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.24 (9) ~ (all_20_2 = e4) % 189.00/30.24 (10) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.24 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.24 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.24 (11) op(e0, e2) = e4 % 189.00/30.24 (12) op(e0, e2) = all_28_2 % 189.00/30.24 (13) op(e3, e1) = all_36_2 % 189.00/30.24 (14) ~ (e2 = e1) % 189.00/30.24 (15) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.24 (16) all_252_12 = e0 % 189.00/30.24 (17) op(e4, e1) = e0 % 189.00/30.24 (18) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.24 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.24 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.24 (19) op(e2, e1) = e0 % 189.00/30.24 (20) all_252_7 = e0 % 189.00/30.24 (21) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.24 all_250_23 = e0 % 189.00/30.24 (22) ~ (e4 = e0) % 189.00/30.24 (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.24 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.24 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.24 (24) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.24 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.24 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.24 (25) ~ (e4 = e3) % 189.00/30.24 (26) ~ (all_36_2 = e2) % 189.00/30.24 (27) all_252_9 = e0 % 189.00/30.24 (28) ~ (all_40_2 = all_34_2) % 189.00/30.24 (29) ~ (all_244_24 = all_20_2) % 189.00/30.24 (30) op(e1, e4) = e0 % 189.00/30.24 (31) ~ (all_6_2 = e4) % 189.00/30.24 (32) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.24 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.24 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.24 (33) ~ (all_20_2 = e3) % 189.00/30.24 (34) op(all_20_2, e4) = e1 % 189.00/30.24 (35) op(e0, e0) = all_244_24 % 189.00/30.24 (36) op(e0, e1) = all_20_2 % 189.00/30.24 (37) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.24 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.24 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.24 (38) all_252_19 = e4 % 189.00/30.24 (39) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.24 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.24 (40) ~ (all_8_1 = e2) % 189.00/30.24 (41) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.24 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.24 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.24 (42) ~ (all_20_2 = e0) % 189.00/30.24 (43) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.24 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.24 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.24 (44) all_252_17 = e2 % 189.00/30.24 (45) ~ (all_20_2 = e2) % 189.00/30.24 (46) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.24 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.24 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.24 (47) op(e4, e4) = all_244_0 % 189.00/30.24 (48) op(e0, e4) = e2 % 189.00/30.24 (49) ~ (e3 = e0) % 189.00/30.24 (50) ~ (all_20_2 = all_8_1) % 189.00/30.24 (51) ~ (all_28_2 = e0) % 189.00/30.24 (52) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.24 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.24 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.24 (53) ~ (all_244_0 = e2) % 189.00/30.24 (54) op(e2, all_40_2) = e0 % 189.00/30.24 (55) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.24 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.24 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.24 (56) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.24 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.24 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.24 (57) ~ (e3 = e2) % 189.00/30.24 (58) all_252_22 = e4 % 189.00/30.24 (59) op(e4, all_20_2) = e0 % 189.00/30.24 (60) op(e0, e3) = all_8_1 % 189.00/30.24 (61) op(e1, e4) = e1 % 189.00/30.24 (62) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.24 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.24 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.24 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.24 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.24 op(e0, e1) = e0))) % 189.00/30.24 (63) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.24 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.24 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.24 (64) ~ (e4 = e2) % 189.00/30.24 (65) op(e2, e0) = all_40_2 % 189.00/30.24 (66) op(all_28_2, all_40_2) = e2 % 189.00/30.24 (67) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.24 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.24 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.24 (68) ~ (e1 = e0) % 189.00/30.24 (69) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.24 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.24 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.24 (70) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.24 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.24 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.24 (71) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.24 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.24 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.24 (72) op(e0, e4) = all_12_2 % 189.00/30.24 (73) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.24 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.24 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.24 (74) all_250_23 = all_20_2 % 189.00/30.24 (75) ~ (e3 = e1) % 189.00/30.24 (76) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.24 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.24 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.24 (77) ~ (e2 = e0) % 189.00/30.24 (78) op(e1, e0) = all_34_2 % 189.00/30.24 (79) ~ (all_244_24 = e1) % 189.00/30.24 (80) ~ (all_8_1 = e1) % 189.00/30.24 (81) ~ (all_12_2 = e3) % 189.00/30.24 (82) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.24 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.24 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.24 (83) ~ (all_34_2 = e2) % 189.00/30.24 (84) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.24 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.24 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.24 (85) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.24 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.24 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.24 (86) op(e4, e2) = all_6_2 % 189.00/30.24 (87) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.24 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.24 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.24 (88) all_252_5 = e0 % 189.00/30.24 (89) ~ (e4 = e1) % 189.00/30.24 (90) op(e2, e0) = e1 % 189.00/30.24 % 189.00/30.24 Begin of proof % 189.00/30.24 | % 189.00/30.24 | BETA: splitting (18) gives: % 189.00/30.24 | % 189.00/30.24 | Case 1: % 189.00/30.24 | | % 189.00/30.24 | | (91) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.24 | | e3) % 189.00/30.24 | | % 189.00/30.24 | | REF_CLOSE: (4), (8), (17), (25), (49), (91) are inconsistent by sub-proof % 189.00/30.24 | | #218. % 189.00/30.24 | | % 189.00/30.24 | Case 2: % 189.00/30.24 | | % 189.00/30.24 | | (92) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) % 189.00/30.24 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.24 | | % 189.00/30.24 | | BETA: splitting (92) gives: % 189.00/30.24 | | % 189.00/30.24 | | Case 1: % 189.00/30.24 | | | % 189.00/30.24 | | | (93) all_252_11 = e3 & op(e2, e1) = e3 % 189.00/30.24 | | | % 189.00/30.24 | | | ALPHA: (93) implies: % 189.00/30.24 | | | (94) all_252_11 = e3 % 189.00/30.24 | | | % 189.00/30.24 | | | BETA: splitting (39) gives: % 189.00/30.24 | | | % 189.00/30.24 | | | Case 1: % 189.00/30.24 | | | | % 189.00/30.24 | | | | (95) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, % 189.00/30.24 | | | | e3) = e1) % 189.00/30.24 | | | | % 189.00/30.24 | | | | REF_CLOSE: (8), (14), (48), (60), (80), (95) are inconsistent by % 189.00/30.24 | | | | sub-proof #244. % 189.00/30.24 | | | | % 189.00/30.24 | | | Case 2: % 189.00/30.24 | | | | % 189.00/30.24 | | | | (96) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.24 | | | | e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.24 | | | | % 189.00/30.24 | | | | BETA: splitting (96) gives: % 189.00/30.24 | | | | % 189.00/30.24 | | | | Case 1: % 189.00/30.24 | | | | | % 189.00/30.24 | | | | | (97) all_252_22 = e1 & op(e0, e2) = e1 % 189.00/30.24 | | | | | % 189.00/30.24 | | | | | ALPHA: (97) implies: % 189.00/30.24 | | | | | (98) op(e0, e2) = e1 % 189.00/30.24 | | | | | % 189.00/30.24 | | | | | REF_CLOSE: (8), (11), (89), (98) are inconsistent by sub-proof #256. % 189.00/30.24 | | | | | % 189.00/30.24 | | | | Case 2: % 189.00/30.24 | | | | | % 189.00/30.24 | | | | | (99) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 189.00/30.24 | | | | | op(e0, e0) = e1) % 189.00/30.24 | | | | | % 189.00/30.24 | | | | | BETA: splitting (99) gives: % 189.00/30.24 | | | | | % 189.00/30.24 | | | | | Case 1: % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | (100) all_252_23 = e1 & op(e0, e1) = e1 % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | ALPHA: (100) implies: % 189.00/30.24 | | | | | | (101) all_252_23 = e1 % 189.00/30.24 | | | | | | (102) op(e0, e1) = e1 % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | BETA: splitting (10) gives: % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | Case 1: % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | | (103) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & % 189.00/30.24 | | | | | | | op(e3, e1) = e2) % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | | REF_CLOSE: (8), (13), (26), (27), (77), (103) are inconsistent by % 189.00/30.24 | | | | | | | sub-proof #111. % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | Case 2: % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | | (104) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & % 189.00/30.24 | | | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | | BETA: splitting (104) gives: % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | | Case 1: % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | | (105) all_252_11 = e2 & op(e2, e1) = e2 % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | | ALPHA: (105) implies: % 189.00/30.24 | | | | | | | | (106) all_252_11 = e2 % 189.00/30.24 | | | | | | | | (107) op(e2, e1) = e2 % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (13), (16), % 189.00/30.24 | | | | | | | | (17), (18), (19), (22), (25), (26), (28), (29), (30), % 189.00/30.24 | | | | | | | | (33), (34), (35), (36), (39), (42), (45), (46), (48), % 189.00/30.24 | | | | | | | | (49), (50), (55), (57), (59), (60), (64), (65), (67), % 189.00/30.24 | | | | | | | | (74), (77), (78), (90), (106), (107) are inconsistent % 189.00/30.24 | | | | | | | | by sub-proof #117. % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | Case 2: % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | | (108) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 % 189.00/30.24 | | | | | | | | & op(e0, e1) = e2) % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | | BETA: splitting (108) gives: % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | | Case 1: % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | | (109) all_252_15 = e2 & op(e1, e1) = e2 % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | | ALPHA: (109) implies: % 189.00/30.24 | | | | | | | | | (110) all_252_15 = e2 % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | | BETA: splitting (67) gives: % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | | Case 1: % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | (111) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = % 189.00/30.24 | | | | | | | | | | e1 & op(e1, e3) = e1) % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | BETA: splitting (111) gives: % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | Case 1: % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | (112) all_252_12 = e1 & op(e1, e4) = e1 % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | REF_CLOSE: (2), (8), (9), (11), (15), (16), (29), (35), (39), % 189.00/30.24 | | | | | | | | | | | (42), (45), (50), (60), (74), (101), (112) are % 189.00/30.24 | | | | | | | | | | | inconsistent by sub-proof #181. % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | Case 2: % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | (113) all_252_13 = e1 & op(e1, e3) = e1 % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | REF_CLOSE: (1), (14), (113) are inconsistent by sub-proof % 189.00/30.24 | | | | | | | | | | | #125. % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | End of split % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | Case 2: % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | (114) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = % 189.00/30.24 | | | | | | | | | | e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.24 | | | | | | | | | | e0) = e1) % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | BETA: splitting (114) gives: % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | Case 1: % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | (115) all_252_14 = e1 & op(e1, e2) = e1 % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | ALPHA: (115) implies: % 189.00/30.24 | | | | | | | | | | | (116) all_252_14 = e1 % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), % 189.00/30.24 | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), % 189.00/30.24 | | | | | | | | | | | (20), (21), (22), (23), (24), (25), (26), (27), % 189.00/30.24 | | | | | | | | | | | (28), (29), (30), (31), (32), (33), (34), (35), % 189.00/30.24 | | | | | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), % 189.00/30.24 | | | | | | | | | | | (44), (45), (46), (47), (48), (49), (50), (51), % 189.00/30.24 | | | | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), % 189.00/30.24 | | | | | | | | | | | (60), (61), (62), (63), (64), (65), (66), (67), % 189.00/30.24 | | | | | | | | | | | (68), (69), (70), (71), (72), (73), (74), (75), % 189.00/30.24 | | | | | | | | | | | (76), (77), (78), (81), (82), (83), (84), (85), % 189.00/30.24 | | | | | | | | | | | (86), (87), (88), (89), (90), (94), (102), (116) % 189.00/30.24 | | | | | | | | | | | are inconsistent by sub-proof #107. % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | Case 2: % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | (117) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 % 189.00/30.24 | | | | | | | | | | | = e1 & op(e1, e0) = e1) % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | BETA: splitting (117) gives: % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | Case 1: % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | | (118) all_252_15 = e1 & op(e1, e1) = e1 % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | | REF_CLOSE: (14), (110), (118) are inconsistent by sub-proof % 189.00/30.24 | | | | | | | | | | | | #415. % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | Case 2: % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | | (119) all_252_19 = e1 & op(e1, e0) = e1 % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | | ALPHA: (119) implies: % 189.00/30.24 | | | | | | | | | | | | (120) op(e1, e0) = e1 % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | | REF_CLOSE: (8), (28), (65), (78), (90), (120) are % 189.00/30.24 | | | | | | | | | | | | inconsistent by sub-proof #352. % 189.00/30.24 | | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | | End of split % 189.00/30.24 | | | | | | | | | | | % 189.00/30.24 | | | | | | | | | | End of split % 189.00/30.24 | | | | | | | | | | % 189.00/30.24 | | | | | | | | | End of split % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | Case 2: % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | | (121) all_252_23 = e2 & op(e0, e1) = e2 % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | | REF_CLOSE: (8), (36), (45), (121) are inconsistent by % 189.00/30.24 | | | | | | | | | sub-proof #540. % 189.00/30.24 | | | | | | | | | % 189.00/30.24 | | | | | | | | End of split % 189.00/30.24 | | | | | | | | % 189.00/30.24 | | | | | | | End of split % 189.00/30.24 | | | | | | | % 189.00/30.24 | | | | | | End of split % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | Case 2: % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | (122) all_252_24 = e1 & op(e0, e0) = e1 % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | ALPHA: (122) implies: % 189.00/30.24 | | | | | | (123) op(e0, e0) = e1 % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | | REF_CLOSE: (8), (35), (79), (123) are inconsistent by sub-proof % 189.00/30.24 | | | | | | #474. % 189.00/30.24 | | | | | | % 189.00/30.24 | | | | | End of split % 189.00/30.24 | | | | | % 189.00/30.24 | | | | End of split % 189.00/30.24 | | | | % 189.00/30.24 | | | End of split % 189.00/30.24 | | | % 189.00/30.24 | | Case 2: % 189.00/30.24 | | | % 189.00/30.24 | | | (124) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.24 | | | e1) = e3) % 189.00/30.24 | | | % 189.00/30.24 | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14), % 189.00/30.24 | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 189.00/30.24 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 189.00/30.24 | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), % 189.00/30.24 | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (55), % 189.00/30.24 | | | (56), (57), (58), (59), (60), (62), (63), (64), (65), (66), % 189.00/30.24 | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76), % 189.00/30.24 | | | (77), (78), (81), (82), (83), (84), (85), (86), (87), (88), % 189.00/30.24 | | | (89), (90), (124) are inconsistent by sub-proof #112. % 189.00/30.24 | | | % 189.00/30.24 | | End of split % 189.00/30.24 | | % 189.00/30.24 | End of split % 189.00/30.24 | % 189.00/30.24 End of proof % 189.00/30.24 % 189.00/30.24 Sub-proof #107 shows that the following formulas are inconsistent: % 189.00/30.24 ---------------------------------------------------------------- % 189.00/30.24 (1) all_252_13 = e2 % 189.00/30.24 (2) all_252_20 = e2 % 189.00/30.24 (3) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.24 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.24 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.24 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.24 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.24 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.25 (5) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.25 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.25 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.25 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.25 (7) ~ (all_20_2 = e4) % 189.00/30.25 (8) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.25 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.25 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.25 (9) op(e0, e2) = e4 % 189.00/30.25 (10) op(e0, e2) = all_28_2 % 189.00/30.25 (11) op(e3, e1) = all_36_2 % 189.00/30.25 (12) ~ (e2 = e1) % 189.00/30.25 (13) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.25 (14) all_252_12 = e0 % 189.00/30.25 (15) op(e4, e1) = e0 % 189.00/30.25 (16) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.25 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.25 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.25 (17) op(e2, e1) = e0 % 189.00/30.25 (18) all_252_7 = e0 % 189.00/30.25 (19) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.25 all_250_23 = e0 % 189.00/30.25 (20) ~ (e4 = e0) % 189.00/30.25 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.25 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.25 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.25 (22) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.25 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.25 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.25 (23) ~ (e4 = e3) % 189.00/30.25 (24) ~ (all_36_2 = e2) % 189.00/30.25 (25) all_252_9 = e0 % 189.00/30.25 (26) ~ (all_40_2 = all_34_2) % 189.00/30.25 (27) ~ (all_244_24 = all_20_2) % 189.00/30.25 (28) op(e1, e4) = e0 % 189.00/30.25 (29) ~ (all_6_2 = e4) % 189.00/30.25 (30) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.25 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.25 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.25 (31) ~ (all_20_2 = e3) % 189.00/30.25 (32) op(all_20_2, e4) = e1 % 189.00/30.25 (33) op(e0, e0) = all_244_24 % 189.00/30.25 (34) op(e0, e1) = all_20_2 % 189.00/30.25 (35) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.25 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.25 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.25 (36) all_252_19 = e4 % 189.00/30.25 (37) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.25 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.25 (38) ~ (all_8_1 = e2) % 189.00/30.25 (39) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.25 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.25 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.25 (40) ~ (all_20_2 = e0) % 189.00/30.25 (41) all_252_11 = e3 % 189.00/30.25 (42) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.25 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.25 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.25 (43) all_252_17 = e2 % 189.00/30.25 (44) ~ (all_20_2 = e2) % 189.00/30.25 (45) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.25 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.25 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.25 (46) all_252_14 = e1 % 189.00/30.25 (47) op(e4, e4) = all_244_0 % 189.00/30.25 (48) op(e0, e4) = e2 % 189.00/30.25 (49) ~ (e3 = e0) % 189.00/30.25 (50) ~ (all_20_2 = all_8_1) % 189.00/30.25 (51) ~ (all_28_2 = e0) % 189.00/30.25 (52) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.25 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.25 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.25 (53) ~ (all_244_0 = e2) % 189.00/30.25 (54) op(e2, all_40_2) = e0 % 189.00/30.25 (55) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.25 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.25 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.25 (56) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.25 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.25 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.25 (57) ~ (e3 = e2) % 189.00/30.25 (58) all_252_22 = e4 % 189.00/30.25 (59) op(e4, all_20_2) = e0 % 189.00/30.25 (60) op(e0, e3) = all_8_1 % 189.00/30.25 (61) op(e1, e4) = e1 % 189.00/30.25 (62) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.25 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.25 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.25 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.25 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.25 op(e0, e1) = e0))) % 189.00/30.25 (63) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.25 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.25 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.25 (64) ~ (e4 = e2) % 189.00/30.25 (65) op(e2, e0) = all_40_2 % 189.00/30.25 (66) op(all_28_2, all_40_2) = e2 % 189.00/30.25 (67) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.25 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.25 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.25 (68) ~ (e1 = e0) % 189.00/30.25 (69) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.25 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.25 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.25 (70) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.25 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.25 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.25 (71) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.25 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.25 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.25 (72) op(e0, e4) = all_12_2 % 189.00/30.25 (73) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.25 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.25 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.25 (74) all_250_23 = all_20_2 % 189.00/30.25 (75) ~ (e3 = e1) % 189.00/30.25 (76) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.25 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.25 (77) ~ (e2 = e0) % 189.00/30.25 (78) op(e0, e1) = e1 % 189.00/30.25 (79) op(e1, e0) = all_34_2 % 189.00/30.25 (80) ~ (all_12_2 = e3) % 189.00/30.25 (81) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.25 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.25 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.25 (82) ~ (all_34_2 = e2) % 189.00/30.25 (83) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.25 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.25 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.25 (84) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.25 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.25 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.25 (85) op(e4, e2) = all_6_2 % 189.00/30.25 (86) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.25 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.25 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.25 (87) all_252_5 = e0 % 189.00/30.25 (88) ~ (e4 = e1) % 189.00/30.25 (89) op(e2, e0) = e1 % 189.00/30.25 % 189.00/30.25 Begin of proof % 189.00/30.25 | % 189.00/30.25 | BETA: splitting (52) gives: % 189.00/30.25 | % 189.00/30.25 | Case 1: % 189.00/30.25 | | % 189.00/30.25 | | (90) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) % 189.00/30.25 | | = e3) % 189.00/30.25 | | % 189.00/30.25 | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (11), (12), (13), (14), (15), (16), % 189.00/30.25 | | (20), (23), (24), (27), (28), (31), (33), (34), (37), (40), (41), % 189.00/30.25 | | (44), (45), (49), (50), (55), (57), (60), (61), (64), (68), (74), % 189.00/30.25 | | (75), (77), (78), (88), (90) are inconsistent by sub-proof #108. % 189.00/30.25 | | % 189.00/30.25 | Case 2: % 189.00/30.25 | | % 189.00/30.25 | | (91) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) % 189.00/30.25 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.25 | | % 189.00/30.25 | | BETA: splitting (91) gives: % 189.00/30.25 | | % 189.00/30.25 | | Case 1: % 189.00/30.25 | | | % 189.00/30.25 | | | (92) all_252_14 = e3 & op(e1, e2) = e3 % 189.00/30.25 | | | % 189.00/30.25 | | | ALPHA: (92) implies: % 189.00/30.25 | | | (93) all_252_14 = e3 % 189.00/30.25 | | | % 189.00/30.25 | | | REF_CLOSE: (46), (75), (93) are inconsistent by sub-proof #179. % 189.00/30.25 | | | % 189.00/30.25 | | Case 2: % 189.00/30.25 | | | % 189.00/30.25 | | | (94) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.25 | | | e0) = e3) % 189.00/30.25 | | | % 189.00/30.25 | | | BETA: splitting (94) gives: % 189.00/30.25 | | | % 189.00/30.25 | | | Case 1: % 189.00/30.25 | | | | % 189.00/30.25 | | | | (95) all_252_15 = e3 & op(e1, e1) = e3 % 189.00/30.25 | | | | % 189.00/30.25 | | | | ALPHA: (95) implies: % 189.00/30.25 | | | | (96) all_252_15 = e3 % 189.00/30.25 | | | | % 189.00/30.25 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.25 | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.25 | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 189.00/30.25 | | | | (34), (35), (36), (37), (38), (39), (40), (42), (43), (44), % 189.00/30.25 | | | | (45), (47), (48), (49), (50), (51), (52), (53), (54), (55), % 189.00/30.25 | | | | (56), (57), (58), (59), (60), (62), (63), (64), (65), (66), % 189.00/30.25 | | | | (67), (68), (69), (70), (71), (72), (73), (74), (75), (76), % 189.00/30.25 | | | | (77), (79), (80), (81), (82), (83), (84), (85), (86), (87), % 189.00/30.25 | | | | (88), (89), (96) are inconsistent by sub-proof #113. % 189.00/30.25 | | | | % 189.00/30.25 | | | Case 2: % 189.00/30.25 | | | | % 189.00/30.25 | | | | (97) all_252_19 = e3 & op(e1, e0) = e3 % 189.00/30.25 | | | | % 189.00/30.25 | | | | REF_CLOSE: (23), (36), (97) are inconsistent by sub-proof #177. % 189.00/30.25 | | | | % 189.00/30.25 | | | End of split % 189.00/30.25 | | | % 189.00/30.25 | | End of split % 189.00/30.25 | | % 189.00/30.25 | End of split % 189.00/30.25 | % 189.00/30.25 End of proof % 189.00/30.25 % 189.00/30.25 Sub-proof #108 shows that the following formulas are inconsistent: % 189.00/30.25 ---------------------------------------------------------------- % 189.00/30.25 (1) all_252_13 = e2 % 189.00/30.25 (2) all_252_20 = e2 % 189.00/30.25 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.25 (4) ~ (all_20_2 = e4) % 189.00/30.25 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.25 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.25 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.25 (6) op(e0, e2) = e4 % 189.00/30.25 (7) op(e3, e1) = all_36_2 % 189.00/30.25 (8) ~ (e2 = e1) % 189.00/30.25 (9) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.25 (10) all_252_12 = e0 % 189.00/30.25 (11) op(e4, e1) = e0 % 189.00/30.25 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.25 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.25 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.25 (13) ~ (e4 = e0) % 189.00/30.25 (14) ~ (e4 = e3) % 189.00/30.25 (15) ~ (all_36_2 = e2) % 189.00/30.25 (16) ~ (all_244_24 = all_20_2) % 189.00/30.25 (17) op(e1, e4) = e0 % 189.00/30.25 (18) ~ (all_20_2 = e3) % 189.00/30.25 (19) op(e0, e0) = all_244_24 % 189.00/30.25 (20) op(e0, e1) = all_20_2 % 189.00/30.25 (21) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.25 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.25 (22) ~ (all_20_2 = e0) % 189.00/30.25 (23) all_252_11 = e3 % 189.00/30.25 (24) ~ (all_20_2 = e2) % 189.00/30.25 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.25 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.25 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.25 (26) ~ (e3 = e0) % 189.00/30.25 (27) ~ (all_20_2 = all_8_1) % 189.00/30.25 (28) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.25 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.25 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.25 (29) ~ (e3 = e2) % 189.00/30.25 (30) op(e0, e3) = all_8_1 % 189.00/30.25 (31) op(e1, e4) = e1 % 189.00/30.25 (32) ~ (e4 = e2) % 189.00/30.25 (33) ~ (e1 = e0) % 189.00/30.25 (34) all_250_23 = all_20_2 % 189.00/30.25 (35) ~ (e3 = e1) % 189.00/30.25 (36) ~ (e2 = e0) % 189.00/30.25 (37) op(e0, e1) = e1 % 189.00/30.25 (38) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.25 e3) % 189.00/30.25 (39) ~ (e4 = e1) % 189.00/30.25 % 189.00/30.25 Begin of proof % 189.00/30.25 | % 189.00/30.25 | BETA: splitting (38) gives: % 189.00/30.25 | % 189.00/30.25 | Case 1: % 189.00/30.25 | | % 189.00/30.25 | | (40) all_252_12 = e3 & op(e1, e4) = e3 % 189.00/30.25 | | % 189.00/30.25 | | ALPHA: (40) implies: % 189.00/30.25 | | (41) all_252_12 = e3 % 189.00/30.25 | | % 189.00/30.25 | | COMBINE_EQS: (10), (41) imply: % 189.00/30.25 | | (42) e3 = e0 % 189.00/30.25 | | % 189.00/30.25 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 189.00/30.25 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 189.00/30.25 | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 189.00/30.25 | | (37), (39), (42) are inconsistent by sub-proof #110. % 189.00/30.25 | | % 189.00/30.25 | Case 2: % 189.00/30.25 | | % 189.00/30.25 | | (43) all_252_13 = e3 & op(e1, e3) = e3 % 189.00/30.25 | | % 189.00/30.25 | | REF_CLOSE: (1), (29), (43) are inconsistent by sub-proof #109. % 189.00/30.25 | | % 189.00/30.25 | End of split % 189.00/30.25 | % 189.00/30.25 End of proof % 189.00/30.25 % 189.00/30.25 Sub-proof #109 shows that the following formulas are inconsistent: % 189.00/30.25 ---------------------------------------------------------------- % 189.00/30.25 (1) all_252_13 = e3 & op(e1, e3) = e3 % 189.00/30.25 (2) all_252_13 = e2 % 189.00/30.25 (3) ~ (e3 = e2) % 189.00/30.25 % 189.00/30.25 Begin of proof % 189.00/30.25 | % 189.00/30.25 | ALPHA: (1) implies: % 189.00/30.25 | (4) all_252_13 = e3 % 189.00/30.25 | % 189.00/30.25 | COMBINE_EQS: (2), (4) imply: % 189.00/30.25 | (5) e3 = e2 % 189.00/30.25 | % 189.00/30.25 | SIMP: (5) implies: % 189.00/30.25 | (6) e3 = e2 % 189.00/30.25 | % 189.00/30.25 | REDUCE: (3), (6) imply: % 189.00/30.25 | (7) $false % 189.00/30.25 | % 189.00/30.25 | CLOSE: (7) is inconsistent. % 189.00/30.25 | % 189.00/30.25 End of proof % 189.00/30.25 % 189.00/30.25 Sub-proof #110 shows that the following formulas are inconsistent: % 189.00/30.25 ---------------------------------------------------------------- % 189.00/30.25 (1) all_252_20 = e2 % 189.00/30.25 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.25 (3) ~ (all_20_2 = e4) % 189.00/30.25 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.25 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.25 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.25 (5) op(e0, e2) = e4 % 189.00/30.25 (6) op(e3, e1) = all_36_2 % 189.00/30.25 (7) ~ (e2 = e1) % 189.00/30.25 (8) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.25 (9) op(e4, e1) = e0 % 189.00/30.25 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.25 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.25 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.25 (11) ~ (e4 = e0) % 189.00/30.25 (12) ~ (e4 = e3) % 189.00/30.25 (13) ~ (all_36_2 = e2) % 189.00/30.25 (14) ~ (all_244_24 = all_20_2) % 189.00/30.25 (15) op(e1, e4) = e0 % 189.00/30.25 (16) ~ (all_20_2 = e3) % 189.00/30.25 (17) op(e0, e0) = all_244_24 % 189.00/30.25 (18) op(e0, e1) = all_20_2 % 189.00/30.25 (19) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.25 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.25 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.25 (20) ~ (all_20_2 = e0) % 189.00/30.25 (21) all_252_11 = e3 % 189.00/30.25 (22) ~ (all_20_2 = e2) % 189.00/30.25 (23) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.25 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.25 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.25 (24) ~ (e3 = e0) % 189.00/30.25 (25) ~ (all_20_2 = all_8_1) % 189.00/30.25 (26) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.25 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.25 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.25 (27) e3 = e0 % 189.00/30.25 (28) ~ (e3 = e2) % 189.00/30.25 (29) op(e0, e3) = all_8_1 % 189.00/30.25 (30) op(e1, e4) = e1 % 189.00/30.25 (31) ~ (e4 = e2) % 189.00/30.25 (32) ~ (e1 = e0) % 189.00/30.25 (33) all_250_23 = all_20_2 % 189.00/30.25 (34) ~ (e3 = e1) % 189.00/30.25 (35) ~ (e2 = e0) % 189.00/30.25 (36) op(e0, e1) = e1 % 189.00/30.25 (37) ~ (e4 = e1) % 189.00/30.25 % 189.00/30.25 Begin of proof % 189.00/30.25 | % 189.00/30.25 | SIMP: (27) implies: % 189.00/30.25 | (38) e3 = e0 % 189.00/30.25 | % 189.00/30.25 | COMBINE_EQS: (21), (38) imply: % 189.00/30.25 | (39) all_252_11 = e0 % 189.00/30.25 | % 189.00/30.25 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.25 | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24), % 189.00/30.25 | (25), (26), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 189.00/30.25 | (37), (39) are inconsistent by sub-proof #191. % 189.00/30.25 | % 189.00/30.25 End of proof % 189.00/30.25 % 189.00/30.25 Sub-proof #111 shows that the following formulas are inconsistent: % 189.00/30.25 ---------------------------------------------------------------- % 189.00/30.25 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.25 (2) op(e3, e1) = all_36_2 % 189.00/30.25 (3) ~ (all_36_2 = e2) % 189.00/30.25 (4) all_252_9 = e0 % 189.00/30.25 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.25 (6) ~ (e2 = e0) % 189.00/30.25 % 189.00/30.25 Begin of proof % 189.00/30.25 | % 189.00/30.25 | BETA: splitting (5) gives: % 189.00/30.25 | % 189.00/30.25 | Case 1: % 189.00/30.25 | | % 189.00/30.25 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 189.00/30.25 | | % 189.00/30.25 | | ALPHA: (7) implies: % 189.00/30.25 | | (8) all_252_9 = e2 % 189.00/30.25 | | % 189.00/30.25 | | COMBINE_EQS: (4), (8) imply: % 189.00/30.25 | | (9) e2 = e0 % 189.00/30.25 | | % 189.00/30.25 | | REDUCE: (6), (9) imply: % 189.00/30.25 | | (10) $false % 189.00/30.25 | | % 189.00/30.25 | | CLOSE: (10) is inconsistent. % 189.00/30.25 | | % 189.00/30.25 | Case 2: % 189.00/30.25 | | % 189.00/30.25 | | (11) all_252_10 = e2 & op(e3, e1) = e2 % 189.00/30.25 | | % 189.00/30.25 | | ALPHA: (11) implies: % 189.00/30.25 | | (12) op(e3, e1) = e2 % 189.00/30.25 | | % 189.00/30.25 | | REF_CLOSE: (1), (2), (3), (12) are inconsistent by sub-proof #557. % 189.00/30.25 | | % 189.00/30.25 | End of split % 189.00/30.25 | % 189.00/30.25 End of proof % 189.00/30.25 % 189.00/30.25 Sub-proof #112 shows that the following formulas are inconsistent: % 189.00/30.25 ---------------------------------------------------------------- % 189.00/30.25 (1) all_252_20 = e2 % 189.00/30.25 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.25 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.25 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.25 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.25 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.25 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.25 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.25 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.25 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.25 (6) ~ (all_20_2 = e4) % 189.00/30.25 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.25 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.25 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.25 (8) op(e0, e2) = e4 % 189.00/30.25 (9) op(e0, e2) = all_28_2 % 189.00/30.26 (10) op(e3, e1) = all_36_2 % 189.00/30.26 (11) ~ (e2 = e1) % 189.00/30.26 (12) all_252_12 = e0 % 189.00/30.26 (13) op(e4, e1) = e0 % 189.00/30.26 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.26 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.26 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.26 (15) op(e2, e1) = e0 % 189.00/30.26 (16) all_252_7 = e0 % 189.00/30.26 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.26 all_250_23 = e0 % 189.00/30.26 (18) ~ (e4 = e0) % 189.00/30.26 (19) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.26 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.26 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.26 (20) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.26 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.26 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.26 (21) ~ (e4 = e3) % 189.00/30.26 (22) ~ (all_36_2 = e2) % 189.00/30.26 (23) all_252_9 = e0 % 189.00/30.26 (24) ~ (all_40_2 = all_34_2) % 189.00/30.26 (25) ~ (all_244_24 = all_20_2) % 189.00/30.26 (26) op(e1, e4) = e0 % 189.00/30.26 (27) ~ (all_6_2 = e4) % 189.00/30.26 (28) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.26 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.26 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.26 (29) ~ (all_20_2 = e3) % 189.00/30.26 (30) op(all_20_2, e4) = e1 % 189.00/30.26 (31) op(e0, e0) = all_244_24 % 189.00/30.26 (32) op(e0, e1) = all_20_2 % 189.00/30.26 (33) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.26 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.26 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.26 (34) all_252_19 = e4 % 189.00/30.26 (35) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.26 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.26 (36) ~ (all_8_1 = e2) % 189.00/30.26 (37) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.26 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.26 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.26 (38) ~ (all_20_2 = e0) % 189.00/30.26 (39) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.26 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.26 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.26 (40) all_252_17 = e2 % 189.00/30.26 (41) ~ (all_20_2 = e2) % 189.00/30.26 (42) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.26 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.26 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.26 (43) op(e4, e4) = all_244_0 % 189.00/30.26 (44) op(e0, e4) = e2 % 189.00/30.26 (45) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = % 189.00/30.26 e3) % 189.00/30.26 (46) ~ (e3 = e0) % 189.00/30.26 (47) ~ (all_20_2 = all_8_1) % 189.00/30.26 (48) ~ (all_28_2 = e0) % 189.00/30.26 (49) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.26 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.26 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.26 (50) ~ (all_244_0 = e2) % 189.00/30.26 (51) op(e2, all_40_2) = e0 % 189.00/30.26 (52) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.26 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.26 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.26 (53) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.26 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.26 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.26 (54) ~ (e3 = e2) % 189.00/30.26 (55) all_252_22 = e4 % 189.00/30.26 (56) op(e4, all_20_2) = e0 % 189.00/30.26 (57) op(e0, e3) = all_8_1 % 189.00/30.26 (58) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.26 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.26 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.26 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.26 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.26 op(e0, e1) = e0))) % 189.00/30.26 (59) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.26 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.26 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.26 (60) ~ (e4 = e2) % 189.00/30.26 (61) op(e2, e0) = all_40_2 % 189.00/30.26 (62) op(all_28_2, all_40_2) = e2 % 189.00/30.26 (63) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.26 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.26 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.26 (64) ~ (e1 = e0) % 189.00/30.26 (65) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.26 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.26 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.26 (66) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.26 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.26 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.26 (67) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.26 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.26 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.26 (68) op(e0, e4) = all_12_2 % 189.00/30.26 (69) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.26 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.26 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.26 (70) all_250_23 = all_20_2 % 189.00/30.26 (71) ~ (e3 = e1) % 189.00/30.26 (72) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.26 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.26 (73) ~ (e2 = e0) % 189.00/30.26 (74) op(e1, e0) = all_34_2 % 189.00/30.26 (75) ~ (all_12_2 = e3) % 189.00/30.26 (76) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.26 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.26 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.26 (77) ~ (all_34_2 = e2) % 189.00/30.26 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.26 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.26 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.26 (79) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.26 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.26 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.26 (80) op(e4, e2) = all_6_2 % 189.00/30.26 (81) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.26 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.26 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.26 (82) all_252_5 = e0 % 189.00/30.26 (83) ~ (e4 = e1) % 189.00/30.26 (84) op(e2, e0) = e1 % 189.00/30.26 % 189.00/30.26 Begin of proof % 189.00/30.26 | % 189.00/30.26 | BETA: splitting (45) gives: % 189.00/30.26 | % 189.00/30.26 | Case 1: % 189.00/30.26 | | % 189.00/30.26 | | (85) all_252_15 = e3 & op(e1, e1) = e3 % 189.00/30.26 | | % 189.00/30.26 | | ALPHA: (85) implies: % 189.00/30.26 | | (86) all_252_15 = e3 % 189.00/30.26 | | % 189.00/30.26 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.26 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.26 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), % 189.00/30.26 | | (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (46), % 189.00/30.26 | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), % 189.00/30.26 | | (58), (59), (60), (61), (62), (63), (64), (65), (66), (67), (68), % 189.00/30.26 | | (69), (70), (71), (72), (73), (74), (75), (76), (77), (78), (79), % 189.00/30.26 | | (80), (81), (82), (83), (84), (86) are inconsistent by sub-proof % 189.00/30.26 | | #113. % 189.00/30.26 | | % 189.00/30.26 | Case 2: % 189.00/30.26 | | % 189.00/30.26 | | (87) all_252_23 = e3 & op(e0, e1) = e3 % 189.00/30.26 | | % 189.00/30.26 | | ALPHA: (87) implies: % 189.00/30.26 | | (88) op(e0, e1) = e3 % 189.00/30.26 | | % 189.00/30.26 | | REF_CLOSE: (5), (29), (32), (88) are inconsistent by sub-proof #508. % 189.00/30.26 | | % 189.00/30.26 | End of split % 189.00/30.26 | % 189.00/30.26 End of proof % 189.00/30.26 % 189.00/30.26 Sub-proof #113 shows that the following formulas are inconsistent: % 189.00/30.26 ---------------------------------------------------------------- % 189.00/30.26 (1) all_252_20 = e2 % 189.00/30.26 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.26 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.26 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.26 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.26 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.26 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.26 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.26 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.26 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.26 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.26 (6) ~ (all_20_2 = e4) % 189.00/30.26 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.26 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.26 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.26 (8) op(e0, e2) = e4 % 189.00/30.26 (9) op(e0, e2) = all_28_2 % 189.00/30.26 (10) op(e3, e1) = all_36_2 % 189.00/30.26 (11) ~ (e2 = e1) % 189.00/30.26 (12) all_252_12 = e0 % 189.00/30.26 (13) op(e4, e1) = e0 % 189.00/30.26 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.26 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.26 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.26 (15) op(e2, e1) = e0 % 189.00/30.26 (16) all_252_15 = e3 % 189.00/30.26 (17) all_252_7 = e0 % 189.00/30.26 (18) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.26 all_250_23 = e0 % 189.00/30.26 (19) ~ (e4 = e0) % 189.00/30.26 (20) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.26 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.26 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.26 (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.26 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.26 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.26 (22) ~ (e4 = e3) % 189.00/30.26 (23) ~ (all_36_2 = e2) % 189.00/30.26 (24) all_252_9 = e0 % 189.00/30.26 (25) ~ (all_40_2 = all_34_2) % 189.00/30.26 (26) ~ (all_244_24 = all_20_2) % 189.00/30.26 (27) op(e1, e4) = e0 % 189.00/30.26 (28) ~ (all_6_2 = e4) % 189.00/30.26 (29) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.26 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.26 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.26 (30) ~ (all_20_2 = e3) % 189.00/30.26 (31) op(all_20_2, e4) = e1 % 189.00/30.26 (32) op(e0, e0) = all_244_24 % 189.00/30.26 (33) op(e0, e1) = all_20_2 % 189.00/30.26 (34) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.26 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.26 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.26 (35) all_252_19 = e4 % 189.00/30.26 (36) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.26 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.26 (37) ~ (all_8_1 = e2) % 189.00/30.26 (38) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.26 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.26 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.26 (39) ~ (all_20_2 = e0) % 189.00/30.26 (40) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.26 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.26 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.26 (41) all_252_17 = e2 % 189.00/30.26 (42) ~ (all_20_2 = e2) % 189.00/30.26 (43) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.26 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.26 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.26 (44) op(e4, e4) = all_244_0 % 189.00/30.26 (45) op(e0, e4) = e2 % 189.00/30.26 (46) ~ (e3 = e0) % 189.00/30.26 (47) ~ (all_20_2 = all_8_1) % 189.00/30.26 (48) ~ (all_28_2 = e0) % 189.00/30.26 (49) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.26 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.26 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.26 (50) ~ (all_244_0 = e2) % 189.00/30.26 (51) op(e2, all_40_2) = e0 % 189.00/30.26 (52) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.26 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.26 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.26 (53) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.26 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.26 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.26 (54) ~ (e3 = e2) % 189.00/30.26 (55) all_252_22 = e4 % 189.00/30.26 (56) op(e4, all_20_2) = e0 % 189.00/30.26 (57) op(e0, e3) = all_8_1 % 189.00/30.26 (58) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.26 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.26 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.26 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.26 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.26 op(e0, e1) = e0))) % 189.00/30.26 (59) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.26 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.26 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.26 (60) ~ (e4 = e2) % 189.00/30.26 (61) op(e2, e0) = all_40_2 % 189.00/30.26 (62) op(all_28_2, all_40_2) = e2 % 189.00/30.26 (63) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.26 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.26 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.26 (64) ~ (e1 = e0) % 189.00/30.26 (65) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.26 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.26 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.26 (66) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.26 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.26 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.26 (67) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.26 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.26 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.26 (68) op(e0, e4) = all_12_2 % 189.00/30.26 (69) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.26 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.26 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.26 (70) all_250_23 = all_20_2 % 189.00/30.26 (71) ~ (e3 = e1) % 189.00/30.26 (72) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.26 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.26 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.26 (73) ~ (e2 = e0) % 189.00/30.26 (74) op(e1, e0) = all_34_2 % 189.00/30.26 (75) ~ (all_12_2 = e3) % 189.00/30.26 (76) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.26 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.26 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.26 (77) ~ (all_34_2 = e2) % 189.00/30.26 (78) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.26 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.26 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.26 (79) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.26 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.26 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.26 (80) op(e4, e2) = all_6_2 % 189.00/30.26 (81) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.26 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.26 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.26 (82) all_252_5 = e0 % 189.00/30.26 (83) ~ (e4 = e1) % 189.00/30.26 (84) op(e2, e0) = e1 % 189.00/30.26 % 189.00/30.26 Begin of proof % 189.00/30.26 | % 189.00/30.26 | BETA: splitting (7) gives: % 189.00/30.26 | % 189.00/30.26 | Case 1: % 189.00/30.26 | | % 189.00/30.26 | | (85) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = % 189.00/30.26 | | e2) % 189.00/30.26 | | % 189.00/30.26 | | REF_CLOSE: (5), (10), (23), (24), (73), (85) are inconsistent by sub-proof % 189.00/30.26 | | #207. % 189.00/30.26 | | % 189.00/30.26 | Case 2: % 189.00/30.26 | | % 189.00/30.26 | | (86) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) % 189.00/30.26 | | = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.26 | | % 189.00/30.26 | | BETA: splitting (86) gives: % 189.00/30.26 | | % 189.00/30.26 | | Case 1: % 189.00/30.26 | | | % 189.00/30.26 | | | (87) all_252_11 = e2 & op(e2, e1) = e2 % 189.00/30.26 | | | % 189.00/30.26 | | | ALPHA: (87) implies: % 189.00/30.26 | | | (88) all_252_11 = e2 % 189.00/30.26 | | | (89) op(e2, e1) = e2 % 189.00/30.26 | | | % 189.00/30.26 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.00/30.26 | | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), % 189.00/30.26 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 189.00/30.26 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 189.00/30.26 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53), % 189.00/30.26 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63), % 189.00/30.26 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73), % 189.00/30.26 | | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83), % 189.00/30.26 | | | (84), (88), (89) are inconsistent by sub-proof #115. % 189.00/30.26 | | | % 189.00/30.26 | | Case 2: % 189.00/30.26 | | | % 189.00/30.26 | | | (90) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, % 189.00/30.26 | | | e1) = e2) % 189.00/30.26 | | | % 189.00/30.26 | | | BETA: splitting (90) gives: % 189.00/30.26 | | | % 189.00/30.26 | | | Case 1: % 189.00/30.26 | | | | % 189.00/30.26 | | | | (91) all_252_15 = e2 & op(e1, e1) = e2 % 189.00/30.26 | | | | % 189.00/30.26 | | | | REF_CLOSE: (16), (54), (91) are inconsistent by sub-proof #114. % 189.00/30.26 | | | | % 189.00/30.26 | | | Case 2: % 189.00/30.26 | | | | % 189.00/30.26 | | | | (92) all_252_23 = e2 & op(e0, e1) = e2 % 189.00/30.26 | | | | % 189.00/30.26 | | | | REF_CLOSE: (5), (33), (42), (92) are inconsistent by sub-proof #540. % 189.00/30.26 | | | | % 189.00/30.26 | | | End of split % 189.00/30.26 | | | % 189.00/30.26 | | End of split % 189.00/30.26 | | % 189.00/30.26 | End of split % 189.00/30.26 | % 189.00/30.26 End of proof % 189.00/30.26 % 189.00/30.26 Sub-proof #114 shows that the following formulas are inconsistent: % 189.00/30.26 ---------------------------------------------------------------- % 189.00/30.26 (1) all_252_15 = e2 & op(e1, e1) = e2 % 189.00/30.26 (2) all_252_15 = e3 % 189.00/30.26 (3) ~ (e3 = e2) % 189.00/30.26 % 189.00/30.26 Begin of proof % 189.00/30.26 | % 189.00/30.26 | ALPHA: (1) implies: % 189.00/30.27 | (4) all_252_15 = e2 % 189.00/30.27 | % 189.00/30.27 | COMBINE_EQS: (2), (4) imply: % 189.00/30.27 | (5) e3 = e2 % 189.00/30.27 | % 189.00/30.27 | REDUCE: (3), (5) imply: % 189.00/30.27 | (6) $false % 189.00/30.27 | % 189.00/30.27 | CLOSE: (6) is inconsistent. % 189.00/30.27 | % 189.00/30.27 End of proof % 189.00/30.27 % 189.00/30.27 Sub-proof #115 shows that the following formulas are inconsistent: % 189.00/30.27 ---------------------------------------------------------------- % 189.00/30.27 (1) all_252_20 = e2 % 189.00/30.27 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.00/30.27 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.00/30.27 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.00/30.27 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.00/30.27 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.00/30.27 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.00/30.27 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.00/30.27 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.00/30.27 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.00/30.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.00/30.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.00/30.27 (6) ~ (all_20_2 = e4) % 189.00/30.27 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.00/30.27 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.00/30.27 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.00/30.27 (8) op(e0, e2) = e4 % 189.00/30.27 (9) op(e0, e2) = all_28_2 % 189.00/30.27 (10) op(e3, e1) = all_36_2 % 189.00/30.27 (11) ~ (e2 = e1) % 189.00/30.27 (12) all_252_12 = e0 % 189.00/30.27 (13) op(e2, e1) = e2 % 189.00/30.27 (14) op(e4, e1) = e0 % 189.00/30.27 (15) all_252_11 = e2 % 189.00/30.27 (16) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.00/30.27 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.00/30.27 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.00/30.27 (17) op(e2, e1) = e0 % 189.00/30.27 (18) all_252_7 = e0 % 189.00/30.27 (19) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.00/30.27 all_250_23 = e0 % 189.00/30.27 (20) ~ (e4 = e0) % 189.00/30.27 (21) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.00/30.27 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.00/30.27 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.00/30.27 (22) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.00/30.27 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.00/30.27 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.27 (23) ~ (e4 = e3) % 189.00/30.27 (24) ~ (all_36_2 = e2) % 189.00/30.27 (25) all_252_9 = e0 % 189.00/30.27 (26) ~ (all_40_2 = all_34_2) % 189.00/30.27 (27) ~ (all_244_24 = all_20_2) % 189.00/30.27 (28) op(e1, e4) = e0 % 189.00/30.27 (29) ~ (all_6_2 = e4) % 189.00/30.27 (30) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) % 189.00/30.27 | (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.00/30.27 e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.00/30.27 (31) ~ (all_20_2 = e3) % 189.00/30.27 (32) op(all_20_2, e4) = e1 % 189.00/30.27 (33) op(e0, e0) = all_244_24 % 189.00/30.27 (34) op(e0, e1) = all_20_2 % 189.00/30.27 (35) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.00/30.27 | (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.00/30.27 e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.00/30.27 (36) all_252_19 = e4 % 189.00/30.27 (37) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.00/30.27 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.00/30.27 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.00/30.27 (38) ~ (all_8_1 = e2) % 189.00/30.27 (39) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.00/30.27 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.00/30.27 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.27 (40) ~ (all_20_2 = e0) % 189.00/30.27 (41) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.27 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.00/30.27 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.00/30.27 (42) all_252_17 = e2 % 189.00/30.27 (43) ~ (all_20_2 = e2) % 189.00/30.27 (44) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.00/30.27 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.00/30.27 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.00/30.27 (45) op(e4, e4) = all_244_0 % 189.00/30.27 (46) op(e0, e4) = e2 % 189.00/30.27 (47) ~ (e3 = e0) % 189.00/30.27 (48) ~ (all_20_2 = all_8_1) % 189.00/30.27 (49) ~ (all_28_2 = e0) % 189.00/30.27 (50) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.00/30.27 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.00/30.27 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.00/30.27 (51) ~ (all_244_0 = e2) % 189.00/30.27 (52) op(e2, all_40_2) = e0 % 189.00/30.27 (53) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.00/30.27 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.00/30.27 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.00/30.27 (54) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 189.00/30.27 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.00/30.27 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.00/30.27 (55) ~ (e3 = e2) % 189.00/30.27 (56) all_252_22 = e4 % 189.00/30.27 (57) op(e4, all_20_2) = e0 % 189.00/30.27 (58) op(e0, e3) = all_8_1 % 189.00/30.27 (59) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.00/30.27 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.00/30.27 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.00/30.27 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.00/30.27 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.00/30.27 op(e0, e1) = e0))) % 189.00/30.27 (60) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.00/30.27 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.00/30.27 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.00/30.27 (61) ~ (e4 = e2) % 189.00/30.27 (62) op(e2, e0) = all_40_2 % 189.00/30.27 (63) op(all_28_2, all_40_2) = e2 % 189.00/30.27 (64) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.00/30.27 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.00/30.27 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.00/30.27 (65) ~ (e1 = e0) % 189.00/30.27 (66) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.00/30.27 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.00/30.27 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.00/30.27 (67) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.00/30.27 | (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = e4 & op(e2, e1) = % 189.00/30.27 e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.00/30.27 (68) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.27 | (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = e4 & op(e1, e3) = % 189.00/30.27 e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 189.00/30.27 (69) op(e0, e4) = all_12_2 % 189.00/30.27 (70) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.00/30.27 | (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = e3 & op(e4, e1) = % 189.00/30.27 e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 189.00/30.27 (71) all_250_23 = all_20_2 % 189.00/30.27 (72) ~ (e3 = e1) % 189.00/30.27 (73) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = e1 & op(e3, e2) = e1) % 189.00/30.27 | (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = e1 & op(e1, e2) = % 189.00/30.27 e1) | (all_252_22 = e1 & op(e0, e2) = e1) % 189.00/30.27 (74) ~ (e2 = e0) % 189.00/30.27 (75) op(e1, e0) = all_34_2 % 189.00/30.27 (76) ~ (all_12_2 = e3) % 189.00/30.27 (77) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.00/30.27 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.00/30.27 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.00/30.27 (78) ~ (all_34_2 = e2) % 189.00/30.27 (79) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.00/30.27 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.00/30.27 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.00/30.27 (80) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.00/30.27 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.00/30.27 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.00/30.27 (81) op(e4, e2) = all_6_2 % 189.00/30.27 (82) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = e2 & op(e4, e3) = e2) % 189.00/30.27 | (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = e2 & op(e4, e1) = % 189.00/30.27 e2) | (all_252_16 = e2 & op(e4, e0) = e2) % 189.00/30.27 (83) all_252_5 = e0 % 189.00/30.27 (84) ~ (e4 = e1) % 189.00/30.27 (85) op(e2, e0) = e1 % 189.00/30.27 % 189.00/30.27 Begin of proof % 189.00/30.27 | % 189.00/30.27 | BETA: splitting (19) gives: % 189.00/30.27 | % 189.00/30.27 | Case 1: % 189.00/30.27 | | % 189.00/30.27 | | (86) all_250_23 = e4 % 189.00/30.27 | | % 189.00/30.27 | | REF_CLOSE: (6), (71), (86) are inconsistent by sub-proof #489. % 189.00/30.27 | | % 189.00/30.27 | Case 2: % 189.00/30.27 | | % 189.00/30.27 | | (87) ~ (all_250_23 = e4) % 189.00/30.27 | | (88) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 189.00/30.27 | | e0 % 189.00/30.27 | | % 189.00/30.27 | | BETA: splitting (88) gives: % 189.00/30.27 | | % 189.00/30.27 | | Case 1: % 189.00/30.27 | | | % 189.00/30.27 | | | (89) all_250_23 = e3 % 189.00/30.27 | | | % 189.00/30.27 | | | REF_CLOSE: (31), (71), (89) are inconsistent by sub-proof #488. % 189.00/30.27 | | | % 189.00/30.27 | | Case 2: % 189.00/30.27 | | | % 189.00/30.27 | | | (90) ~ (all_250_23 = e3) % 189.00/30.27 | | | (91) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.00/30.27 | | | % 189.00/30.27 | | | BETA: splitting (44) gives: % 189.00/30.27 | | | % 189.00/30.27 | | | Case 1: % 189.00/30.27 | | | | % 189.00/30.27 | | | | (92) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, % 189.00/30.27 | | | | e1) = e4) % 189.00/30.27 | | | | % 189.00/30.27 | | | | BETA: splitting (92) gives: % 189.00/30.27 | | | | % 189.00/30.27 | | | | Case 1: % 189.00/30.27 | | | | | % 189.00/30.27 | | | | | (93) all_252_9 = e4 & op(e4, e1) = e4 % 189.00/30.27 | | | | | % 189.00/30.27 | | | | | REF_CLOSE: (20), (25), (93) are inconsistent by sub-proof #211. % 189.00/30.27 | | | | | % 189.00/30.27 | | | | Case 2: % 189.00/30.27 | | | | | % 189.00/30.27 | | | | | (94) all_252_10 = e4 & op(e3, e1) = e4 % 189.00/30.27 | | | | | % 189.00/30.27 | | | | | ALPHA: (94) implies: % 189.00/30.27 | | | | | (95) all_252_10 = e4 % 189.00/30.27 | | | | | % 189.00/30.27 | | | | | BETA: splitting (54) gives: % 189.00/30.27 | | | | | % 189.00/30.27 | | | | | Case 1: % 189.00/30.27 | | | | | | % 189.00/30.27 | | | | | | (96) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & % 189.00/30.27 | | | | | | op(e3, e3) = e2) % 189.00/30.27 | | | | | | % 189.00/30.27 | | | | | | BETA: splitting (96) gives: % 189.00/30.27 | | | | | | % 189.00/30.27 | | | | | | Case 1: % 189.00/30.27 | | | | | | | % 189.00/30.27 | | | | | | | (97) all_252_1 = e2 & op(e4, e3) = e2 % 189.00/30.27 | | | | | | | % 189.00/30.27 | | | | | | | ALPHA: (97) implies: % 189.00/30.27 | | | | | | | (98) all_252_1 = e2 % 189.00/30.27 | | | | | | | % 189.00/30.27 | | | | | | | BETA: splitting (16) gives: % 189.00/30.27 | | | | | | | % 189.00/30.27 | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | % 189.00/30.27 | | | | | | | | (99) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & % 189.00/30.27 | | | | | | | | op(e3, e1) = e3) % 189.00/30.27 | | | | | | | | % 189.00/30.27 | | | | | | | | REF_CLOSE: (5), (14), (23), (47), (95), (99) are inconsistent by % 189.00/30.27 | | | | | | | | sub-proof #218. % 189.00/30.27 | | | | | | | | % 189.00/30.27 | | | | | | | Case 2: % 189.00/30.27 | | | | | | | | % 189.00/30.27 | | | | | | | | (100) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 % 189.00/30.27 | | | | | | | | & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = % 189.00/30.27 | | | | | | | | e3) % 189.00/30.27 | | | | | | | | % 189.00/30.27 | | | | | | | | BETA: splitting (100) gives: % 189.00/30.27 | | | | | | | | % 189.00/30.27 | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | % 189.00/30.27 | | | | | | | | | (101) all_252_11 = e3 & op(e2, e1) = e3 % 189.00/30.27 | | | | | | | | | % 189.00/30.27 | | | | | | | | | REF_CLOSE: (15), (55), (101) are inconsistent by sub-proof % 189.00/30.27 | | | | | | | | | #356. % 189.00/30.27 | | | | | | | | | % 189.00/30.27 | | | | | | | | Case 2: % 189.00/30.27 | | | | | | | | | % 189.00/30.27 | | | | | | | | | (102) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = % 189.00/30.27 | | | | | | | | | e3 & op(e0, e1) = e3) % 189.00/30.27 | | | | | | | | | % 189.00/30.27 | | | | | | | | | BETA: splitting (102) gives: % 189.00/30.27 | | | | | | | | | % 189.00/30.27 | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | (103) all_252_15 = e3 & op(e1, e1) = e3 % 189.00/30.27 | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | ALPHA: (103) implies: % 189.00/30.27 | | | | | | | | | | (104) all_252_15 = e3 % 189.00/30.27 | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | BETA: splitting (91) gives: % 189.00/30.27 | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | (105) all_250_23 = e2 % 189.00/30.27 | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | REF_CLOSE: (43), (71), (105) are inconsistent by sub-proof % 189.00/30.27 | | | | | | | | | | | #487. % 189.00/30.27 | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | Case 2: % 189.00/30.27 | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | (106) ~ (all_250_23 = e2) % 189.00/30.27 | | | | | | | | | | | (107) all_250_23 = e1 | all_250_23 = e0 % 189.00/30.27 | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | BETA: splitting (107) gives: % 189.00/30.27 | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | (108) all_250_23 = e1 % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | COMBINE_EQS: (71), (108) imply: % 189.00/30.27 | | | | | | | | | | | | (109) all_20_2 = e1 % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | SIMP: (109) implies: % 189.00/30.27 | | | | | | | | | | | | (110) all_20_2 = e1 % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | REDUCE: (27), (110) imply: % 189.00/30.27 | | | | | | | | | | | | (111) ~ (all_244_24 = e1) % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | REDUCE: (48), (110) imply: % 189.00/30.27 | | | | | | | | | | | | (112) ~ (all_8_1 = e1) % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | SIMP: (112) implies: % 189.00/30.27 | | | | | | | | | | | | (113) ~ (all_8_1 = e1) % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | REDUCE: (6), (110) imply: % 189.00/30.27 | | | | | | | | | | | | (114) ~ (e4 = e1) % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | REDUCE: (31), (110) imply: % 189.00/30.27 | | | | | | | | | | | | (115) ~ (e3 = e1) % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | REDUCE: (43), (110) imply: % 189.00/30.27 | | | | | | | | | | | | (116) ~ (e2 = e1) % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | REDUCE: (32), (110) imply: % 189.00/30.27 | | | | | | | | | | | | (117) op(e1, e4) = e1 % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | BETA: splitting (67) gives: % 189.00/30.27 | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | (118) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = % 189.00/30.27 | | | | | | | | | | | | | e4 & op(e2, e3) = e4) % 189.00/30.27 | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), % 189.00/30.27 | | | | | | | | | | | | | (12), (16), (17), (18), (19), (20), (21), (22), % 189.00/30.27 | | | | | | | | | | | | | (23), (24), (25), (26), (27), (28), (29), (31), % 189.00/30.27 | | | | | | | | | | | | | (32), (33), (34), (36), (37), (39), (40), (41), % 189.00/30.27 | | | | | | | | | | | | | (42), (43), (44), (46), (47), (48), (50), (53), % 189.00/30.27 | | | | | | | | | | | | | (55), (56), (57), (58), (59), (60), (61), (62), % 189.00/30.27 | | | | | | | | | | | | | (64), (65), (66), (69), (71), (72), (74), (75), % 189.00/30.27 | | | | | | | | | | | | | (76), (77), (78), (81), (83), (84), (85), (95), % 189.00/30.27 | | | | | | | | | | | | | (98), (111), (118) are inconsistent by sub-proof % 189.00/30.27 | | | | | | | | | | | | | #164. % 189.00/30.27 | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | Case 2: % 189.00/30.27 | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | (119) (all_252_8 = e4 & op(e2, e2) = e4) | (all_252_11 = % 189.00/30.27 | | | | | | | | | | | | | e4 & op(e2, e1) = e4) | (all_252_18 = e4 & % 189.00/30.27 | | | | | | | | | | | | | op(e2, e0) = e4) % 189.00/30.27 | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | BETA: splitting (119) gives: % 189.00/30.27 | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | (120) all_252_8 = e4 & op(e2, e2) = e4 % 189.00/30.27 | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | ALPHA: (120) implies: % 189.00/30.27 | | | | | | | | | | | | | | (121) all_252_8 = e4 % 189.00/30.27 | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | BETA: splitting (21) gives: % 189.00/30.27 | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | (122) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = % 189.00/30.27 | | | | | | | | | | | | | | | e4 & op(e4, e3) = e4) % 189.00/30.27 | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 189.00/30.27 | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | (123) all_252_0 = e4 & op(e4, e4) = e4 % 189.00/30.27 | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | ALPHA: (123) implies: % 189.00/30.27 | | | | | | | | | | | | | | | | (124) all_252_0 = e4 % 189.00/30.27 | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | BETA: splitting (37) gives: % 189.00/30.27 | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | (125) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 189.00/30.27 | | | | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 189.00/30.27 | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (46), (58), (113), (125) are % 189.00/30.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #244. % 189.00/30.27 | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | Case 2: % 189.00/30.27 | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | (126) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 189.00/30.27 | | | | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 189.00/30.27 | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 189.00/30.27 | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 189.00/30.27 | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | (127) all_252_22 = e1 & op(e0, e2) = e1 % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 189.00/30.27 | | | | | | | | | | | | | | | | | | (128) op(e0, e2) = e1 % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (84), (128) are inconsistent by % 189.00/30.27 | | | | | | | | | | | | | | | | | | sub-proof #256. % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | Case 2: % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | (129) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 189.00/30.27 | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives: % 189.00/30.27 | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | | (130) all_252_23 = e1 & op(e0, e1) = e1 % 189.00/30.27 | | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies: % 189.00/30.27 | | | | | | | | | | | | | | | | | | | (131) all_252_23 = e1 % 189.00/30.27 | | | | | | | | | | | | | | | | | | | (132) op(e0, e1) = e1 % 189.00/30.27 | | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 189.00/30.27 | | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | | Case 1: % 189.00/30.27 | | | | | | | | | | | | | | | | | | | | % 189.00/30.27 | | | | | | | | | | | | | | | | | | | | (133) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 189.00/30.27 | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 189.00/30.27 | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (55), (98), (124), (133) are inconsistent by % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | sub-proof #156. % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | (134) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_9 = % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e1) = e3) | (all_252_16 = e3 & % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e3) % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | (135) all_252_4 = e3 & op(e4, e2) = e3 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | (136) all_252_4 = e3 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | (137) (all_252_4 = e1 & op(e4, e2) = e1) | (all_252_5 = % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e2) = e1) % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (138) all_252_4 = e1 & op(e4, e2) = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (136), (138) are inconsistent by sub-proof % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | #348. % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (139) all_252_5 = e1 & op(e3, e2) = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (83), (139) are inconsistent by sub-proof % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | #155. % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | (140) (all_252_8 = e1 & op(e2, e2) = e1) | (all_252_14 = % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e2) = e1) | (all_252_22 = e1 & % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e1) % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (141) all_252_8 = e1 & op(e2, e2) = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (142) all_252_8 = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (142) imply: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (143) e4 = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (143) implies: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (144) e4 = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (84), (144) imply: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (145) $false % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (145) is inconsistent. % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | (146) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e2) = e1) % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | (147) all_252_14 = e1 & op(e1, e2) = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | (148) all_252_14 = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (11), (30), (49), (52), (55), (61), % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | (63), (74), (83), (121), (136), (148) are % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #154. % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | (149) all_252_22 = e1 & op(e0, e2) = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies: % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | (150) op(e0, e2) = e1 % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (84), (150) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #256. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | (151) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e0) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | (152) all_252_9 = e3 & op(e4, e1) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (47), (152) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | sub-proof #275. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | (153) all_252_16 = e3 & op(e4, e0) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | (154) op(e4, e0) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | (155) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (42), (72), (154), (155) are % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | (156) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | (157) all_252_18 = e1 & op(e2, e0) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | (158) all_252_18 = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | (159) all_252_24 = e0 & op(e0, e0) = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | (160) all_252_24 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (161) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e3, e3) = e4) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (162) all_252_1 = e4 & op(e4, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (98), (162) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (163) all_252_3 = e4 & op(e3, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_252_3 = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e3) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_252_2 = e1 & op(e3, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167) all_252_2 = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e3) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_252_2 = e3 & op(e3, e4) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (167), (169) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #151. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_252_3 = e3 & op(e3, e3) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (164), (170) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #150. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (172) all_252_5 = e3 & op(e3, e2) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (83), (172) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #217. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (173) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (173) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_252_10 = e3 & op(e3, e1) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (95), (174) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #274. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_252_17 = e3 & op(e3, e0) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (55), (175) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_252_3 = e1 & op(e3, e3) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (164), (176) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #149. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (177) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (178) all_252_5 = e1 & op(e3, e2) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (83), (178) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #155. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (179) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_252_10 = e1 & op(e3, e1) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (95), (180) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #277. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_252_17 = e1 & op(e3, e0) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (42), (181) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #162. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (182) (all_252_7 = e4 & op(e2, e3) = e4) | (all_252_13 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e1, e3) = e4) | (all_252_21 = e4 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = e4) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (183) all_252_7 = e4 & op(e2, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (184) all_252_7 = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (184) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (185) e4 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) e4 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (186) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_252_0 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (123), (187) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) all_252_1 = e4 & op(e4, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (98), (188) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #152. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e4) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_252_4 = e4 & op(e4, e2) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (29), (81), (190) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #388. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_252_9 = e4 & op(e4, e1) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (192) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #211. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_252_16 = e4 & op(e4, e0) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (193) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) op(e4, e0) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_252_16 = e1 & op(e4, e0) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_252_16 = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) op(e4, e0) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (123), (187) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #385. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_252_1 = e4 & op(e4, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_252_1 = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_1 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e3) = e2) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_252_0 = e2 & op(e4, e4) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) op(e4, e4) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (45), (51), (203) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #500. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (98), (200) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) e4 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (61), (204) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) $false % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_9 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e1) = e2) | (all_252_16 = e2 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e4, e0) = e2) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_252_4 = e2 & op(e4, e2) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_252_4 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e4, e3) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_252_0 = e3 & op(e4, e4) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (187), (210) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #148. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_252_1 = e3 & op(e4, e3) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_252_1 = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (200), (212) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) e4 = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (23), (213) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) $false % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (214) is inconsistent. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (134) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_252_4 = e3 & op(e4, e2) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (208), (215) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #147. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_252_9 = e3 & op(e4, e1) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (47), (216) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #275. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (72), (154), (198) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #387. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_16 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e4, e0) = e2) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_252_9 = e2 & op(e4, e1) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (74), (218) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #208. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_252_16 = e2 & op(e4, e0) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_252_16 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (197), (220) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) e2 = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (221) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) $false % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (222) is inconsistent. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_252_4 = e4 & op(e4, e2) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (29), (81), (223) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #388. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_252_9 = e4 & op(e4, e1) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (224) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #211. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (193), (197) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #383. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_252_17 = e1 & op(e3, e0) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (42), (225) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (11), (12), (15), (16), (17), (18), (19), (20), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (27), (28), (31), (32), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (36), (37), (39), (40), (41), (42), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (46), (47), (48), (50), (53), (55), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (64), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (69), (71), (72), (74), (75), (76), (77), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (78), (84), (85), (111), (121), (156), (194) are % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #145. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) (all_252_13 = e4 & op(e1, e3) = e4) | (all_252_21 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e4 & op(e0, e3) = e4) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_252_13 = e4 & op(e1, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) op(e1, e3) = e4 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e3) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_252_6 = e3 & op(e2, e4) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_252_6 = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (77) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e3, e4) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_252_0 = e1 & op(e4, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (124), (233) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #231. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_252_2 = e1 & op(e3, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_252_2 = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e3) = e2) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_252_12 = e2 & op(e1, e4) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (237) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_252_12 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (238) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) e2 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (239) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_252_11 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (14), (16), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (20), (23), (24), (27), (28), (31), (33), (34), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (40), (43), (44), (47), (48), (53), (55), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (58), (61), (65), (71), (72), (74), (84), (107), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (132), (240) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #191. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_252_13 = e2 & op(e1, e3) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) op(e1, e3) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (61), (228), (242) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #529. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e2) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_252_14 = e2 & op(e1, e2) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_252_14 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (13), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (14), (15), (16), (17), (20), (23), (24), (26), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (27), (28), (31), (33), (34), (37), (40), (43), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (47), (48), (53), (55), (58), (61), (62), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (64), (65), (71), (72), (74), (75), (84), (85), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (107), (117), (131), (132), (245) are % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e1, e0) = e2) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_252_15 = e2 & op(e1, e1) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_252_15 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (104), (248) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) e3 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (249) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) e3 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (231), (250) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_252_6 = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (11), (20), (23), (46), (47), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (60), (61), (65), (69), (72), (74), (76), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (77), (84), (124), (235), (251) are inconsistent % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #227. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_252_19 = e2 & op(e1, e0) = e2 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (75), (78), (252) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #438. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e4) = e1) | (all_252_20 = e1 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e4) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_252_6 = e1 & op(e2, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (231), (254) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #555. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e4) = e1) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_252_12 = e1 & op(e1, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_252_12 = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (257) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) e1 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (258) imply: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_252_18 = e0 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (11), (19), (22), (26), (27), (31), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (40), (42), (43), (62), (65), (71), (72), % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (75), (85), (154), (259) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #141. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_252_20 = e1 & op(e0, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (260) implies: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) op(e0, e4) = e1 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (46), (261) are inconsistent by % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #323. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_252_7 = e3 & op(e2, e3) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (47), (262) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #358. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e1) = e3) | (all_252_18 = e3 & % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e3) % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) all_252_8 = e3 & op(e2, e2) = e3 % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (121), (264) are inconsistent by sub-proof % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #140. % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & op(e2, e0) = e3) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_252_11 = e3 & op(e2, e1) = e3 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (55), (266) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #146. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_252_18 = e3 & op(e2, e0) = e3 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (267) implies: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_252_18 = e3 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_252_16 = e1 & op(e4, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) op(e4, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with e1, e3, e0, e4, simplifying % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | with (154), (271) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) e3 = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (272) imply: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) $false % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (273) is inconsistent. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_252_17 = e1 & op(e3, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (42), (274) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #247. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (158), (268) imply: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) e3 = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (72), (275) imply: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) $false % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (276) is inconsistent. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_252_19 = e1 & op(e1, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (84), (278) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #354. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_252_24 = e1 & op(e0, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_252_24 = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (160), (280) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #139. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_252_21 = e4 & op(e0, e3) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (12), (16), (17), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (19), (20), (23), (24), (25), (26), (27), (28), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (36), (37), (40), (41), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (43), (44), (46), (47), (48), (50), (53), (55), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (61), (62), (64), (69), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (74), (75), (76), (78), (79), (85), (281) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (282) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (all_252_23 = e0 & op(e0, e1) = e0)) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (283) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (13), (14), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (15), (16), (17), (20), (23), (24), (27), (28), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (31), (33), (34), (37), (40), (43), (44), (46), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (47), (48), (53), (55), (58), (61), (65), (71), % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | (72), (74), (84), (107), (111), (117), (283) are % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #135. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | (284) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (26), (33), (62), (75), (85), (111), (284) % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #166. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | (285) all_252_24 = e1 & op(e0, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | (286) op(e0, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (33), (111), (286) are inconsistent by % 189.41/30.29 | | | | | | | | | | | | | | | | | | | sub-proof #474. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | (287) all_252_1 = e4 & op(e4, e3) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | REF_CLOSE: (61), (98), (287) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | #152. % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | (288) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = % 189.41/30.29 | | | | | | | | | | | | | | | e4 & op(e4, e1) = e4) | (all_252_16 = e4 & % 189.41/30.29 | | | | | | | | | | | | | | | op(e4, e0) = e4) % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | BETA: splitting (288) gives: % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | (289) all_252_4 = e4 & op(e4, e2) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (29), (81), (289) are inconsistent by % 189.41/30.29 | | | | | | | | | | | | | | | | sub-proof #388. % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | (290) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = % 189.41/30.29 | | | | | | | | | | | | | | | | e4 & op(e4, e0) = e4) % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | BETA: splitting (290) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | (291) all_252_9 = e4 & op(e4, e1) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (25), (291) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | #211. % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | (292) all_252_16 = e4 & op(e4, e0) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | ALPHA: (292) implies: % 189.41/30.29 | | | | | | | | | | | | | | | | | (293) all_252_16 = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | | (294) op(e4, e0) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | BETA: splitting (22) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | (295) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 % 189.41/30.29 | | | | | | | | | | | | | | | | | | = e1 & op(e3, e0) = e1) % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives: % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | (296) all_252_16 = e1 & op(e4, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (293), (296) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | | | #538. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | (297) all_252_17 = e1 & op(e3, e0) = e1 % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (42), (297) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | | | | | | | | #247. % 189.41/30.29 | | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | (298) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 % 189.41/30.29 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 189.41/30.29 | | | | | | | | | | | | | | | | | | op(e0, e0) = e1) % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (11), (12), (15), (16), (17), (18), (19), (20), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (23), (24), (25), (26), (27), (28), (31), (32), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (33), (34), (36), (37), (39), (40), (41), (42), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (43), (44), (46), (47), (48), (50), (53), (55), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (56), (57), (58), (59), (60), (61), (62), (64), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (65), (69), (71), (72), (74), (75), (76), (77), % 189.41/30.29 | | | | | | | | | | | | | | | | | | (78), (84), (85), (111), (121), (294), (298) are % 189.41/30.29 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #145. % 189.41/30.29 | | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | (299) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 % 189.41/30.29 | | | | | | | | | | | | | | = e4 & op(e2, e0) = e4) % 189.41/30.29 | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | BETA: splitting (299) gives: % 189.41/30.29 | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | (300) all_252_11 = e4 & op(e2, e1) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | ALPHA: (300) implies: % 189.41/30.29 | | | | | | | | | | | | | | | (301) all_252_11 = e4 % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | COMBINE_EQS: (15), (301) imply: % 189.41/30.29 | | | | | | | | | | | | | | | (302) e4 = e2 % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | REDUCE: (61), (302) imply: % 189.41/30.29 | | | | | | | | | | | | | | | (303) $false % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent. % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | (304) all_252_18 = e4 & op(e2, e0) = e4 % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | ALPHA: (304) implies: % 189.41/30.29 | | | | | | | | | | | | | | | (305) all_252_18 = e4 % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (12), (16), % 189.41/30.29 | | | | | | | | | | | | | | | (17), (19), (20), (22), (23), (24), (25), (26), % 189.41/30.29 | | | | | | | | | | | | | | | (27), (28), (31), (32), (33), (34), (36), (37), % 189.41/30.29 | | | | | | | | | | | | | | | (39), (40), (41), (42), (43), (44), (46), (47), % 189.41/30.29 | | | | | | | | | | | | | | | (48), (50), (53), (55), (56), (57), (58), (59), % 189.41/30.29 | | | | | | | | | | | | | | | (61), (62), (64), (65), (71), (72), (74), (75), % 189.41/30.29 | | | | | | | | | | | | | | | (78), (84), (85), (305) are inconsistent by % 189.41/30.29 | | | | | | | | | | | | | | | sub-proof #158. % 189.41/30.29 | | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | (306) all_250_23 = e0 % 189.41/30.29 | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | | REF_CLOSE: (40), (71), (306) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | | | | | #486. % 189.41/30.29 | | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | | % 189.41/30.29 | | | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | (307) all_252_23 = e3 & op(e0, e1) = e3 % 189.41/30.29 | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | ALPHA: (307) implies: % 189.41/30.29 | | | | | | | | | | (308) op(e0, e1) = e3 % 189.41/30.29 | | | | | | | | | | % 189.41/30.29 | | | | | | | | | | REF_CLOSE: (5), (31), (34), (308) are inconsistent by % 189.41/30.29 | | | | | | | | | | sub-proof #508. % 189.41/30.29 | | | | | | | | | | % 189.41/30.29 | | | | | | | | | End of split % 189.41/30.29 | | | | | | | | | % 189.41/30.29 | | | | | | | | End of split % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | End of split % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | Case 2: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | (309) all_252_3 = e2 & op(e3, e3) = e2 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | ALPHA: (309) implies: % 189.41/30.29 | | | | | | | (310) all_252_3 = e2 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | REF_CLOSE: (11), (20), (23), (35), (42), (47), (55), (61), (65), % 189.41/30.29 | | | | | | | (66), (72), (80), (83), (84), (95), (310) are % 189.41/30.29 | | | | | | | inconsistent by sub-proof #127. % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | End of split % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | Case 2: % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | (311) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 189.41/30.29 | | | | | | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | BETA: splitting (311) gives: % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | Case 1: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | (312) all_252_7 = e2 & op(e2, e3) = e2 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | ALPHA: (312) implies: % 189.41/30.29 | | | | | | | (313) all_252_7 = e2 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | COMBINE_EQS: (18), (313) imply: % 189.41/30.29 | | | | | | | (314) e2 = e0 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | SIMP: (314) implies: % 189.41/30.29 | | | | | | | (315) e2 = e0 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | COMBINE_EQS: (15), (315) imply: % 189.41/30.29 | | | | | | | (316) all_252_11 = e0 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (16), (20), (23), (24), % 189.41/30.29 | | | | | | | (27), (28), (31), (32), (33), (34), (37), (40), (43), % 189.41/30.29 | | | | | | | (44), (47), (48), (53), (55), (57), (58), (61), (71), % 189.41/30.29 | | | | | | | (74), (91), (316) are inconsistent by sub-proof #126. % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | Case 2: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | (317) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 189.41/30.29 | | | | | | | op(e0, e3) = e2) % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | BETA: splitting (317) gives: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | (318) all_252_13 = e2 & op(e1, e3) = e2 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | ALPHA: (318) implies: % 189.41/30.29 | | | | | | | | (319) all_252_13 = e2 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (12), (13), (14), % 189.41/30.29 | | | | | | | | (15), (16), (17), (20), (23), (24), (26), (27), (28), % 189.41/30.29 | | | | | | | | (31), (32), (33), (34), (37), (40), (43), (44), (46), % 189.41/30.29 | | | | | | | | (47), (48), (53), (55), (57), (58), (61), (62), (64), % 189.41/30.29 | | | | | | | | (71), (74), (75), (85), (91), (95), (319) are % 189.41/30.29 | | | | | | | | inconsistent by sub-proof #117. % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | (320) all_252_21 = e2 & op(e0, e3) = e2 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | REF_CLOSE: (5), (38), (58), (320) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | #289. % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | End of split % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | End of split % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | End of split % 189.41/30.29 | | | | | % 189.41/30.29 | | | | End of split % 189.41/30.29 | | | | % 189.41/30.29 | | | Case 2: % 189.41/30.29 | | | | % 189.41/30.29 | | | | (321) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, % 189.41/30.29 | | | | e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.29 | | | | % 189.41/30.29 | | | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (12), (15), (16), (20), (23), % 189.41/30.29 | | | | (24), (26), (27), (28), (31), (32), (33), (34), (36), (37), % 189.41/30.29 | | | | (40), (41), (43), (44), (46), (47), (48), (50), (53), (55), % 189.41/30.29 | | | | (57), (58), (61), (62), (64), (71), (74), (75), (78), (85), % 189.41/30.29 | | | | (91), (321) are inconsistent by sub-proof #116. % 189.41/30.29 | | | | % 189.41/30.29 | | | End of split % 189.41/30.29 | | | % 189.41/30.29 | | End of split % 189.41/30.29 | | % 189.41/30.29 | End of split % 189.41/30.29 | % 189.41/30.29 End of proof % 189.41/30.29 % 189.41/30.29 Sub-proof #116 shows that the following formulas are inconsistent: % 189.41/30.29 ---------------------------------------------------------------- % 189.41/30.29 (1) all_252_20 = e2 % 189.41/30.29 (2) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.41/30.29 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.29 (4) ~ (all_20_2 = e4) % 189.41/30.29 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.29 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.29 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.29 (6) op(e0, e2) = e4 % 189.41/30.29 (7) op(e3, e1) = all_36_2 % 189.41/30.29 (8) all_252_12 = e0 % 189.41/30.29 (9) all_252_11 = e2 % 189.41/30.29 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.29 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.29 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.29 (11) ~ (e4 = e0) % 189.41/30.29 (12) ~ (e4 = e3) % 189.41/30.29 (13) ~ (all_36_2 = e2) % 189.41/30.29 (14) ~ (all_40_2 = all_34_2) % 189.41/30.29 (15) ~ (all_244_24 = all_20_2) % 189.41/30.29 (16) op(e1, e4) = e0 % 189.41/30.29 (17) ~ (all_20_2 = e3) % 189.41/30.29 (18) op(all_20_2, e4) = e1 % 189.41/30.29 (19) op(e0, e0) = all_244_24 % 189.41/30.29 (20) op(e0, e1) = all_20_2 % 189.41/30.29 (21) all_252_19 = e4 % 189.41/30.29 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.29 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.29 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.29 (23) ~ (all_20_2 = e0) % 189.41/30.29 (24) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.41/30.29 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.41/30.29 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.41/30.29 (25) ~ (all_20_2 = e2) % 189.41/30.29 (26) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.29 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.29 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.29 (27) op(e0, e4) = e2 % 189.41/30.29 (28) ~ (e3 = e0) % 189.41/30.29 (29) ~ (all_20_2 = all_8_1) % 189.41/30.29 (30) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.41/30.29 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.41/30.29 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.41/30.29 (31) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.29 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.29 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.29 (32) ~ (e3 = e2) % 189.41/30.29 (33) op(e4, all_20_2) = e0 % 189.41/30.29 (34) op(e0, e3) = all_8_1 % 189.41/30.29 (35) ~ (e4 = e2) % 189.41/30.29 (36) op(e2, e0) = all_40_2 % 189.41/30.29 (37) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.29 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.41/30.29 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.29 (38) all_250_23 = all_20_2 % 189.41/30.29 (39) ~ (e2 = e0) % 189.41/30.29 (40) op(e1, e0) = all_34_2 % 189.41/30.29 (41) ~ (all_34_2 = e2) % 189.41/30.29 (42) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.29 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.29 (43) op(e2, e0) = e1 % 189.41/30.29 % 189.41/30.29 Begin of proof % 189.41/30.29 | % 189.41/30.29 | BETA: splitting (42) gives: % 189.41/30.29 | % 189.41/30.29 | Case 1: % 189.41/30.29 | | % 189.41/30.29 | | (44) all_252_11 = e4 & op(e2, e1) = e4 % 189.41/30.29 | | % 189.41/30.29 | | REF_CLOSE: (9), (35), (44) are inconsistent by sub-proof #261. % 189.41/30.29 | | % 189.41/30.29 | Case 2: % 189.41/30.29 | | % 189.41/30.29 | | (45) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, e1) % 189.41/30.29 | | = e4) % 189.41/30.29 | | % 189.41/30.29 | | BETA: splitting (45) gives: % 189.41/30.29 | | % 189.41/30.29 | | Case 1: % 189.41/30.29 | | | % 189.41/30.29 | | | (46) all_252_15 = e4 & op(e1, e1) = e4 % 189.41/30.29 | | | % 189.41/30.29 | | | ALPHA: (46) implies: % 189.41/30.29 | | | (47) all_252_15 = e4 % 189.41/30.29 | | | % 189.41/30.29 | | | BETA: splitting (2) gives: % 189.41/30.29 | | | % 189.41/30.29 | | | Case 1: % 189.41/30.29 | | | | % 189.41/30.29 | | | | (48) all_250_23 = e2 % 189.41/30.29 | | | | % 189.41/30.29 | | | | REF_CLOSE: (25), (38), (48) are inconsistent by sub-proof #487. % 189.41/30.29 | | | | % 189.41/30.29 | | | Case 2: % 189.41/30.29 | | | | % 189.41/30.29 | | | | (49) ~ (all_250_23 = e2) % 189.41/30.29 | | | | (50) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.29 | | | | % 189.41/30.29 | | | | BETA: splitting (50) gives: % 189.41/30.29 | | | | % 189.41/30.29 | | | | Case 1: % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | (51) all_250_23 = e1 % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | COMBINE_EQS: (38), (51) imply: % 189.41/30.29 | | | | | (52) all_20_2 = e1 % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | SIMP: (52) implies: % 189.41/30.29 | | | | | (53) all_20_2 = e1 % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (15), (53) imply: % 189.41/30.29 | | | | | (54) ~ (all_244_24 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (29), (53) imply: % 189.41/30.29 | | | | | (55) ~ (all_8_1 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | SIMP: (55) implies: % 189.41/30.29 | | | | | (56) ~ (all_8_1 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (4), (53) imply: % 189.41/30.29 | | | | | (57) ~ (e4 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | SIMP: (57) implies: % 189.41/30.29 | | | | | (58) ~ (e4 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (17), (53) imply: % 189.41/30.29 | | | | | (59) ~ (e3 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | SIMP: (59) implies: % 189.41/30.29 | | | | | (60) ~ (e3 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (25), (53) imply: % 189.41/30.29 | | | | | (61) ~ (e2 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | SIMP: (61) implies: % 189.41/30.29 | | | | | (62) ~ (e2 = e1) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (23), (53) imply: % 189.41/30.29 | | | | | (63) ~ (e1 = e0) % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (18), (53) imply: % 189.41/30.29 | | | | | (64) op(e1, e4) = e1 % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REDUCE: (33), (53) imply: % 189.41/30.29 | | | | | (65) op(e4, e1) = e0 % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | BETA: splitting (22) gives: % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | Case 1: % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | (66) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & % 189.41/30.29 | | | | | | op(e0, e3) = e1) % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | REF_CLOSE: (3), (27), (34), (56), (62), (66) are inconsistent by % 189.41/30.29 | | | | | | sub-proof #244. % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | Case 2: % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | (67) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & % 189.41/30.29 | | | | | | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | BETA: splitting (67) gives: % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | | Case 1: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | (68) all_252_22 = e1 & op(e0, e2) = e1 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | ALPHA: (68) implies: % 189.41/30.29 | | | | | | | (69) op(e0, e2) = e1 % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | REF_CLOSE: (3), (6), (58), (69) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | #256. % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | Case 2: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | (70) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 189.41/30.29 | | | | | | | op(e0, e0) = e1) % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | BETA: splitting (70) gives: % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | | Case 1: % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | (71) all_252_23 = e1 & op(e0, e1) = e1 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | ALPHA: (71) implies: % 189.41/30.29 | | | | | | | | (72) all_252_23 = e1 % 189.41/30.29 | | | | | | | | (73) op(e0, e1) = e1 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 189.41/30.29 | | | | | | | | (12), (13), (14), (15), (16), (17), (19), (20), (21), % 189.41/30.29 | | | | | | | | (22), (23), (24), (25), (26), (28), (29), (30), (31), % 189.41/30.29 | | | | | | | | (32), (34), (35), (36), (37), (38), (39), (40), (41), % 189.41/30.29 | | | | | | | | (43), (47), (50), (58), (60), (62), (63), (64), (65), % 189.41/30.29 | | | | | | | | (72), (73) are inconsistent by sub-proof #173. % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | Case 2: % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | (74) all_252_24 = e1 & op(e0, e0) = e1 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | ALPHA: (74) implies: % 189.41/30.29 | | | | | | | | (75) op(e0, e0) = e1 % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | | REF_CLOSE: (3), (19), (54), (75) are inconsistent by sub-proof % 189.41/30.29 | | | | | | | | #474. % 189.41/30.29 | | | | | | | | % 189.41/30.29 | | | | | | | End of split % 189.41/30.29 | | | | | | | % 189.41/30.29 | | | | | | End of split % 189.41/30.29 | | | | | | % 189.41/30.29 | | | | | End of split % 189.41/30.29 | | | | | % 189.41/30.29 | | | | Case 2: % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | (76) all_250_23 = e0 % 189.41/30.29 | | | | | % 189.41/30.29 | | | | | REF_CLOSE: (23), (38), (76) are inconsistent by sub-proof #486. % 189.41/30.29 | | | | | % 189.41/30.29 | | | | End of split % 189.41/30.29 | | | | % 189.41/30.29 | | | End of split % 189.41/30.29 | | | % 189.41/30.29 | | Case 2: % 189.41/30.29 | | | % 189.41/30.29 | | | (77) all_252_23 = e4 & op(e0, e1) = e4 % 189.41/30.29 | | | % 189.41/30.29 | | | REF_CLOSE: (3), (4), (20), (77) are inconsistent by sub-proof #518. % 189.41/30.29 | | | % 189.41/30.29 | | End of split % 189.41/30.29 | | % 189.41/30.29 | End of split % 189.41/30.29 | % 189.41/30.29 End of proof % 189.41/30.29 % 189.41/30.29 Sub-proof #117 shows that the following formulas are inconsistent: % 189.41/30.29 ---------------------------------------------------------------- % 189.41/30.29 (1) all_252_13 = e2 % 189.41/30.29 (2) all_252_20 = e2 % 189.41/30.29 (3) all_252_10 = e4 % 189.41/30.30 (4) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.41/30.30 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.30 (6) ~ (all_20_2 = e4) % 189.41/30.30 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.30 (8) op(e0, e2) = e4 % 189.41/30.30 (9) op(e3, e1) = all_36_2 % 189.41/30.30 (10) all_252_12 = e0 % 189.41/30.30 (11) op(e2, e1) = e2 % 189.41/30.30 (12) op(e4, e1) = e0 % 189.41/30.30 (13) all_252_11 = e2 % 189.41/30.30 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.30 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.30 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.30 (15) op(e2, e1) = e0 % 189.41/30.30 (16) ~ (e4 = e0) % 189.41/30.30 (17) ~ (e4 = e3) % 189.41/30.30 (18) ~ (all_36_2 = e2) % 189.41/30.30 (19) ~ (all_40_2 = all_34_2) % 189.41/30.30 (20) ~ (all_244_24 = all_20_2) % 189.41/30.30 (21) op(e1, e4) = e0 % 189.41/30.30 (22) ~ (all_20_2 = e3) % 189.41/30.30 (23) op(all_20_2, e4) = e1 % 189.41/30.30 (24) op(e0, e0) = all_244_24 % 189.41/30.30 (25) op(e0, e1) = all_20_2 % 189.41/30.30 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.30 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.30 (27) ~ (all_20_2 = e0) % 189.41/30.30 (28) ~ (all_20_2 = e2) % 189.41/30.30 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.30 (30) op(e0, e4) = e2 % 189.41/30.30 (31) ~ (e3 = e0) % 189.41/30.30 (32) ~ (all_20_2 = all_8_1) % 189.41/30.30 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.30 (34) ~ (e3 = e2) % 189.41/30.30 (35) op(e4, all_20_2) = e0 % 189.41/30.30 (36) op(e0, e3) = all_8_1 % 189.41/30.30 (37) ~ (e4 = e2) % 189.41/30.30 (38) op(e2, e0) = all_40_2 % 189.41/30.30 (39) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.30 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.41/30.30 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.30 (40) all_250_23 = all_20_2 % 189.41/30.30 (41) ~ (e2 = e0) % 189.41/30.30 (42) op(e1, e0) = all_34_2 % 189.41/30.30 (43) op(e2, e0) = e1 % 189.41/30.30 % 189.41/30.30 Begin of proof % 189.41/30.30 | % 189.41/30.30 | BETA: splitting (14) gives: % 189.41/30.30 | % 189.41/30.30 | Case 1: % 189.41/30.30 | | % 189.41/30.30 | | (44) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.41/30.30 | | e3) % 189.41/30.30 | | % 189.41/30.30 | | BETA: splitting (44) gives: % 189.41/30.30 | | % 189.41/30.30 | | Case 1: % 189.41/30.30 | | | % 189.41/30.30 | | | (45) all_252_9 = e3 & op(e4, e1) = e3 % 189.41/30.30 | | | % 189.41/30.30 | | | REF_CLOSE: (5), (12), (31), (45) are inconsistent by sub-proof #275. % 189.41/30.30 | | | % 189.41/30.30 | | Case 2: % 189.41/30.30 | | | % 189.41/30.30 | | | (46) all_252_10 = e3 & op(e3, e1) = e3 % 189.41/30.30 | | | % 189.41/30.30 | | | REF_CLOSE: (3), (17), (46) are inconsistent by sub-proof #274. % 189.41/30.30 | | | % 189.41/30.30 | | End of split % 189.41/30.30 | | % 189.41/30.30 | Case 2: % 189.41/30.30 | | % 189.41/30.30 | | (47) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) % 189.41/30.30 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.30 | | % 189.41/30.30 | | BETA: splitting (47) gives: % 189.41/30.30 | | % 189.41/30.30 | | Case 1: % 189.41/30.30 | | | % 189.41/30.30 | | | (48) all_252_11 = e3 & op(e2, e1) = e3 % 189.41/30.30 | | | % 189.41/30.30 | | | REF_CLOSE: (13), (34), (48) are inconsistent by sub-proof #356. % 189.41/30.30 | | | % 189.41/30.30 | | Case 2: % 189.41/30.30 | | | % 189.41/30.30 | | | (49) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, % 189.41/30.30 | | | e1) = e3) % 189.41/30.30 | | | % 189.41/30.30 | | | BETA: splitting (49) gives: % 189.41/30.30 | | | % 189.41/30.30 | | | Case 1: % 189.41/30.30 | | | | % 189.41/30.30 | | | | (50) all_252_15 = e3 & op(e1, e1) = e3 % 189.41/30.30 | | | | % 189.41/30.30 | | | | ALPHA: (50) implies: % 189.41/30.30 | | | | (51) all_252_15 = e3 % 189.41/30.30 | | | | % 189.41/30.30 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), % 189.41/30.30 | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 189.41/30.30 | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 189.41/30.30 | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 189.41/30.30 | | | | (51) are inconsistent by sub-proof #118. % 189.41/30.30 | | | | % 189.41/30.30 | | | Case 2: % 189.41/30.30 | | | | % 189.41/30.30 | | | | (52) all_252_23 = e3 & op(e0, e1) = e3 % 189.41/30.30 | | | | % 189.41/30.30 | | | | ALPHA: (52) implies: % 189.41/30.30 | | | | (53) op(e0, e1) = e3 % 189.41/30.30 | | | | % 189.41/30.30 | | | | REF_CLOSE: (5), (22), (25), (53) are inconsistent by sub-proof #508. % 189.41/30.30 | | | | % 189.41/30.30 | | | End of split % 189.41/30.30 | | | % 189.41/30.30 | | End of split % 189.41/30.30 | | % 189.41/30.30 | End of split % 189.41/30.30 | % 189.41/30.30 End of proof % 189.41/30.30 % 189.41/30.30 Sub-proof #118 shows that the following formulas are inconsistent: % 189.41/30.30 ---------------------------------------------------------------- % 189.41/30.30 (1) all_252_13 = e2 % 189.41/30.30 (2) all_252_20 = e2 % 189.41/30.30 (3) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.41/30.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.30 (5) ~ (all_20_2 = e4) % 189.41/30.30 (6) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.30 (7) op(e0, e2) = e4 % 189.41/30.30 (8) op(e3, e1) = all_36_2 % 189.41/30.30 (9) all_252_12 = e0 % 189.41/30.30 (10) op(e2, e1) = e2 % 189.41/30.30 (11) all_252_11 = e2 % 189.41/30.30 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.30 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.30 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.30 (13) op(e2, e1) = e0 % 189.41/30.30 (14) all_252_15 = e3 % 189.41/30.30 (15) ~ (e4 = e0) % 189.41/30.30 (16) ~ (e4 = e3) % 189.41/30.30 (17) ~ (all_36_2 = e2) % 189.41/30.30 (18) ~ (all_40_2 = all_34_2) % 189.41/30.30 (19) ~ (all_244_24 = all_20_2) % 189.41/30.30 (20) op(e1, e4) = e0 % 189.41/30.30 (21) ~ (all_20_2 = e3) % 189.41/30.30 (22) op(all_20_2, e4) = e1 % 189.41/30.30 (23) op(e0, e0) = all_244_24 % 189.41/30.30 (24) op(e0, e1) = all_20_2 % 189.41/30.30 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.30 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.30 (26) ~ (all_20_2 = e0) % 189.41/30.30 (27) ~ (all_20_2 = e2) % 189.41/30.30 (28) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.30 (29) op(e0, e4) = e2 % 189.41/30.30 (30) ~ (e3 = e0) % 189.41/30.30 (31) ~ (all_20_2 = all_8_1) % 189.41/30.30 (32) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.30 (33) ~ (e3 = e2) % 189.41/30.30 (34) op(e4, all_20_2) = e0 % 189.41/30.30 (35) op(e0, e3) = all_8_1 % 189.41/30.30 (36) ~ (e4 = e2) % 189.41/30.30 (37) op(e2, e0) = all_40_2 % 189.41/30.30 (38) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.30 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.41/30.30 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.30 (39) all_250_23 = all_20_2 % 189.41/30.30 (40) ~ (e2 = e0) % 189.41/30.30 (41) op(e1, e0) = all_34_2 % 189.41/30.30 (42) op(e2, e0) = e1 % 189.41/30.30 % 189.41/30.30 Begin of proof % 189.41/30.30 | % 189.41/30.30 | BETA: splitting (3) gives: % 189.41/30.30 | % 189.41/30.30 | Case 1: % 189.41/30.30 | | % 189.41/30.30 | | (43) all_250_23 = e2 % 189.41/30.30 | | % 189.41/30.30 | | REF_CLOSE: (27), (39), (43) are inconsistent by sub-proof #487. % 189.41/30.30 | | % 189.41/30.30 | Case 2: % 189.41/30.30 | | % 189.41/30.30 | | (44) ~ (all_250_23 = e2) % 189.41/30.30 | | (45) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.30 | | % 189.41/30.30 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 189.41/30.30 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 189.41/30.30 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 189.41/30.30 | | (36), (37), (38), (39), (40), (41), (42), (45) are inconsistent % 189.41/30.30 | | by sub-proof #119. % 189.41/30.30 | | % 189.41/30.30 | End of split % 189.41/30.30 | % 189.41/30.30 End of proof % 189.41/30.30 % 189.41/30.30 Sub-proof #119 shows that the following formulas are inconsistent: % 189.41/30.30 ---------------------------------------------------------------- % 189.41/30.30 (1) all_252_13 = e2 % 189.41/30.30 (2) all_252_20 = e2 % 189.41/30.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.30 (4) ~ (all_20_2 = e4) % 189.41/30.30 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.30 (6) op(e0, e2) = e4 % 189.41/30.30 (7) op(e3, e1) = all_36_2 % 189.41/30.30 (8) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.30 (9) all_252_12 = e0 % 189.41/30.30 (10) op(e2, e1) = e2 % 189.41/30.30 (11) all_252_11 = e2 % 189.41/30.30 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.30 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.30 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.30 (13) op(e2, e1) = e0 % 189.41/30.30 (14) all_252_15 = e3 % 189.41/30.30 (15) ~ (e4 = e0) % 189.41/30.30 (16) ~ (e4 = e3) % 189.41/30.30 (17) ~ (all_36_2 = e2) % 189.41/30.30 (18) ~ (all_40_2 = all_34_2) % 189.41/30.30 (19) ~ (all_244_24 = all_20_2) % 189.41/30.30 (20) op(e1, e4) = e0 % 189.41/30.30 (21) ~ (all_20_2 = e3) % 189.41/30.30 (22) op(all_20_2, e4) = e1 % 189.41/30.30 (23) op(e0, e0) = all_244_24 % 189.41/30.30 (24) op(e0, e1) = all_20_2 % 189.41/30.30 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.30 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.30 (26) ~ (all_20_2 = e0) % 189.41/30.30 (27) ~ (all_20_2 = e2) % 189.41/30.30 (28) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.30 (29) op(e0, e4) = e2 % 189.41/30.30 (30) ~ (e3 = e0) % 189.41/30.30 (31) ~ (all_20_2 = all_8_1) % 189.41/30.30 (32) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.30 (33) ~ (e3 = e2) % 189.41/30.30 (34) op(e4, all_20_2) = e0 % 189.41/30.30 (35) op(e0, e3) = all_8_1 % 189.41/30.30 (36) ~ (e4 = e2) % 189.41/30.30 (37) op(e2, e0) = all_40_2 % 189.41/30.30 (38) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.30 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.41/30.30 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.30 (39) all_250_23 = all_20_2 % 189.41/30.30 (40) ~ (e2 = e0) % 189.41/30.30 (41) op(e1, e0) = all_34_2 % 189.41/30.30 (42) op(e2, e0) = e1 % 189.41/30.30 % 189.41/30.30 Begin of proof % 189.41/30.30 | % 189.41/30.30 | BETA: splitting (8) gives: % 189.41/30.30 | % 189.41/30.30 | Case 1: % 189.41/30.30 | | % 189.41/30.30 | | (43) all_250_23 = e1 % 189.41/30.30 | | % 189.41/30.30 | | COMBINE_EQS: (39), (43) imply: % 189.41/30.30 | | (44) all_20_2 = e1 % 189.41/30.30 | | % 189.41/30.30 | | SIMP: (44) implies: % 189.41/30.30 | | (45) all_20_2 = e1 % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (19), (45) imply: % 189.41/30.30 | | (46) ~ (all_244_24 = e1) % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (31), (45) imply: % 189.41/30.30 | | (47) ~ (all_8_1 = e1) % 189.41/30.30 | | % 189.41/30.30 | | SIMP: (47) implies: % 189.41/30.30 | | (48) ~ (all_8_1 = e1) % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (4), (45) imply: % 189.41/30.30 | | (49) ~ (e4 = e1) % 189.41/30.30 | | % 189.41/30.30 | | SIMP: (49) implies: % 189.41/30.30 | | (50) ~ (e4 = e1) % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (21), (45) imply: % 189.41/30.30 | | (51) ~ (e3 = e1) % 189.41/30.30 | | % 189.41/30.30 | | SIMP: (51) implies: % 189.41/30.30 | | (52) ~ (e3 = e1) % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (27), (45) imply: % 189.41/30.30 | | (53) ~ (e2 = e1) % 189.41/30.30 | | % 189.41/30.30 | | SIMP: (53) implies: % 189.41/30.30 | | (54) ~ (e2 = e1) % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (26), (45) imply: % 189.41/30.30 | | (55) ~ (e1 = e0) % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (22), (45) imply: % 189.41/30.30 | | (56) op(e1, e4) = e1 % 189.41/30.30 | | % 189.41/30.30 | | REDUCE: (34), (45) imply: % 189.41/30.30 | | (57) op(e4, e1) = e0 % 189.41/30.30 | | % 189.41/30.30 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.41/30.30 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24), % 189.41/30.30 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (35), (36), % 189.41/30.30 | | (37), (38), (39), (40), (41), (42), (46), (48), (50), (52), (54), % 189.41/30.30 | | (55), (56), (57) are inconsistent by sub-proof #120. % 189.41/30.30 | | % 189.41/30.30 | Case 2: % 189.41/30.30 | | % 189.41/30.30 | | (58) all_250_23 = e0 % 189.41/30.30 | | % 189.41/30.30 | | REF_CLOSE: (26), (39), (58) are inconsistent by sub-proof #486. % 189.41/30.30 | | % 189.41/30.30 | End of split % 189.41/30.30 | % 189.41/30.30 End of proof % 189.41/30.30 % 189.41/30.30 Sub-proof #120 shows that the following formulas are inconsistent: % 189.41/30.30 ---------------------------------------------------------------- % 189.41/30.30 (1) all_252_13 = e2 % 189.41/30.30 (2) all_252_20 = e2 % 189.41/30.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.30 (4) ~ (all_20_2 = e4) % 189.41/30.30 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.30 (6) op(e0, e2) = e4 % 189.41/30.30 (7) op(e3, e1) = all_36_2 % 189.41/30.30 (8) ~ (e2 = e1) % 189.41/30.30 (9) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.30 (10) all_252_12 = e0 % 189.41/30.30 (11) op(e2, e1) = e2 % 189.41/30.30 (12) op(e4, e1) = e0 % 189.41/30.30 (13) all_252_11 = e2 % 189.41/30.30 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.30 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.30 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.30 (15) op(e2, e1) = e0 % 189.41/30.30 (16) all_252_15 = e3 % 189.41/30.30 (17) ~ (e4 = e0) % 189.41/30.30 (18) ~ (e4 = e3) % 189.41/30.30 (19) ~ (all_36_2 = e2) % 189.41/30.30 (20) ~ (all_40_2 = all_34_2) % 189.41/30.30 (21) ~ (all_244_24 = all_20_2) % 189.41/30.30 (22) op(e1, e4) = e0 % 189.41/30.30 (23) ~ (all_20_2 = e3) % 189.41/30.30 (24) op(e0, e0) = all_244_24 % 189.41/30.30 (25) op(e0, e1) = all_20_2 % 189.41/30.30 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.30 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.30 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.30 (27) ~ (all_20_2 = e0) % 189.41/30.30 (28) ~ (all_20_2 = e2) % 189.41/30.30 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.30 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.30 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.30 (30) op(e0, e4) = e2 % 189.41/30.30 (31) ~ (e3 = e0) % 189.41/30.30 (32) ~ (all_20_2 = all_8_1) % 189.41/30.30 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.30 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.30 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.30 (34) ~ (e3 = e2) % 189.41/30.30 (35) op(e0, e3) = all_8_1 % 189.41/30.30 (36) op(e1, e4) = e1 % 189.41/30.30 (37) ~ (e4 = e2) % 189.41/30.30 (38) op(e2, e0) = all_40_2 % 189.41/30.30 (39) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.30 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.41/30.30 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.30 (40) ~ (e1 = e0) % 189.41/30.30 (41) all_250_23 = all_20_2 % 189.41/30.30 (42) ~ (e3 = e1) % 189.41/30.30 (43) ~ (e2 = e0) % 189.41/30.30 (44) op(e1, e0) = all_34_2 % 189.41/30.30 (45) ~ (all_244_24 = e1) % 189.41/30.30 (46) ~ (all_8_1 = e1) % 189.41/30.30 (47) ~ (e4 = e1) % 189.41/30.30 (48) op(e2, e0) = e1 % 189.41/30.30 % 189.41/30.30 Begin of proof % 189.41/30.30 | % 189.41/30.30 | BETA: splitting (26) gives: % 189.41/30.30 | % 189.41/30.30 | Case 1: % 189.41/30.30 | | % 189.41/30.30 | | (49) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.41/30.30 | | = e1) % 189.41/30.30 | | % 189.41/30.30 | | REF_CLOSE: (3), (8), (30), (35), (46), (49) are inconsistent by sub-proof % 189.41/30.30 | | #244. % 189.41/30.30 | | % 189.41/30.30 | Case 2: % 189.41/30.30 | | % 189.41/30.30 | | (50) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.41/30.30 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.30 | | % 189.41/30.30 | | BETA: splitting (50) gives: % 189.41/30.30 | | % 189.41/30.30 | | Case 1: % 189.41/30.30 | | | % 189.41/30.30 | | | (51) all_252_22 = e1 & op(e0, e2) = e1 % 189.41/30.30 | | | % 189.41/30.30 | | | ALPHA: (51) implies: % 189.41/30.30 | | | (52) op(e0, e2) = e1 % 189.41/30.30 | | | % 189.41/30.30 | | | REF_CLOSE: (3), (6), (47), (52) are inconsistent by sub-proof #256. % 189.41/30.30 | | | % 189.41/30.30 | | Case 2: % 189.41/30.30 | | | % 189.41/30.30 | | | (53) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.41/30.30 | | | e0) = e1) % 189.41/30.30 | | | % 189.41/30.30 | | | BETA: splitting (53) gives: % 189.41/30.30 | | | % 189.41/30.30 | | | Case 1: % 189.41/30.30 | | | | % 189.41/30.30 | | | | (54) all_252_23 = e1 & op(e0, e1) = e1 % 189.41/30.30 | | | | % 189.41/30.30 | | | | ALPHA: (54) implies: % 189.41/30.30 | | | | (55) all_252_23 = e1 % 189.41/30.30 | | | | (56) op(e0, e1) = e1 % 189.41/30.30 | | | | % 189.41/30.30 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 189.41/30.30 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 189.41/30.30 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (31), (32), % 189.41/30.30 | | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42), % 189.41/30.30 | | | | (43), (44), (47), (48), (55), (56) are inconsistent by % 189.41/30.30 | | | | sub-proof #121. % 189.41/30.30 | | | | % 189.41/30.30 | | | Case 2: % 189.41/30.30 | | | | % 189.41/30.30 | | | | (57) all_252_24 = e1 & op(e0, e0) = e1 % 189.41/30.30 | | | | % 189.41/30.30 | | | | ALPHA: (57) implies: % 189.41/30.30 | | | | (58) op(e0, e0) = e1 % 189.41/30.30 | | | | % 189.41/30.30 | | | | REF_CLOSE: (3), (24), (45), (58) are inconsistent by sub-proof #474. % 189.41/30.30 | | | | % 189.41/30.30 | | | End of split % 189.41/30.30 | | | % 189.41/30.30 | | End of split % 189.41/30.30 | | % 189.41/30.30 | End of split % 189.41/30.30 | % 189.41/30.30 End of proof % 189.41/30.30 % 189.41/30.30 Sub-proof #121 shows that the following formulas are inconsistent: % 189.41/30.30 ---------------------------------------------------------------- % 189.41/30.30 (1) all_252_13 = e2 % 189.41/30.30 (2) all_252_20 = e2 % 189.41/30.30 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.30 (4) ~ (all_20_2 = e4) % 189.41/30.30 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.30 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.30 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.30 (6) op(e0, e2) = e4 % 189.41/30.30 (7) op(e3, e1) = all_36_2 % 189.41/30.30 (8) ~ (e2 = e1) % 189.41/30.30 (9) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.30 (10) all_252_12 = e0 % 189.41/30.30 (11) op(e2, e1) = e2 % 189.41/30.30 (12) op(e4, e1) = e0 % 189.41/30.30 (13) all_252_11 = e2 % 189.41/30.31 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.31 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.31 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.31 (15) op(e2, e1) = e0 % 189.41/30.31 (16) all_252_15 = e3 % 189.41/30.31 (17) ~ (e4 = e0) % 189.41/30.31 (18) ~ (e4 = e3) % 189.41/30.31 (19) ~ (all_36_2 = e2) % 189.41/30.31 (20) ~ (all_40_2 = all_34_2) % 189.41/30.31 (21) ~ (all_244_24 = all_20_2) % 189.41/30.31 (22) op(e1, e4) = e0 % 189.41/30.31 (23) all_252_23 = e1 % 189.41/30.31 (24) ~ (all_20_2 = e3) % 189.41/30.31 (25) op(e0, e0) = all_244_24 % 189.41/30.31 (26) op(e0, e1) = all_20_2 % 189.41/30.31 (27) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.31 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.31 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.31 (28) ~ (all_20_2 = e0) % 189.41/30.31 (29) ~ (all_20_2 = e2) % 189.41/30.31 (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.31 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.31 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.31 (31) ~ (e3 = e0) % 189.41/30.31 (32) ~ (all_20_2 = all_8_1) % 189.41/30.31 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.31 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.31 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.31 (34) ~ (e3 = e2) % 189.41/30.31 (35) op(e0, e3) = all_8_1 % 189.41/30.31 (36) op(e1, e4) = e1 % 189.41/30.31 (37) ~ (e4 = e2) % 189.41/30.31 (38) op(e2, e0) = all_40_2 % 189.41/30.31 (39) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.31 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.41/30.31 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.31 (40) ~ (e1 = e0) % 189.41/30.31 (41) all_250_23 = all_20_2 % 189.41/30.31 (42) ~ (e3 = e1) % 189.41/30.31 (43) ~ (e2 = e0) % 189.41/30.31 (44) op(e0, e1) = e1 % 189.41/30.31 (45) op(e1, e0) = all_34_2 % 189.41/30.31 (46) ~ (e4 = e1) % 189.41/30.31 (47) op(e2, e0) = e1 % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (39) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (48) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 189.41/30.31 | | = e1) % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (21), (23), (25), (27), % 189.41/30.31 | | (28), (29), (32), (35), (41), (48) are inconsistent by sub-proof % 189.41/30.31 | | #124. % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (49) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) % 189.41/30.31 | | = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.31 | | % 189.41/30.31 | | BETA: splitting (49) gives: % 189.41/30.31 | | % 189.41/30.31 | | Case 1: % 189.41/30.31 | | | % 189.41/30.31 | | | % 189.41/30.31 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14), % 189.41/30.31 | | | (15), (17), (18), (19), (21), (22), (24), (25), (26), (27), % 189.41/30.31 | | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 189.41/30.31 | | | (40), (41), (42), (43), (44), (46) are inconsistent by % 189.41/30.31 | | | sub-proof #144. % 189.41/30.31 | | | % 189.41/30.31 | | Case 2: % 189.41/30.31 | | | % 189.41/30.31 | | | (50) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 189.41/30.31 | | | e0) = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | REF_CLOSE: (3), (16), (20), (38), (42), (45), (47), (50) are inconsistent % 189.41/30.31 | | | by sub-proof #122. % 189.41/30.31 | | | % 189.41/30.31 | | End of split % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #122 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.31 (2) all_252_15 = e3 % 189.41/30.31 (3) ~ (all_40_2 = all_34_2) % 189.41/30.31 (4) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.41/30.31 (5) op(e2, e0) = all_40_2 % 189.41/30.31 (6) ~ (e3 = e1) % 189.41/30.31 (7) op(e1, e0) = all_34_2 % 189.41/30.31 (8) op(e2, e0) = e1 % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (4) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (9) all_252_15 = e1 & op(e1, e1) = e1 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #123. % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (10) all_252_19 = e1 & op(e1, e0) = e1 % 189.41/30.31 | | % 189.41/30.31 | | ALPHA: (10) implies: % 189.41/30.31 | | (11) op(e1, e0) = e1 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (1), (3), (5), (7), (8), (11) are inconsistent by sub-proof #352. % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #123 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) all_252_15 = e1 & op(e1, e1) = e1 % 189.41/30.31 (2) all_252_15 = e3 % 189.41/30.31 (3) ~ (e3 = e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | ALPHA: (1) implies: % 189.41/30.31 | (4) all_252_15 = e1 % 189.41/30.31 | % 189.41/30.31 | COMBINE_EQS: (2), (4) imply: % 189.41/30.31 | (5) e3 = e1 % 189.41/30.31 | % 189.41/30.31 | REDUCE: (3), (5) imply: % 189.41/30.31 | (6) $false % 189.41/30.31 | % 189.41/30.31 | CLOSE: (6) is inconsistent. % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #124 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) all_252_13 = e2 % 189.41/30.31 (2) all_252_20 = e2 % 189.41/30.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.31 (4) ~ (all_20_2 = e4) % 189.41/30.31 (5) op(e0, e2) = e4 % 189.41/30.31 (6) ~ (e2 = e1) % 189.41/30.31 (7) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.31 (8) all_252_12 = e0 % 189.41/30.31 (9) ~ (all_244_24 = all_20_2) % 189.41/30.31 (10) all_252_23 = e1 % 189.41/30.31 (11) op(e0, e0) = all_244_24 % 189.41/30.31 (12) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.31 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.31 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.31 (13) ~ (all_20_2 = e0) % 189.41/30.31 (14) ~ (all_20_2 = e2) % 189.41/30.31 (15) ~ (all_20_2 = all_8_1) % 189.41/30.31 (16) op(e0, e3) = all_8_1 % 189.41/30.31 (17) all_250_23 = all_20_2 % 189.41/30.31 (18) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.41/30.31 e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (18) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (19) all_252_12 = e1 & op(e1, e4) = e1 % 189.41/30.31 | | % 189.41/30.31 | | ALPHA: (19) implies: % 189.41/30.31 | | (20) all_252_12 = e1 % 189.41/30.31 | | % 189.41/30.31 | | COMBINE_EQS: (8), (20) imply: % 189.41/30.31 | | (21) e1 = e0 % 189.41/30.31 | | % 189.41/30.31 | | COMBINE_EQS: (10), (21) imply: % 189.41/30.31 | | (22) all_252_23 = e0 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (11), (12), (13), (14), (15), (16), % 189.41/30.31 | | (17), (22) are inconsistent by sub-proof #192. % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (23) all_252_13 = e1 & op(e1, e3) = e1 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (1), (6), (23) are inconsistent by sub-proof #125. % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #125 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) all_252_13 = e1 & op(e1, e3) = e1 % 189.41/30.31 (2) all_252_13 = e2 % 189.41/30.31 (3) ~ (e2 = e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | ALPHA: (1) implies: % 189.41/30.31 | (4) all_252_13 = e1 % 189.41/30.31 | % 189.41/30.31 | COMBINE_EQS: (2), (4) imply: % 189.41/30.31 | (5) e2 = e1 % 189.41/30.31 | % 189.41/30.31 | REDUCE: (3), (5) imply: % 189.41/30.31 | (6) $false % 189.41/30.31 | % 189.41/30.31 | CLOSE: (6) is inconsistent. % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #126 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) all_252_20 = e2 % 189.41/30.31 (2) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.41/30.31 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.31 (4) ~ (all_20_2 = e4) % 189.41/30.31 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.31 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.31 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.31 (6) op(e0, e2) = e4 % 189.41/30.31 (7) op(e3, e1) = all_36_2 % 189.41/30.31 (8) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.31 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.31 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.31 (9) ~ (e4 = e0) % 189.41/30.31 (10) ~ (e4 = e3) % 189.41/30.31 (11) ~ (all_36_2 = e2) % 189.41/30.31 (12) ~ (all_244_24 = all_20_2) % 189.41/30.31 (13) op(e1, e4) = e0 % 189.41/30.31 (14) ~ (all_20_2 = e3) % 189.41/30.31 (15) op(all_20_2, e4) = e1 % 189.41/30.31 (16) all_252_11 = e0 % 189.41/30.31 (17) op(e0, e0) = all_244_24 % 189.41/30.31 (18) op(e0, e1) = all_20_2 % 189.41/30.31 (19) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.31 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.31 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.31 (20) ~ (all_20_2 = e0) % 189.41/30.31 (21) ~ (all_20_2 = e2) % 189.41/30.31 (22) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.31 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.31 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.31 (23) ~ (e3 = e0) % 189.41/30.31 (24) ~ (all_20_2 = all_8_1) % 189.41/30.31 (25) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.31 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.31 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.31 (26) ~ (e3 = e2) % 189.41/30.31 (27) op(e4, all_20_2) = e0 % 189.41/30.31 (28) op(e0, e3) = all_8_1 % 189.41/30.31 (29) ~ (e4 = e2) % 189.41/30.31 (30) all_250_23 = all_20_2 % 189.41/30.31 (31) ~ (e2 = e0) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (2) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (32) all_250_23 = e2 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (21), (30), (32) are inconsistent by sub-proof #487. % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (33) ~ (all_250_23 = e2) % 189.41/30.31 | | (34) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.31 | | % 189.41/30.31 | | BETA: splitting (34) gives: % 189.41/30.31 | | % 189.41/30.31 | | Case 1: % 189.41/30.31 | | | % 189.41/30.31 | | | (35) all_250_23 = e1 % 189.41/30.31 | | | % 189.41/30.31 | | | COMBINE_EQS: (30), (35) imply: % 189.41/30.31 | | | (36) all_20_2 = e1 % 189.41/30.31 | | | % 189.41/30.31 | | | SIMP: (36) implies: % 189.41/30.31 | | | (37) all_20_2 = e1 % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (4), (37) imply: % 189.41/30.31 | | | (38) ~ (e4 = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | SIMP: (38) implies: % 189.41/30.31 | | | (39) ~ (e4 = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (14), (37) imply: % 189.41/30.31 | | | (40) ~ (e3 = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | SIMP: (40) implies: % 189.41/30.31 | | | (41) ~ (e3 = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (21), (37) imply: % 189.41/30.31 | | | (42) ~ (e2 = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | SIMP: (42) implies: % 189.41/30.31 | | | (43) ~ (e2 = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (20), (37) imply: % 189.41/30.31 | | | (44) ~ (e1 = e0) % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (15), (37) imply: % 189.41/30.31 | | | (45) op(e1, e4) = e1 % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (27), (37) imply: % 189.41/30.31 | | | (46) op(e4, e1) = e0 % 189.41/30.31 | | | % 189.41/30.31 | | | REDUCE: (18), (37) imply: % 189.41/30.31 | | | (47) op(e0, e1) = e1 % 189.41/30.31 | | | % 189.41/30.31 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 189.41/30.31 | | | (14), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 189.41/30.31 | | | (25), (26), (28), (29), (30), (31), (34), (39), (41), (43), % 189.41/30.31 | | | (44), (45), (46), (47) are inconsistent by sub-proof #191. % 189.41/30.31 | | | % 189.41/30.31 | | Case 2: % 189.41/30.31 | | | % 189.41/30.31 | | | (48) all_250_23 = e0 % 189.41/30.31 | | | % 189.41/30.31 | | | REF_CLOSE: (20), (30), (48) are inconsistent by sub-proof #486. % 189.41/30.31 | | | % 189.41/30.31 | | End of split % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #127 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) all_252_10 = e4 % 189.41/30.31 (2) ~ (e2 = e1) % 189.41/30.31 (3) ~ (e4 = e0) % 189.41/30.31 (4) ~ (e4 = e3) % 189.41/30.31 (5) all_252_3 = e2 % 189.41/30.31 (6) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.41/30.31 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.31 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.41/30.31 (7) all_252_17 = e2 % 189.41/30.31 (8) ~ (e3 = e0) % 189.41/30.31 (9) ~ (e3 = e2) % 189.41/30.31 (10) ~ (e4 = e2) % 189.41/30.31 (11) ~ (e1 = e0) % 189.41/30.31 (12) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.41/30.31 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.41/30.31 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.41/30.31 (13) ~ (e3 = e1) % 189.41/30.31 (14) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.41/30.31 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.41/30.31 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.41/30.31 (15) all_252_5 = e0 % 189.41/30.31 (16) ~ (e4 = e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (6) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (17) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = % 189.41/30.31 | | e1) % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 189.41/30.31 | | (14), (15), (16), (17) are inconsistent by sub-proof #129. % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (18) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.41/30.31 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.41/30.31 | | % 189.41/30.31 | | BETA: splitting (18) gives: % 189.41/30.31 | | % 189.41/30.31 | | Case 1: % 189.41/30.31 | | | % 189.41/30.31 | | | (19) all_252_5 = e1 & op(e3, e2) = e1 % 189.41/30.31 | | | % 189.41/30.31 | | | REF_CLOSE: (11), (15), (19) are inconsistent by sub-proof #155. % 189.41/30.31 | | | % 189.41/30.31 | | Case 2: % 189.41/30.31 | | | % 189.41/30.31 | | | (20) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, % 189.41/30.31 | | | e0) = e1) % 189.41/30.31 | | | % 189.41/30.31 | | | REF_CLOSE: (1), (2), (7), (16), (20) are inconsistent by sub-proof #128. % 189.41/30.31 | | | % 189.41/30.31 | | End of split % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #128 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) all_252_10 = e4 % 189.41/30.31 (2) ~ (e2 = e1) % 189.41/30.31 (3) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.41/30.31 (4) all_252_17 = e2 % 189.41/30.31 (5) ~ (e4 = e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (3) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (6) all_252_10 = e1 & op(e3, e1) = e1 % 189.41/30.31 | | % 189.41/30.31 | | ALPHA: (6) implies: % 189.41/30.31 | | (7) all_252_10 = e1 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #197. % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (8) all_252_17 = e1 & op(e3, e0) = e1 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #247. % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #129 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) % 189.41/30.31 (2) ~ (e2 = e1) % 189.41/30.31 (3) ~ (e4 = e0) % 189.41/30.31 (4) ~ (e4 = e3) % 189.41/30.31 (5) all_252_3 = e2 % 189.41/30.31 (6) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.41/30.31 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.31 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.41/30.31 (7) all_252_17 = e2 % 189.41/30.31 (8) ~ (e3 = e0) % 189.41/30.31 (9) ~ (e3 = e2) % 189.41/30.31 (10) ~ (e4 = e2) % 189.41/30.31 (11) ~ (e1 = e0) % 189.41/30.31 (12) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.41/30.31 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.41/30.31 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.41/30.31 (13) ~ (e3 = e1) % 189.41/30.31 (14) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.41/30.31 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.41/30.31 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.41/30.31 (15) all_252_5 = e0 % 189.41/30.31 (16) ~ (e4 = e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (1) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (17) all_252_2 = e1 & op(e3, e4) = e1 % 189.41/30.31 | | % 189.41/30.31 | | ALPHA: (17) implies: % 189.41/30.31 | | (18) all_252_2 = e1 % 189.41/30.31 | | % 189.41/30.31 | | BETA: splitting (12) gives: % 189.41/30.31 | | % 189.41/30.31 | | Case 1: % 189.41/30.31 | | | % 189.41/30.31 | | | (19) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) % 189.41/30.31 | | | = e3) % 189.41/30.31 | | | % 189.41/30.31 | | | BETA: splitting (19) gives: % 189.41/30.31 | | | % 189.41/30.31 | | | Case 1: % 189.41/30.31 | | | | % 189.41/30.31 | | | | (20) all_252_2 = e3 & op(e3, e4) = e3 % 189.41/30.31 | | | | % 189.41/30.31 | | | | REF_CLOSE: (13), (18), (20) are inconsistent by sub-proof #151. % 189.41/30.31 | | | | % 189.41/30.31 | | | Case 2: % 189.41/30.31 | | | | % 189.41/30.31 | | | | (21) all_252_3 = e3 & op(e3, e3) = e3 % 189.41/30.31 | | | | % 189.41/30.31 | | | | ALPHA: (21) implies: % 189.41/30.31 | | | | (22) all_252_3 = e3 % 189.41/30.31 | | | | % 189.41/30.31 | | | | COMBINE_EQS: (5), (22) imply: % 189.41/30.31 | | | | (23) e3 = e2 % 189.41/30.31 | | | | % 189.41/30.31 | | | | SIMP: (23) implies: % 189.41/30.31 | | | | (24) e3 = e2 % 189.41/30.31 | | | | % 189.41/30.31 | | | | REDUCE: (9), (24) imply: % 189.41/30.31 | | | | (25) $false % 189.41/30.31 | | | | % 189.41/30.31 | | | | CLOSE: (25) is inconsistent. % 189.41/30.31 | | | | % 189.41/30.31 | | | End of split % 189.41/30.31 | | | % 189.41/30.31 | | Case 2: % 189.41/30.31 | | | % 189.41/30.31 | | | (26) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) % 189.41/30.31 | | | = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.41/30.31 | | | % 189.41/30.31 | | | BETA: splitting (26) gives: % 189.41/30.31 | | | % 189.41/30.31 | | | Case 1: % 189.41/30.31 | | | | % 189.41/30.31 | | | | (27) all_252_5 = e3 & op(e3, e2) = e3 % 189.41/30.31 | | | | % 189.41/30.31 | | | | REF_CLOSE: (8), (15), (27) are inconsistent by sub-proof #134. % 189.41/30.31 | | | | % 189.41/30.31 | | | Case 2: % 189.41/30.31 | | | | % 189.41/30.31 | | | | (28) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, % 189.41/30.31 | | | | e0) = e3) % 189.41/30.31 | | | | % 189.41/30.31 | | | | BETA: splitting (28) gives: % 189.41/30.31 | | | | % 189.41/30.31 | | | | Case 1: % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | (29) all_252_10 = e3 & op(e3, e1) = e3 % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (13), (14), (15), % 189.41/30.31 | | | | | (16), (29) are inconsistent by sub-proof #130. % 189.41/30.31 | | | | | % 189.41/30.31 | | | | Case 2: % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | (30) all_252_17 = e3 & op(e3, e0) = e3 % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | REF_CLOSE: (7), (9), (30) are inconsistent by sub-proof #249. % 189.41/30.31 | | | | | % 189.41/30.31 | | | | End of split % 189.41/30.31 | | | | % 189.41/30.31 | | | End of split % 189.41/30.31 | | | % 189.41/30.31 | | End of split % 189.41/30.31 | | % 189.41/30.31 | Case 2: % 189.41/30.31 | | % 189.41/30.31 | | (31) all_252_3 = e1 & op(e3, e3) = e1 % 189.41/30.31 | | % 189.41/30.31 | | REF_CLOSE: (2), (5), (31) are inconsistent by sub-proof #133. % 189.41/30.31 | | % 189.41/30.31 | End of split % 189.41/30.31 | % 189.41/30.31 End of proof % 189.41/30.31 % 189.41/30.31 Sub-proof #130 shows that the following formulas are inconsistent: % 189.41/30.31 ---------------------------------------------------------------- % 189.41/30.31 (1) ~ (e2 = e1) % 189.41/30.31 (2) all_252_10 = e3 & op(e3, e1) = e3 % 189.41/30.31 (3) ~ (e4 = e0) % 189.41/30.31 (4) ~ (e4 = e3) % 189.41/30.31 (5) all_252_3 = e2 % 189.41/30.31 (6) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 189.41/30.31 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.31 | (all_252_17 = e1 & op(e3, e0) = e1) % 189.41/30.31 (7) all_252_17 = e2 % 189.41/30.31 (8) ~ (e4 = e2) % 189.41/30.31 (9) ~ (e1 = e0) % 189.41/30.31 (10) ~ (e3 = e1) % 189.41/30.31 (11) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 189.41/30.31 | (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.41/30.31 e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.41/30.31 (12) all_252_5 = e0 % 189.41/30.31 (13) ~ (e4 = e1) % 189.41/30.31 % 189.41/30.31 Begin of proof % 189.41/30.31 | % 189.41/30.31 | ALPHA: (2) implies: % 189.41/30.31 | (14) all_252_10 = e3 % 189.41/30.31 | % 189.41/30.31 | BETA: splitting (11) gives: % 189.41/30.31 | % 189.41/30.31 | Case 1: % 189.41/30.31 | | % 189.41/30.31 | | (15) (all_252_2 = e4 & op(e3, e4) = e4) | (all_252_3 = e4 & op(e3, e3) = % 189.41/30.31 | | e4) % 189.41/30.31 | | % 189.41/30.31 | | BETA: splitting (15) gives: % 189.41/30.31 | | % 189.41/30.31 | | Case 1: % 189.41/30.31 | | | % 189.41/30.31 | | | (16) all_252_2 = e4 & op(e3, e4) = e4 % 189.41/30.31 | | | % 189.41/30.31 | | | ALPHA: (16) implies: % 189.41/30.31 | | | (17) all_252_2 = e4 % 189.41/30.31 | | | % 189.41/30.31 | | | BETA: splitting (6) gives: % 189.41/30.31 | | | % 189.41/30.31 | | | Case 1: % 189.41/30.31 | | | | % 189.41/30.31 | | | | (18) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, % 189.41/30.31 | | | | e3) = e1) % 189.41/30.31 | | | | % 189.41/30.31 | | | | BETA: splitting (18) gives: % 189.41/30.31 | | | | % 189.41/30.31 | | | | Case 1: % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | (19) all_252_2 = e1 & op(e3, e4) = e1 % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | ALPHA: (19) implies: % 189.41/30.31 | | | | | (20) all_252_2 = e1 % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | REF_CLOSE: (13), (17), (20) are inconsistent by sub-proof #226. % 189.41/30.31 | | | | | % 189.41/30.31 | | | | Case 2: % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | (21) all_252_3 = e1 & op(e3, e3) = e1 % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | REF_CLOSE: (1), (5), (21) are inconsistent by sub-proof #133. % 189.41/30.31 | | | | | % 189.41/30.31 | | | | End of split % 189.41/30.31 | | | | % 189.41/30.31 | | | Case 2: % 189.41/30.31 | | | | % 189.41/30.31 | | | | (22) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, % 189.41/30.31 | | | | e1) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.41/30.31 | | | | % 189.41/30.31 | | | | BETA: splitting (22) gives: % 189.41/30.31 | | | | % 189.41/30.31 | | | | Case 1: % 189.41/30.31 | | | | | % 189.41/30.31 | | | | | (23) all_252_5 = e1 & op(e3, e2) = e1 % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | ALPHA: (23) implies: % 189.41/30.32 | | | | | (24) all_252_5 = e1 % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | COMBINE_EQS: (12), (24) imply: % 189.41/30.32 | | | | | (25) e1 = e0 % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | REDUCE: (9), (25) imply: % 189.41/30.32 | | | | | (26) $false % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | CLOSE: (26) is inconsistent. % 189.41/30.32 | | | | | % 189.41/30.32 | | | | Case 2: % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | (27) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & % 189.41/30.32 | | | | | op(e3, e0) = e1) % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | BETA: splitting (27) gives: % 189.41/30.32 | | | | | % 189.41/30.32 | | | | | Case 1: % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | | (28) all_252_10 = e1 & op(e3, e1) = e1 % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | | ALPHA: (28) implies: % 189.41/30.32 | | | | | | (29) all_252_10 = e1 % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | | REF_CLOSE: (10), (14), (29) are inconsistent by sub-proof #267. % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | Case 2: % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | | (30) all_252_17 = e1 & op(e3, e0) = e1 % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | | REF_CLOSE: (1), (7), (30) are inconsistent by sub-proof #162. % 189.41/30.32 | | | | | | % 189.41/30.32 | | | | | End of split % 189.41/30.32 | | | | | % 189.41/30.32 | | | | End of split % 189.41/30.32 | | | | % 189.41/30.32 | | | End of split % 189.41/30.32 | | | % 189.41/30.32 | | Case 2: % 189.41/30.32 | | | % 189.41/30.32 | | | (31) all_252_3 = e4 & op(e3, e3) = e4 % 189.41/30.32 | | | % 189.41/30.32 | | | ALPHA: (31) implies: % 189.41/30.32 | | | (32) all_252_3 = e4 % 189.41/30.32 | | | % 189.41/30.32 | | | COMBINE_EQS: (5), (32) imply: % 189.41/30.32 | | | (33) e4 = e2 % 189.41/30.32 | | | % 189.41/30.32 | | | REDUCE: (8), (33) imply: % 189.41/30.32 | | | (34) $false % 189.41/30.32 | | | % 189.41/30.32 | | | CLOSE: (34) is inconsistent. % 189.41/30.32 | | | % 189.41/30.32 | | End of split % 189.41/30.32 | | % 189.41/30.32 | Case 2: % 189.41/30.32 | | % 189.41/30.32 | | (35) (all_252_5 = e4 & op(e3, e2) = e4) | (all_252_10 = e4 & op(e3, e1) = % 189.41/30.32 | | e4) | (all_252_17 = e4 & op(e3, e0) = e4) % 189.41/30.32 | | % 189.41/30.32 | | BETA: splitting (35) gives: % 189.41/30.32 | | % 189.41/30.32 | | Case 1: % 189.41/30.32 | | | % 189.41/30.32 | | | (36) all_252_5 = e4 & op(e3, e2) = e4 % 189.41/30.32 | | | % 189.41/30.32 | | | REF_CLOSE: (3), (12), (36) are inconsistent by sub-proof #132. % 189.41/30.32 | | | % 189.41/30.32 | | Case 2: % 189.41/30.32 | | | % 189.41/30.32 | | | (37) (all_252_10 = e4 & op(e3, e1) = e4) | (all_252_17 = e4 & op(e3, % 189.41/30.32 | | | e0) = e4) % 189.41/30.32 | | | % 189.41/30.32 | | | BETA: splitting (37) gives: % 189.41/30.32 | | | % 189.41/30.32 | | | Case 1: % 189.41/30.32 | | | | % 189.41/30.32 | | | | (38) all_252_10 = e4 & op(e3, e1) = e4 % 189.41/30.32 | | | | % 189.41/30.32 | | | | REF_CLOSE: (4), (14), (38) are inconsistent by sub-proof #195. % 189.41/30.32 | | | | % 189.41/30.32 | | | Case 2: % 189.41/30.32 | | | | % 189.41/30.32 | | | | (39) all_252_17 = e4 & op(e3, e0) = e4 % 189.41/30.32 | | | | % 189.41/30.32 | | | | REF_CLOSE: (7), (8), (39) are inconsistent by sub-proof #131. % 189.41/30.32 | | | | % 189.41/30.32 | | | End of split % 189.41/30.32 | | | % 189.41/30.32 | | End of split % 189.41/30.32 | | % 189.41/30.32 | End of split % 189.41/30.32 | % 189.41/30.32 End of proof % 189.41/30.32 % 189.41/30.32 Sub-proof #131 shows that the following formulas are inconsistent: % 189.41/30.32 ---------------------------------------------------------------- % 189.41/30.32 (1) all_252_17 = e4 & op(e3, e0) = e4 % 189.41/30.32 (2) all_252_17 = e2 % 189.41/30.32 (3) ~ (e4 = e2) % 189.41/30.32 % 189.41/30.32 Begin of proof % 189.41/30.32 | % 189.41/30.32 | ALPHA: (1) implies: % 189.41/30.32 | (4) all_252_17 = e4 % 189.41/30.32 | % 189.41/30.32 | COMBINE_EQS: (2), (4) imply: % 189.41/30.32 | (5) e4 = e2 % 189.41/30.32 | % 189.41/30.32 | REDUCE: (3), (5) imply: % 189.41/30.32 | (6) $false % 189.41/30.32 | % 189.41/30.32 | CLOSE: (6) is inconsistent. % 189.41/30.32 | % 189.41/30.32 End of proof % 189.41/30.32 % 189.41/30.32 Sub-proof #132 shows that the following formulas are inconsistent: % 189.41/30.32 ---------------------------------------------------------------- % 189.41/30.32 (1) all_252_5 = e4 & op(e3, e2) = e4 % 189.41/30.32 (2) all_252_5 = e0 % 189.41/30.32 (3) ~ (e4 = e0) % 189.41/30.32 % 189.41/30.32 Begin of proof % 189.41/30.32 | % 189.41/30.32 | ALPHA: (1) implies: % 189.41/30.32 | (4) all_252_5 = e4 % 189.41/30.32 | % 189.41/30.32 | COMBINE_EQS: (2), (4) imply: % 189.41/30.32 | (5) e4 = e0 % 189.41/30.32 | % 189.41/30.32 | REDUCE: (3), (5) imply: % 189.41/30.32 | (6) $false % 189.41/30.32 | % 189.41/30.32 | CLOSE: (6) is inconsistent. % 189.41/30.32 | % 189.41/30.32 End of proof % 189.41/30.32 % 189.41/30.32 Sub-proof #133 shows that the following formulas are inconsistent: % 189.41/30.32 ---------------------------------------------------------------- % 189.41/30.32 (1) all_252_3 = e1 & op(e3, e3) = e1 % 189.41/30.32 (2) all_252_3 = e2 % 189.41/30.32 (3) ~ (e2 = e1) % 189.41/30.32 % 189.41/30.32 Begin of proof % 189.41/30.32 | % 189.41/30.32 | ALPHA: (1) implies: % 189.41/30.32 | (4) all_252_3 = e1 % 189.41/30.32 | % 189.41/30.32 | COMBINE_EQS: (2), (4) imply: % 189.41/30.32 | (5) e2 = e1 % 189.41/30.32 | % 189.41/30.32 | REDUCE: (3), (5) imply: % 189.41/30.32 | (6) $false % 189.41/30.32 | % 189.41/30.32 | CLOSE: (6) is inconsistent. % 189.41/30.32 | % 189.41/30.32 End of proof % 189.41/30.32 % 189.41/30.32 Sub-proof #134 shows that the following formulas are inconsistent: % 189.41/30.32 ---------------------------------------------------------------- % 189.41/30.32 (1) all_252_5 = e3 & op(e3, e2) = e3 % 189.41/30.32 (2) all_252_5 = e0 % 189.41/30.32 (3) ~ (e3 = e0) % 189.41/30.32 % 189.41/30.32 Begin of proof % 189.41/30.32 | % 189.41/30.32 | ALPHA: (1) implies: % 189.41/30.32 | (4) all_252_5 = e3 % 189.41/30.32 | % 189.41/30.32 | COMBINE_EQS: (2), (4) imply: % 189.41/30.32 | (5) e3 = e0 % 189.41/30.32 | % 189.41/30.32 | REDUCE: (3), (5) imply: % 189.41/30.32 | (6) $false % 189.41/30.32 | % 189.41/30.32 | CLOSE: (6) is inconsistent. % 189.41/30.32 | % 189.41/30.32 End of proof % 189.41/30.32 % 189.41/30.32 Sub-proof #135 shows that the following formulas are inconsistent: % 189.41/30.32 ---------------------------------------------------------------- % 189.41/30.32 (1) all_252_20 = e2 % 189.41/30.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.32 (3) ~ (all_20_2 = e4) % 189.41/30.32 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.41/30.32 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.41/30.32 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.41/30.32 (5) op(e0, e2) = e4 % 189.41/30.32 (6) op(e3, e1) = all_36_2 % 189.41/30.32 (7) ~ (e2 = e1) % 189.41/30.32 (8) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.32 (9) op(e2, e1) = e2 % 189.41/30.32 (10) op(e4, e1) = e0 % 189.41/30.32 (11) all_252_11 = e2 % 189.41/30.32 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.41/30.32 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.41/30.32 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.41/30.32 (13) op(e2, e1) = e0 % 189.41/30.32 (14) ~ (e4 = e0) % 189.41/30.32 (15) ~ (e4 = e3) % 189.41/30.32 (16) ~ (all_36_2 = e2) % 189.41/30.32 (17) ~ (all_244_24 = all_20_2) % 189.41/30.32 (18) op(e1, e4) = e0 % 189.41/30.32 (19) ~ (all_20_2 = e3) % 189.41/30.32 (20) op(e0, e0) = all_244_24 % 189.41/30.32 (21) op(e0, e1) = all_20_2 % 189.41/30.32 (22) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.41/30.32 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, % 189.41/30.32 e1) = e0) % 189.41/30.32 (23) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.41/30.32 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.41/30.32 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.32 (24) ~ (all_20_2 = e0) % 189.41/30.32 (25) ~ (all_20_2 = e2) % 189.41/30.32 (26) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.41/30.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.41/30.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.41/30.32 (27) op(e0, e4) = e2 % 189.41/30.32 (28) ~ (e3 = e0) % 189.41/30.32 (29) ~ (all_20_2 = all_8_1) % 189.41/30.32 (30) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.41/30.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.41/30.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.41/30.32 (31) ~ (e3 = e2) % 189.41/30.32 (32) op(e0, e3) = all_8_1 % 189.41/30.32 (33) op(e1, e4) = e1 % 189.41/30.32 (34) ~ (e4 = e2) % 189.41/30.32 (35) ~ (e1 = e0) % 189.41/30.32 (36) all_250_23 = all_20_2 % 189.41/30.32 (37) ~ (e3 = e1) % 189.41/30.32 (38) ~ (e2 = e0) % 189.41/30.32 (39) ~ (all_244_24 = e1) % 189.41/30.32 (40) ~ (e4 = e1) % 189.41/30.32 % 189.41/30.32 Begin of proof % 189.41/30.32 | % 189.41/30.32 | BETA: splitting (22) gives: % 189.41/30.32 | % 189.41/30.32 | Case 1: % 189.41/30.32 | | % 189.41/30.32 | | (41) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 189.41/30.32 | | = e0) % 189.41/30.32 | | % 189.41/30.32 | | BETA: splitting (41) gives: % 189.41/30.32 | | % 189.41/30.32 | | Case 1: % 189.41/30.32 | | | % 189.41/30.32 | | | (42) all_252_20 = e0 & op(e0, e4) = e0 % 189.41/30.32 | | | % 189.41/30.32 | | | REF_CLOSE: (2), (27), (38), (42) are inconsistent by sub-proof #255. % 189.41/30.32 | | | % 189.41/30.32 | | Case 2: % 189.41/30.32 | | | % 189.41/30.32 | | | (43) all_252_21 = e0 & op(e0, e3) = e0 % 189.41/30.32 | | | % 189.41/30.32 | | | ALPHA: (43) implies: % 189.41/30.32 | | | (44) op(e0, e3) = e0 % 189.41/30.32 | | | % 189.41/30.32 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.41/30.32 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), % 189.41/30.32 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), % 189.41/30.32 | | | (34), (35), (36), (37), (38), (39), (40), (44) are inconsistent % 189.41/30.32 | | | by sub-proof #190. % 189.41/30.32 | | | % 189.41/30.32 | | End of split % 189.41/30.32 | | % 189.41/30.32 | Case 2: % 189.41/30.32 | | % 189.41/30.32 | | (45) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 189.41/30.32 | | = e0) % 189.41/30.32 | | % 189.41/30.32 | | REF_CLOSE: (1), (2), (3), (5), (8), (14), (17), (20), (23), (24), (25), % 189.41/30.32 | | (29), (32), (36), (45) are inconsistent by sub-proof #136. % 189.41/30.32 | | % 189.41/30.32 | End of split % 189.41/30.32 | % 189.41/30.32 End of proof % 189.41/30.32 % 189.41/30.32 Sub-proof #136 shows that the following formulas are inconsistent: % 189.41/30.32 ---------------------------------------------------------------- % 189.41/30.32 (1) all_252_20 = e2 % 189.41/30.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.41/30.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.41/30.32 (3) ~ (all_20_2 = e4) % 189.41/30.32 (4) op(e0, e2) = e4 % 189.41/30.32 (5) all_250_23 = e1 | all_250_23 = e0 % 189.41/30.32 (6) ~ (e4 = e0) % 189.41/30.32 (7) ~ (all_244_24 = all_20_2) % 189.41/30.32 (8) op(e0, e0) = all_244_24 % 189.41/30.32 (9) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.41/30.32 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.41/30.32 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.41/30.32 (10) ~ (all_20_2 = e0) % 189.41/30.32 (11) ~ (all_20_2 = e2) % 189.41/30.32 (12) ~ (all_20_2 = all_8_1) % 189.41/30.32 (13) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) = % 189.41/30.32 e0) % 189.41/30.32 (14) op(e0, e3) = all_8_1 % 189.41/30.32 (15) all_250_23 = all_20_2 % 189.41/30.32 % 189.41/30.32 Begin of proof % 189.41/30.32 | % 189.41/30.32 | BETA: splitting (13) gives: % 189.41/30.32 | % 189.41/30.32 | Case 1: % 189.41/30.32 | | % 189.41/30.32 | | (16) all_252_22 = e0 & op(e0, e2) = e0 % 189.41/30.32 | | % 189.41/30.32 | | ALPHA: (16) implies: % 189.41/30.32 | | (17) op(e0, e2) = e0 % 189.41/30.32 | | % 189.41/30.32 | | REF_CLOSE: (2), (4), (6), (17) are inconsistent by sub-proof #520. % 189.41/30.32 | | % 189.41/30.32 | Case 2: % 189.41/30.32 | | % 189.41/30.32 | | (18) all_252_23 = e0 & op(e0, e1) = e0 % 189.41/30.32 | | % 189.41/30.32 | | ALPHA: (18) implies: % 189.41/30.32 | | (19) all_252_23 = e0 % 189.41/30.32 | | % 189.41/30.32 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14), % 189.41/30.32 | | (15), (19) are inconsistent by sub-proof #192. % 189.41/30.32 | | % 189.41/30.32 | End of split % 189.41/30.32 | % 189.60/30.32 End of proof % 189.60/30.32 % 189.60/30.32 Sub-proof #137 shows that the following formulas are inconsistent: % 189.60/30.32 ---------------------------------------------------------------- % 189.60/30.32 (1) all_252_20 = e2 % 189.60/30.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.32 (3) ~ (all_20_2 = e4) % 189.60/30.32 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.60/30.32 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.60/30.32 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.60/30.32 (5) op(e0, e2) = e4 % 189.60/30.32 (6) op(e3, e1) = all_36_2 % 189.60/30.32 (7) all_252_12 = e0 % 189.60/30.32 (8) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.60/30.32 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.60/30.32 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.60/30.32 (9) op(e2, e1) = e0 % 189.60/30.32 (10) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.60/30.32 all_250_23 = e0 % 189.60/30.32 (11) ~ (e4 = e0) % 189.60/30.32 (12) ~ (e4 = e3) % 189.60/30.32 (13) ~ (all_36_2 = e2) % 189.60/30.32 (14) all_252_9 = e0 % 189.60/30.32 (15) ~ (all_40_2 = all_34_2) % 189.60/30.32 (16) ~ (all_244_24 = all_20_2) % 189.60/30.32 (17) op(e1, e4) = e0 % 189.60/30.32 (18) all_252_21 = e4 & op(e0, e3) = e4 % 189.60/30.32 (19) ~ (all_20_2 = e3) % 189.60/30.32 (20) op(all_20_2, e4) = e1 % 189.60/30.32 (21) op(e0, e0) = all_244_24 % 189.60/30.32 (22) op(e0, e1) = all_20_2 % 189.60/30.32 (23) all_252_19 = e4 % 189.60/30.32 (24) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.60/30.32 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.60/30.32 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.32 (25) ~ (all_20_2 = e0) % 189.60/30.32 (26) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.60/30.32 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.60/30.32 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.60/30.32 (27) ~ (all_20_2 = e2) % 189.60/30.32 (28) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.60/30.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.60/30.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.60/30.32 (29) op(e0, e4) = e2 % 189.60/30.32 (30) ~ (e3 = e0) % 189.60/30.32 (31) ~ (all_20_2 = all_8_1) % 189.60/30.32 (32) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.60/30.32 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.60/30.32 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.60/30.32 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.60/30.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.60/30.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.60/30.32 (34) ~ (e3 = e2) % 189.60/30.32 (35) all_252_22 = e4 % 189.60/30.32 (36) op(e4, all_20_2) = e0 % 189.60/30.32 (37) op(e0, e3) = all_8_1 % 189.60/30.32 (38) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.60/30.32 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.60/30.32 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.60/30.32 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.60/30.32 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.60/30.32 op(e0, e1) = e0))) % 189.60/30.32 (39) ~ (e4 = e2) % 189.60/30.32 (40) op(e2, e0) = all_40_2 % 189.60/30.32 (41) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.60/30.32 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.60/30.32 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.60/30.32 (42) op(e0, e4) = all_12_2 % 189.60/30.32 (43) all_250_23 = all_20_2 % 189.60/30.32 (44) ~ (e2 = e0) % 189.60/30.32 (45) op(e1, e0) = all_34_2 % 189.60/30.32 (46) ~ (all_12_2 = e3) % 189.60/30.32 (47) ~ (all_34_2 = e2) % 189.60/30.32 (48) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 189.60/30.32 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 189.60/30.32 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.60/30.32 (49) op(e2, e0) = e1 % 189.60/30.32 % 189.60/30.32 Begin of proof % 189.60/30.32 | % 189.60/30.32 | ALPHA: (18) implies: % 189.60/30.32 | (50) all_252_21 = e4 % 189.60/30.32 | % 189.60/30.32 | BETA: splitting (48) gives: % 189.60/30.32 | % 189.60/30.32 | Case 1: % 189.60/30.32 | | % 189.60/30.32 | | (51) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) % 189.60/30.32 | | = e3) % 189.60/30.32 | | % 189.60/30.32 | | REF_CLOSE: (2), (12), (42), (46), (50), (51) are inconsistent by sub-proof % 189.60/30.32 | | #258. % 189.60/30.32 | | % 189.60/30.32 | Case 2: % 189.60/30.32 | | % 189.60/30.32 | | (52) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) % 189.60/30.32 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.60/30.32 | | % 189.60/30.32 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.60/30.32 | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (23), (24), % 189.60/30.32 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), % 189.60/30.32 | | (36), (37), (38), (39), (40), (41), (43), (44), (45), (47), (49), % 189.60/30.32 | | (52) are inconsistent by sub-proof #138. % 189.60/30.32 | | % 189.60/30.32 | End of split % 189.60/30.32 | % 189.60/30.32 End of proof % 189.60/30.32 % 189.60/30.32 Sub-proof #138 shows that the following formulas are inconsistent: % 189.60/30.32 ---------------------------------------------------------------- % 189.60/30.32 (1) all_252_20 = e2 % 189.60/30.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.32 (3) ~ (all_20_2 = e4) % 189.60/30.32 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.60/30.32 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.60/30.32 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.60/30.32 (5) op(e0, e2) = e4 % 189.60/30.32 (6) op(e3, e1) = all_36_2 % 189.60/30.32 (7) all_252_12 = e0 % 189.60/30.32 (8) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.60/30.32 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.60/30.32 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.60/30.32 (9) op(e2, e1) = e0 % 189.60/30.32 (10) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.60/30.32 all_250_23 = e0 % 189.60/30.32 (11) ~ (e4 = e0) % 189.60/30.32 (12) ~ (e4 = e3) % 189.60/30.32 (13) ~ (all_36_2 = e2) % 189.60/30.32 (14) all_252_9 = e0 % 189.60/30.32 (15) ~ (all_40_2 = all_34_2) % 189.60/30.32 (16) ~ (all_244_24 = all_20_2) % 189.60/30.32 (17) op(e1, e4) = e0 % 189.60/30.32 (18) ~ (all_20_2 = e3) % 189.60/30.32 (19) op(all_20_2, e4) = e1 % 189.60/30.32 (20) op(e0, e0) = all_244_24 % 189.60/30.32 (21) op(e0, e1) = all_20_2 % 189.60/30.32 (22) all_252_19 = e4 % 189.60/30.32 (23) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.60/30.32 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.60/30.32 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.32 (24) ~ (all_20_2 = e0) % 189.60/30.32 (25) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.60/30.32 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.60/30.32 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.60/30.32 (26) ~ (all_20_2 = e2) % 189.60/30.32 (27) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.60/30.32 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.60/30.32 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.60/30.32 (28) op(e0, e4) = e2 % 189.60/30.32 (29) ~ (e3 = e0) % 189.60/30.32 (30) ~ (all_20_2 = all_8_1) % 189.60/30.32 (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.60/30.32 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.60/30.32 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.60/30.32 (32) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.60/30.32 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.60/30.32 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.60/30.32 (33) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) = % 189.60/30.32 e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.60/30.32 (34) ~ (e3 = e2) % 189.60/30.32 (35) all_252_22 = e4 % 189.60/30.32 (36) op(e4, all_20_2) = e0 % 189.60/30.32 (37) op(e0, e3) = all_8_1 % 189.60/30.32 (38) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.60/30.32 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.60/30.32 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.60/30.32 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.60/30.32 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.60/30.32 op(e0, e1) = e0))) % 189.60/30.32 (39) ~ (e4 = e2) % 189.60/30.32 (40) op(e2, e0) = all_40_2 % 189.60/30.32 (41) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.60/30.32 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.60/30.32 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.60/30.32 (42) all_250_23 = all_20_2 % 189.60/30.32 (43) ~ (e2 = e0) % 189.60/30.32 (44) op(e1, e0) = all_34_2 % 189.60/30.32 (45) ~ (all_34_2 = e2) % 189.60/30.33 (46) op(e2, e0) = e1 % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | BETA: splitting (33) gives: % 189.60/30.33 | % 189.60/30.33 | Case 1: % 189.60/30.33 | | % 189.60/30.33 | | (47) all_252_22 = e3 & op(e0, e2) = e3 % 189.60/30.33 | | % 189.60/30.33 | | ALPHA: (47) implies: % 189.60/30.33 | | (48) op(e0, e2) = e3 % 189.60/30.33 | | % 189.60/30.33 | | REF_CLOSE: (2), (5), (12), (48) are inconsistent by sub-proof #328. % 189.60/30.33 | | % 189.60/30.33 | Case 2: % 189.60/30.33 | | % 189.60/30.33 | | (49) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) % 189.60/30.33 | | = e3) % 189.60/30.33 | | % 189.60/30.33 | | BETA: splitting (49) gives: % 189.60/30.33 | | % 189.60/30.33 | | Case 1: % 189.60/30.33 | | | % 189.60/30.33 | | | (50) all_252_23 = e3 & op(e0, e1) = e3 % 189.60/30.33 | | | % 189.60/30.33 | | | ALPHA: (50) implies: % 189.60/30.33 | | | (51) op(e0, e1) = e3 % 189.60/30.33 | | | % 189.60/30.33 | | | REF_CLOSE: (2), (18), (21), (51) are inconsistent by sub-proof #508. % 189.60/30.33 | | | % 189.60/30.33 | | Case 2: % 189.60/30.33 | | | % 189.60/30.33 | | | (52) all_252_24 = e3 & op(e0, e0) = e3 % 189.60/30.33 | | | % 189.60/30.33 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 189.60/30.33 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), % 189.60/30.33 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), % 189.60/30.33 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), % 189.60/30.33 | | | (44), (45), (46), (52) are inconsistent by sub-proof #169. % 189.60/30.33 | | | % 189.60/30.33 | | End of split % 189.60/30.33 | | % 189.60/30.33 | End of split % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #139 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) all_252_24 = e1 % 189.60/30.33 (2) all_252_24 = e0 % 189.60/30.33 (3) ~ (e1 = e0) % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | COMBINE_EQS: (1), (2) imply: % 189.60/30.33 | (4) e1 = e0 % 189.60/30.33 | % 189.60/30.33 | SIMP: (4) implies: % 189.60/30.33 | (5) e1 = e0 % 189.60/30.33 | % 189.60/30.33 | REDUCE: (3), (5) imply: % 189.60/30.33 | (6) $false % 189.60/30.33 | % 189.60/30.33 | CLOSE: (6) is inconsistent. % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #140 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) all_252_8 = e3 & op(e2, e2) = e3 % 189.60/30.33 (2) all_252_8 = e4 % 189.60/30.33 (3) ~ (e4 = e3) % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | ALPHA: (1) implies: % 189.60/30.33 | (4) all_252_8 = e3 % 189.60/30.33 | % 189.60/30.33 | COMBINE_EQS: (2), (4) imply: % 189.60/30.33 | (5) e4 = e3 % 189.60/30.33 | % 189.60/30.33 | REDUCE: (3), (5) imply: % 189.60/30.33 | (6) $false % 189.60/30.33 | % 189.60/30.33 | CLOSE: (6) is inconsistent. % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #141 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.33 (2) ~ (all_20_2 = e4) % 189.60/30.33 (3) ~ (e2 = e1) % 189.60/30.33 (4) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.60/30.33 all_250_23 = e0 % 189.60/30.33 (5) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.60/30.33 | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0) = % 189.60/30.33 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.33 (6) ~ (all_40_2 = all_34_2) % 189.60/30.33 (7) ~ (all_244_24 = all_20_2) % 189.60/30.33 (8) ~ (all_20_2 = e3) % 189.60/30.33 (9) op(e0, e0) = all_244_24 % 189.60/30.33 (10) op(e4, e0) = e3 % 189.60/30.33 (11) ~ (all_20_2 = e0) % 189.60/30.33 (12) all_252_17 = e2 % 189.60/30.33 (13) ~ (all_20_2 = e2) % 189.60/30.33 (14) all_252_18 = e0 % 189.60/30.33 (15) op(e2, e0) = all_40_2 % 189.60/30.33 (16) ~ (e1 = e0) % 189.60/30.33 (17) all_250_23 = all_20_2 % 189.60/30.33 (18) ~ (e3 = e1) % 189.60/30.33 (19) op(e1, e0) = all_34_2 % 189.60/30.33 (20) op(e2, e0) = e1 % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | BETA: splitting (5) gives: % 189.60/30.33 | % 189.60/30.33 | Case 1: % 189.60/30.33 | | % 189.60/30.33 | | (21) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) % 189.60/30.33 | | = e1) % 189.60/30.33 | | % 189.60/30.33 | | REF_CLOSE: (1), (3), (10), (12), (18), (21) are inconsistent by sub-proof % 189.60/30.33 | | #153. % 189.60/30.33 | | % 189.60/30.33 | Case 2: % 189.60/30.33 | | % 189.60/30.33 | | (22) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0) % 189.60/30.33 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.33 | | % 189.60/30.33 | | BETA: splitting (22) gives: % 189.60/30.33 | | % 189.60/30.33 | | Case 1: % 189.60/30.33 | | | % 189.60/30.33 | | | (23) all_252_18 = e1 & op(e2, e0) = e1 % 189.60/30.33 | | | % 189.60/30.33 | | | ALPHA: (23) implies: % 189.60/30.33 | | | (24) all_252_18 = e1 % 189.60/30.33 | | | % 189.60/30.33 | | | COMBINE_EQS: (14), (24) imply: % 189.60/30.33 | | | (25) e1 = e0 % 189.60/30.33 | | | % 189.60/30.33 | | | REDUCE: (16), (25) imply: % 189.60/30.33 | | | (26) $false % 189.60/30.33 | | | % 189.60/30.33 | | | CLOSE: (26) is inconsistent. % 189.60/30.33 | | | % 189.60/30.33 | | Case 2: % 189.60/30.33 | | | % 189.60/30.33 | | | (27) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, % 189.60/30.33 | | | e0) = e1) % 189.60/30.33 | | | % 189.60/30.33 | | | BETA: splitting (27) gives: % 189.60/30.33 | | | % 189.60/30.33 | | | Case 1: % 189.60/30.33 | | | | % 189.60/30.33 | | | | (28) all_252_19 = e1 & op(e1, e0) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | ALPHA: (28) implies: % 189.60/30.33 | | | | (29) op(e1, e0) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | REF_CLOSE: (1), (6), (15), (19), (20), (29) are inconsistent by % 189.60/30.33 | | | | sub-proof #352. % 189.60/30.33 | | | | % 189.60/30.33 | | | Case 2: % 189.60/30.33 | | | | % 189.60/30.33 | | | | (30) all_252_24 = e1 & op(e0, e0) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | ALPHA: (30) implies: % 189.60/30.33 | | | | (31) op(e0, e0) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | BETA: splitting (4) gives: % 189.60/30.33 | | | | % 189.60/30.33 | | | | Case 1: % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | (32) all_250_23 = e4 % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | COMBINE_EQS: (17), (32) imply: % 189.60/30.33 | | | | | (33) all_20_2 = e4 % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | REDUCE: (2), (33) imply: % 189.60/30.33 | | | | | (34) $false % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | CLOSE: (34) is inconsistent. % 189.60/30.33 | | | | | % 189.60/30.33 | | | | Case 2: % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | (35) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.60/30.33 | | | | | all_250_23 = e0 % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | BETA: splitting (35) gives: % 189.60/30.33 | | | | | % 189.60/30.33 | | | | | Case 1: % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | (36) all_250_23 = e3 % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | COMBINE_EQS: (17), (36) imply: % 189.60/30.33 | | | | | | (37) all_20_2 = e3 % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | REDUCE: (8), (37) imply: % 189.60/30.33 | | | | | | (38) $false % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | CLOSE: (38) is inconsistent. % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | Case 2: % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | (39) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | BETA: splitting (39) gives: % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | | Case 1: % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | (40) all_250_23 = e2 % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | COMBINE_EQS: (17), (40) imply: % 189.60/30.33 | | | | | | | (41) all_20_2 = e2 % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | REDUCE: (13), (41) imply: % 189.60/30.33 | | | | | | | (42) $false % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | CLOSE: (42) is inconsistent. % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | Case 2: % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | (43) all_250_23 = e1 | all_250_23 = e0 % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | BETA: splitting (43) gives: % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | | Case 1: % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | (44) all_250_23 = e1 % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | COMBINE_EQS: (17), (44) imply: % 189.60/30.33 | | | | | | | | (45) all_20_2 = e1 % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | SIMP: (45) implies: % 189.60/30.33 | | | | | | | | (46) all_20_2 = e1 % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | REDUCE: (7), (46) imply: % 189.60/30.33 | | | | | | | | (47) ~ (all_244_24 = e1) % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | REF_CLOSE: (1), (9), (31), (47) are inconsistent by sub-proof % 189.60/30.33 | | | | | | | | #474. % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | Case 2: % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | (48) all_250_23 = e0 % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | | REF_CLOSE: (11), (17), (48) are inconsistent by sub-proof #486. % 189.60/30.33 | | | | | | | | % 189.60/30.33 | | | | | | | End of split % 189.60/30.33 | | | | | | | % 189.60/30.33 | | | | | | End of split % 189.60/30.33 | | | | | | % 189.60/30.33 | | | | | End of split % 189.60/30.33 | | | | | % 189.60/30.33 | | | | End of split % 189.60/30.33 | | | | % 189.60/30.33 | | | End of split % 189.60/30.33 | | | % 189.60/30.33 | | End of split % 189.60/30.33 | | % 189.60/30.33 | End of split % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #142 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) all_252_20 = e2 % 189.60/30.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.33 (3) ~ (all_20_2 = e4) % 189.60/30.33 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.60/30.33 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.60/30.33 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.60/30.33 (5) op(e0, e2) = e4 % 189.60/30.33 (6) op(e3, e1) = all_36_2 % 189.60/30.33 (7) ~ (e2 = e1) % 189.60/30.33 (8) all_250_23 = e1 | all_250_23 = e0 % 189.60/30.33 (9) all_252_12 = e0 % 189.60/30.33 (10) op(e2, e1) = e2 % 189.60/30.33 (11) op(e4, e1) = e0 % 189.60/30.33 (12) all_252_11 = e2 % 189.60/30.33 (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.60/30.33 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.60/30.33 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.60/30.33 (14) op(e2, e1) = e0 % 189.60/30.33 (15) all_252_15 = e3 % 189.60/30.33 (16) ~ (e4 = e0) % 189.60/30.33 (17) all_252_14 = e2 % 189.60/30.33 (18) ~ (e4 = e3) % 189.60/30.33 (19) ~ (all_36_2 = e2) % 189.60/30.33 (20) ~ (all_40_2 = all_34_2) % 189.60/30.33 (21) ~ (all_244_24 = all_20_2) % 189.60/30.33 (22) op(e1, e4) = e0 % 189.60/30.33 (23) all_252_23 = e1 % 189.60/30.33 (24) ~ (all_20_2 = e3) % 189.60/30.33 (25) op(e0, e0) = all_244_24 % 189.60/30.33 (26) op(e0, e1) = all_20_2 % 189.60/30.33 (27) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.60/30.33 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.60/30.33 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.33 (28) ~ (all_20_2 = e0) % 189.60/30.33 (29) ~ (all_20_2 = e2) % 189.60/30.33 (30) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.60/30.33 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.60/30.33 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.60/30.33 (31) ~ (e3 = e0) % 189.60/30.33 (32) ~ (all_20_2 = all_8_1) % 189.60/30.33 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.60/30.33 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.60/30.33 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.60/30.33 (34) ~ (e3 = e2) % 189.60/30.33 (35) op(e0, e3) = all_8_1 % 189.60/30.33 (36) op(e1, e4) = e1 % 189.60/30.33 (37) ~ (e4 = e2) % 189.60/30.33 (38) op(e2, e0) = all_40_2 % 189.60/30.33 (39) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.60/30.33 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.60/30.33 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.60/30.33 (40) ~ (e1 = e0) % 189.60/30.33 (41) all_250_23 = all_20_2 % 189.60/30.33 (42) ~ (e3 = e1) % 189.60/30.33 (43) ~ (e2 = e0) % 189.60/30.33 (44) op(e0, e1) = e1 % 189.60/30.33 (45) op(e1, e0) = all_34_2 % 189.60/30.33 (46) ~ (e4 = e1) % 189.60/30.33 (47) op(e2, e0) = e1 % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | BETA: splitting (39) gives: % 189.60/30.33 | % 189.60/30.33 | Case 1: % 189.60/30.33 | | % 189.60/30.33 | | (48) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 189.60/30.33 | | = e1) % 189.60/30.33 | | % 189.60/30.33 | | BETA: splitting (48) gives: % 189.60/30.33 | | % 189.60/30.33 | | Case 1: % 189.60/30.33 | | | % 189.60/30.33 | | | (49) all_252_12 = e1 & op(e1, e4) = e1 % 189.60/30.33 | | | % 189.60/30.33 | | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (21), (23), (25), (27), (28), % 189.60/30.33 | | | (29), (32), (35), (41), (49) are inconsistent by sub-proof % 189.60/30.33 | | | #181. % 189.60/30.33 | | | % 189.60/30.33 | | Case 2: % 189.60/30.33 | | | % 189.60/30.33 | | | % 189.60/30.33 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), % 189.60/30.33 | | | (14), (16), (18), (19), (21), (22), (24), (25), (26), (27), % 189.60/30.33 | | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 189.60/30.33 | | | (40), (41), (42), (43), (44), (46) are inconsistent by % 189.60/30.33 | | | sub-proof #144. % 189.60/30.33 | | | % 189.60/30.33 | | End of split % 189.60/30.33 | | % 189.60/30.33 | Case 2: % 189.60/30.33 | | % 189.60/30.33 | | (50) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) % 189.60/30.33 | | = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.60/30.33 | | % 189.60/30.33 | | BETA: splitting (50) gives: % 189.60/30.33 | | % 189.60/30.33 | | Case 1: % 189.60/30.33 | | | % 189.60/30.33 | | | (51) all_252_14 = e1 & op(e1, e2) = e1 % 189.60/30.33 | | | % 189.60/30.33 | | | ALPHA: (51) implies: % 189.60/30.33 | | | (52) all_252_14 = e1 % 189.60/30.33 | | | % 189.60/30.33 | | | REF_CLOSE: (7), (17), (52) are inconsistent by sub-proof #391. % 189.60/30.33 | | | % 189.60/30.33 | | Case 2: % 189.60/30.33 | | | % 189.60/30.33 | | | (53) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 189.60/30.33 | | | e0) = e1) % 189.60/30.33 | | | % 189.60/30.33 | | | BETA: splitting (53) gives: % 189.60/30.33 | | | % 189.60/30.33 | | | Case 1: % 189.60/30.33 | | | | % 189.60/30.33 | | | | (54) all_252_15 = e1 & op(e1, e1) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | REF_CLOSE: (15), (42), (54) are inconsistent by sub-proof #143. % 189.60/30.33 | | | | % 189.60/30.33 | | | Case 2: % 189.60/30.33 | | | | % 189.60/30.33 | | | | (55) all_252_19 = e1 & op(e1, e0) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | ALPHA: (55) implies: % 189.60/30.33 | | | | (56) op(e1, e0) = e1 % 189.60/30.33 | | | | % 189.60/30.33 | | | | REF_CLOSE: (2), (20), (38), (45), (47), (56) are inconsistent by % 189.60/30.33 | | | | sub-proof #352. % 189.60/30.33 | | | | % 189.60/30.33 | | | End of split % 189.60/30.33 | | | % 189.60/30.33 | | End of split % 189.60/30.33 | | % 189.60/30.33 | End of split % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #143 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) all_252_15 = e1 & op(e1, e1) = e1 % 189.60/30.33 (2) all_252_15 = e3 % 189.60/30.33 (3) ~ (e3 = e1) % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | ALPHA: (1) implies: % 189.60/30.33 | (4) all_252_15 = e1 % 189.60/30.33 | % 189.60/30.33 | COMBINE_EQS: (2), (4) imply: % 189.60/30.33 | (5) e3 = e1 % 189.60/30.33 | % 189.60/30.33 | SIMP: (5) implies: % 189.60/30.33 | (6) e3 = e1 % 189.60/30.33 | % 189.60/30.33 | REDUCE: (3), (6) imply: % 189.60/30.33 | (7) $false % 189.60/30.33 | % 189.60/30.33 | CLOSE: (7) is inconsistent. % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #144 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) all_252_20 = e2 % 189.60/30.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.33 (3) ~ (all_20_2 = e4) % 189.60/30.33 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.60/30.33 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.60/30.33 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.60/30.33 (5) op(e0, e2) = e4 % 189.60/30.33 (6) op(e3, e1) = all_36_2 % 189.60/30.33 (7) ~ (e2 = e1) % 189.60/30.33 (8) all_250_23 = e1 | all_250_23 = e0 % 189.60/30.33 (9) op(e2, e1) = e2 % 189.60/30.33 (10) op(e4, e1) = e0 % 189.60/30.33 (11) all_252_11 = e2 % 189.60/30.33 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.60/30.33 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.60/30.33 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.60/30.33 (13) op(e2, e1) = e0 % 189.60/30.33 (14) ~ (e4 = e0) % 189.60/30.33 (15) ~ (e4 = e3) % 189.60/30.33 (16) ~ (all_36_2 = e2) % 189.60/30.33 (17) ~ (all_244_24 = all_20_2) % 189.60/30.33 (18) op(e1, e4) = e0 % 189.60/30.33 (19) ~ (all_20_2 = e3) % 189.60/30.33 (20) op(e0, e0) = all_244_24 % 189.60/30.33 (21) op(e0, e1) = all_20_2 % 189.60/30.33 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.60/30.33 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.60/30.33 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.33 (23) ~ (all_20_2 = e0) % 189.60/30.33 (24) ~ (all_20_2 = e2) % 189.60/30.33 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.60/30.33 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.60/30.33 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.60/30.33 (26) ~ (e3 = e0) % 189.60/30.33 (27) ~ (all_20_2 = all_8_1) % 189.60/30.33 (28) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.60/30.33 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.60/30.33 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.60/30.33 (29) ~ (e3 = e2) % 189.60/30.33 (30) op(e0, e3) = all_8_1 % 189.60/30.33 (31) op(e1, e4) = e1 % 189.60/30.33 (32) ~ (e4 = e2) % 189.60/30.33 (33) ~ (e1 = e0) % 189.60/30.33 (34) all_250_23 = all_20_2 % 189.60/30.33 (35) ~ (e3 = e1) % 189.60/30.33 (36) ~ (e2 = e0) % 189.60/30.33 (37) op(e0, e1) = e1 % 189.60/30.33 (38) ~ (e4 = e1) % 189.60/30.33 % 189.60/30.33 Begin of proof % 189.60/30.33 | % 189.60/30.33 | GROUND_INST: instantiating (2) with e0, e2, e1, e2, simplifying with (9), (13) % 189.60/30.33 | gives: % 189.60/30.33 | (39) e2 = e0 % 189.60/30.33 | % 189.60/30.33 | COMBINE_EQS: (11), (39) imply: % 189.60/30.33 | (40) all_252_11 = e0 % 189.60/30.33 | % 189.60/30.33 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), (15), % 189.60/30.33 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 189.60/30.33 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 189.60/30.33 | (38), (40) are inconsistent by sub-proof #191. % 189.60/30.33 | % 189.60/30.33 End of proof % 189.60/30.33 % 189.60/30.33 Sub-proof #145 shows that the following formulas are inconsistent: % 189.60/30.33 ---------------------------------------------------------------- % 189.60/30.33 (1) all_252_20 = e2 % 189.60/30.33 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.60/30.33 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.60/30.33 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.60/30.33 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.60/30.33 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.60/30.33 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.60/30.33 (4) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) = e3) | % 189.60/30.33 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) = e3) % 189.60/30.33 | (all_252_18 = e3 & op(e2, e0) = e3) % 189.60/30.33 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.33 (6) ~ (all_20_2 = e4) % 189.60/30.33 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.60/30.33 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.60/30.33 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.60/30.33 (8) op(e0, e2) = e4 % 189.60/30.33 (9) op(e3, e1) = all_36_2 % 189.60/30.33 (10) ~ (e2 = e1) % 189.60/30.33 (11) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0) = % 189.60/30.33 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.33 (12) all_252_12 = e0 % 189.60/30.33 (13) all_252_11 = e2 % 189.60/30.33 (14) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.60/30.33 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.60/30.33 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.60/30.33 (15) op(e2, e1) = e0 % 189.60/30.33 (16) all_252_7 = e0 % 189.60/30.33 (17) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.60/30.33 all_250_23 = e0 % 189.60/30.33 (18) ~ (e4 = e0) % 189.60/30.33 (19) ~ (e4 = e3) % 189.60/30.34 (20) ~ (all_36_2 = e2) % 189.60/30.34 (21) all_252_8 = e4 % 189.60/30.34 (22) all_252_9 = e0 % 189.60/30.34 (23) ~ (all_40_2 = all_34_2) % 189.60/30.34 (24) ~ (all_244_24 = all_20_2) % 189.60/30.34 (25) op(e1, e4) = e0 % 189.60/30.34 (26) ~ (all_20_2 = e3) % 189.60/30.34 (27) op(all_20_2, e4) = e1 % 189.60/30.34 (28) op(e0, e0) = all_244_24 % 189.60/30.34 (29) op(e0, e1) = all_20_2 % 189.60/30.34 (30) all_252_19 = e4 % 189.60/30.34 (31) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.60/30.34 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.60/30.34 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.60/30.34 (32) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.60/30.34 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.60/30.34 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.60/30.34 (33) ~ (all_20_2 = e0) % 189.60/30.34 (34) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.60/30.34 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.60/30.34 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.60/30.34 (35) all_252_17 = e2 % 189.60/30.34 (36) ~ (all_20_2 = e2) % 189.60/30.34 (37) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.60/30.34 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.60/30.34 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.60/30.34 (38) op(e0, e4) = e2 % 189.60/30.34 (39) ~ (e3 = e0) % 189.60/30.34 (40) ~ (all_20_2 = all_8_1) % 189.60/30.34 (41) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.60/30.34 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.60/30.34 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.60/30.34 (42) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.60/30.34 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.60/30.34 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.60/30.34 (43) ~ (e3 = e2) % 189.60/30.34 (44) op(e4, e0) = e4 % 189.60/30.34 (45) all_252_22 = e4 % 189.60/30.34 (46) op(e4, all_20_2) = e0 % 189.60/30.34 (47) op(e0, e3) = all_8_1 % 189.60/30.34 (48) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.60/30.34 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.60/30.34 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.60/30.34 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.60/30.34 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.60/30.34 op(e0, e1) = e0))) % 189.60/30.34 (49) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.60/30.34 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.60/30.34 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.60/30.34 (50) ~ (e4 = e2) % 189.60/30.34 (51) op(e2, e0) = all_40_2 % 189.60/30.34 (52) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.60/30.34 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.60/30.34 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.60/30.34 (53) ~ (e1 = e0) % 189.60/30.34 (54) op(e0, e4) = all_12_2 % 189.60/30.34 (55) all_250_23 = all_20_2 % 189.60/30.34 (56) ~ (e3 = e1) % 189.60/30.34 (57) ~ (e2 = e0) % 189.60/30.34 (58) op(e1, e0) = all_34_2 % 189.60/30.34 (59) ~ (all_244_24 = e1) % 189.60/30.34 (60) ~ (all_12_2 = e3) % 189.60/30.34 (61) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.60/30.34 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.60/30.34 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.60/30.34 (62) ~ (all_34_2 = e2) % 189.60/30.34 (63) ~ (e4 = e1) % 189.60/30.34 (64) op(e2, e0) = e1 % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | BETA: splitting (11) gives: % 189.60/30.34 | % 189.60/30.34 | Case 1: % 189.60/30.34 | | % 189.60/30.34 | | (65) all_252_18 = e1 & op(e2, e0) = e1 % 189.60/30.34 | | % 189.60/30.34 | | ALPHA: (65) implies: % 189.60/30.34 | | (66) all_252_18 = e1 % 189.60/30.34 | | % 189.60/30.34 | | BETA: splitting (4) gives: % 189.60/30.34 | | % 189.60/30.34 | | Case 1: % 189.60/30.34 | | | % 189.60/30.34 | | | (67) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_7 = e3 & op(e2, e3) % 189.60/30.34 | | | = e3) % 189.60/30.34 | | | % 189.60/30.34 | | | BETA: splitting (67) gives: % 189.60/30.34 | | | % 189.60/30.34 | | | Case 1: % 189.60/30.34 | | | | % 189.60/30.34 | | | | (68) all_252_6 = e3 & op(e2, e4) = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | ALPHA: (68) implies: % 189.60/30.34 | | | | (69) all_252_6 = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12), (14), % 189.60/30.34 | | | | (15), (17), (18), (19), (20), (22), (23), (24), (25), (26), % 189.60/30.34 | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), % 189.60/30.34 | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), % 189.60/30.34 | | | | (47), (48), (49), (50), (51), (52), (53), (54), (55), (56), % 189.60/30.34 | | | | (57), (58), (60), (61), (62), (63), (64), (66), (69) are % 189.60/30.34 | | | | inconsistent by sub-proof #168. % 189.60/30.34 | | | | % 189.60/30.34 | | | Case 2: % 189.60/30.34 | | | | % 189.60/30.34 | | | | (70) all_252_7 = e3 & op(e2, e3) = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | REF_CLOSE: (16), (39), (70) are inconsistent by sub-proof #358. % 189.60/30.34 | | | | % 189.60/30.34 | | | End of split % 189.60/30.34 | | | % 189.60/30.34 | | Case 2: % 189.60/30.34 | | | % 189.60/30.34 | | | (71) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_11 = e3 & op(e2, e1) % 189.60/30.34 | | | = e3) | (all_252_18 = e3 & op(e2, e0) = e3) % 189.60/30.34 | | | % 189.60/30.34 | | | BETA: splitting (71) gives: % 189.60/30.34 | | | % 189.60/30.34 | | | Case 1: % 189.60/30.34 | | | | % 189.60/30.34 | | | | (72) all_252_8 = e3 & op(e2, e2) = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | ALPHA: (72) implies: % 189.60/30.34 | | | | (73) all_252_8 = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | COMBINE_EQS: (21), (73) imply: % 189.60/30.34 | | | | (74) e4 = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | SIMP: (74) implies: % 189.60/30.34 | | | | (75) e4 = e3 % 189.60/30.34 | | | | % 189.60/30.34 | | | | REDUCE: (19), (75) imply: % 189.60/30.34 | | | | (76) $false % 189.60/30.34 | | | | % 189.60/30.34 | | | | CLOSE: (76) is inconsistent. % 189.60/30.34 | | | | % 189.60/30.34 | | | Case 2: % 189.60/30.34 | | | | % 189.60/30.34 | | | | (77) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_18 = e3 & op(e2, % 189.60/30.34 | | | | e0) = e3) % 189.60/30.34 | | | | % 189.60/30.34 | | | | BETA: splitting (77) gives: % 189.60/30.34 | | | | % 189.60/30.34 | | | | Case 1: % 189.60/30.34 | | | | | % 189.60/30.34 | | | | | (78) all_252_11 = e3 & op(e2, e1) = e3 % 189.60/30.34 | | | | | % 189.60/30.34 | | | | | REF_CLOSE: (13), (43), (78) are inconsistent by sub-proof #146. % 189.60/30.34 | | | | | % 189.60/30.34 | | | | Case 2: % 189.60/30.34 | | | | | % 189.60/30.34 | | | | | (79) all_252_18 = e3 & op(e2, e0) = e3 % 189.60/30.34 | | | | | % 189.60/30.34 | | | | | REF_CLOSE: (56), (66), (79) are inconsistent by sub-proof #209. % 189.60/30.34 | | | | | % 189.60/30.34 | | | | End of split % 189.60/30.34 | | | | % 189.60/30.34 | | | End of split % 189.60/30.34 | | | % 189.60/30.34 | | End of split % 189.60/30.34 | | % 189.60/30.34 | Case 2: % 189.60/30.34 | | % 189.60/30.34 | | (80) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) % 189.60/30.34 | | = e1) % 189.60/30.34 | | % 189.60/30.34 | | REF_CLOSE: (5), (23), (28), (51), (58), (59), (64), (80) are inconsistent by % 189.60/30.34 | | sub-proof #166. % 189.60/30.34 | | % 189.60/30.34 | End of split % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #146 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_11 = e3 & op(e2, e1) = e3 % 189.60/30.34 (2) all_252_11 = e2 % 189.60/30.34 (3) ~ (e3 = e2) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_11 = e3 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e3 = e2 % 189.60/30.34 | % 189.60/30.34 | SIMP: (5) implies: % 189.60/30.34 | (6) e3 = e2 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (6) imply: % 189.60/30.34 | (7) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (7) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #147 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_4 = e3 & op(e4, e2) = e3 % 189.60/30.34 (2) all_252_4 = e2 % 189.60/30.34 (3) ~ (e3 = e2) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_4 = e3 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e3 = e2 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (5) imply: % 189.60/30.34 | (6) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (6) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #148 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_0 = e3 & op(e4, e4) = e3 % 189.60/30.34 (2) all_252_0 = e0 % 189.60/30.34 (3) ~ (e3 = e0) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_0 = e3 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e3 = e0 % 189.60/30.34 | % 189.60/30.34 | SIMP: (5) implies: % 189.60/30.34 | (6) e3 = e0 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (6) imply: % 189.60/30.34 | (7) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (7) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #149 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_3 = e1 & op(e3, e3) = e1 % 189.60/30.34 (2) all_252_3 = e4 % 189.60/30.34 (3) ~ (e4 = e1) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_3 = e1 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e4 = e1 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (5) imply: % 189.60/30.34 | (6) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (6) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #150 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_3 = e3 & op(e3, e3) = e3 % 189.60/30.34 (2) all_252_3 = e4 % 189.60/30.34 (3) ~ (e4 = e3) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_3 = e3 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e4 = e3 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (5) imply: % 189.60/30.34 | (6) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (6) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #151 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_2 = e3 & op(e3, e4) = e3 % 189.60/30.34 (2) all_252_2 = e1 % 189.60/30.34 (3) ~ (e3 = e1) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_2 = e3 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e3 = e1 % 189.60/30.34 | % 189.60/30.34 | SIMP: (5) implies: % 189.60/30.34 | (6) e3 = e1 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (6) imply: % 189.60/30.34 | (7) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (7) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #152 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_1 = e4 & op(e4, e3) = e4 % 189.60/30.34 (2) all_252_1 = e2 % 189.60/30.34 (3) ~ (e4 = e2) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_1 = e4 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e4 = e2 % 189.60/30.34 | % 189.60/30.34 | SIMP: (5) implies: % 189.60/30.34 | (6) e4 = e2 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (6) imply: % 189.60/30.34 | (7) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (7) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #153 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.34 (2) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.60/30.34 (3) ~ (e2 = e1) % 189.60/30.34 (4) op(e4, e0) = e3 % 189.60/30.34 (5) all_252_17 = e2 % 189.60/30.34 (6) ~ (e3 = e1) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | BETA: splitting (2) gives: % 189.60/30.34 | % 189.60/30.34 | Case 1: % 189.60/30.34 | | % 189.60/30.34 | | (7) all_252_16 = e1 & op(e4, e0) = e1 % 189.60/30.34 | | % 189.60/30.34 | | ALPHA: (7) implies: % 189.60/30.34 | | (8) op(e4, e0) = e1 % 189.60/30.34 | | % 189.60/30.34 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #387. % 189.60/30.34 | | % 189.60/30.34 | Case 2: % 189.60/30.34 | | % 189.60/30.34 | | (9) all_252_17 = e1 & op(e3, e0) = e1 % 189.60/30.34 | | % 189.60/30.34 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #247. % 189.60/30.34 | | % 189.60/30.34 | End of split % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #154 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.60/30.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.60/30.34 (2) op(e0, e2) = all_28_2 % 189.60/30.34 (3) ~ (e2 = e1) % 189.60/30.34 (4) all_252_8 = e4 % 189.60/30.34 (5) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = e2) | % 189.60/30.34 (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = e2) % 189.60/30.34 | (all_252_22 = e2 & op(e0, e2) = e2) % 189.60/30.34 (6) all_252_4 = e3 % 189.60/30.34 (7) all_252_14 = e1 % 189.60/30.34 (8) ~ (all_28_2 = e0) % 189.60/30.34 (9) op(e2, all_40_2) = e0 % 189.60/30.34 (10) ~ (e3 = e2) % 189.60/30.34 (11) ~ (e4 = e2) % 189.60/30.34 (12) op(all_28_2, all_40_2) = e2 % 189.60/30.34 (13) ~ (e2 = e0) % 189.60/30.34 (14) all_252_5 = e0 % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | BETA: splitting (5) gives: % 189.60/30.34 | % 189.60/30.34 | Case 1: % 189.60/30.34 | | % 189.60/30.34 | | (15) (all_252_4 = e2 & op(e4, e2) = e2) | (all_252_5 = e2 & op(e3, e2) = % 189.60/30.34 | | e2) % 189.60/30.34 | | % 189.60/30.34 | | BETA: splitting (15) gives: % 189.60/30.34 | | % 189.60/30.34 | | Case 1: % 189.60/30.34 | | | % 189.60/30.34 | | | (16) all_252_4 = e2 & op(e4, e2) = e2 % 189.60/30.34 | | | % 189.60/30.34 | | | REF_CLOSE: (6), (10), (16) are inconsistent by sub-proof #347. % 189.60/30.34 | | | % 189.60/30.34 | | Case 2: % 189.60/30.34 | | | % 189.60/30.34 | | | (17) all_252_5 = e2 & op(e3, e2) = e2 % 189.60/30.34 | | | % 189.60/30.34 | | | ALPHA: (17) implies: % 189.60/30.34 | | | (18) all_252_5 = e2 % 189.60/30.34 | | | % 189.60/30.34 | | | COMBINE_EQS: (14), (18) imply: % 189.60/30.34 | | | (19) e2 = e0 % 189.60/30.34 | | | % 189.60/30.34 | | | SIMP: (19) implies: % 189.60/30.34 | | | (20) e2 = e0 % 189.60/30.34 | | | % 189.60/30.34 | | | REDUCE: (13), (20) imply: % 189.60/30.34 | | | (21) $false % 189.60/30.34 | | | % 189.60/30.34 | | | CLOSE: (21) is inconsistent. % 189.60/30.34 | | | % 189.60/30.34 | | End of split % 189.60/30.34 | | % 189.60/30.34 | Case 2: % 189.60/30.34 | | % 189.60/30.34 | | (22) (all_252_8 = e2 & op(e2, e2) = e2) | (all_252_14 = e2 & op(e1, e2) = % 189.60/30.34 | | e2) | (all_252_22 = e2 & op(e0, e2) = e2) % 189.60/30.34 | | % 189.60/30.34 | | BETA: splitting (22) gives: % 189.60/30.34 | | % 189.60/30.34 | | Case 1: % 189.60/30.34 | | | % 189.60/30.34 | | | (23) all_252_8 = e2 & op(e2, e2) = e2 % 189.60/30.34 | | | % 189.60/30.34 | | | ALPHA: (23) implies: % 189.60/30.34 | | | (24) all_252_8 = e2 % 189.60/30.34 | | | % 189.60/30.34 | | | REF_CLOSE: (4), (11), (24) are inconsistent by sub-proof #163. % 189.60/30.34 | | | % 189.60/30.34 | | Case 2: % 189.60/30.34 | | | % 189.60/30.34 | | | (25) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_22 = e2 & op(e0, % 189.60/30.34 | | | e2) = e2) % 189.60/30.34 | | | % 189.60/30.34 | | | BETA: splitting (25) gives: % 189.60/30.34 | | | % 189.60/30.34 | | | Case 1: % 189.60/30.34 | | | | % 189.60/30.34 | | | | (26) all_252_14 = e2 & op(e1, e2) = e2 % 189.60/30.34 | | | | % 189.60/30.34 | | | | REF_CLOSE: (3), (7), (26) are inconsistent by sub-proof #422. % 189.60/30.34 | | | | % 189.60/30.34 | | | Case 2: % 189.60/30.34 | | | | % 189.60/30.34 | | | | (27) all_252_22 = e2 & op(e0, e2) = e2 % 189.60/30.34 | | | | % 189.60/30.34 | | | | ALPHA: (27) implies: % 189.60/30.34 | | | | (28) op(e0, e2) = e2 % 189.60/30.34 | | | | % 189.60/30.34 | | | | REF_CLOSE: (1), (2), (8), (9), (12), (28) are inconsistent by sub-proof % 189.60/30.34 | | | | #288. % 189.60/30.34 | | | | % 189.60/30.34 | | | End of split % 189.60/30.34 | | | % 189.60/30.34 | | End of split % 189.60/30.34 | | % 189.60/30.34 | End of split % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #155 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) all_252_5 = e1 & op(e3, e2) = e1 % 189.60/30.34 (2) all_252_5 = e0 % 189.60/30.34 (3) ~ (e1 = e0) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | ALPHA: (1) implies: % 189.60/30.34 | (4) all_252_5 = e1 % 189.60/30.34 | % 189.60/30.34 | COMBINE_EQS: (2), (4) imply: % 189.60/30.34 | (5) e1 = e0 % 189.60/30.34 | % 189.60/30.34 | SIMP: (5) implies: % 189.60/30.34 | (6) e1 = e0 % 189.60/30.34 | % 189.60/30.34 | REDUCE: (3), (6) imply: % 189.60/30.34 | (7) $false % 189.60/30.34 | % 189.60/30.34 | CLOSE: (7) is inconsistent. % 189.60/30.34 | % 189.60/30.34 End of proof % 189.60/30.34 % 189.60/30.34 Sub-proof #156 shows that the following formulas are inconsistent: % 189.60/30.34 ---------------------------------------------------------------- % 189.60/30.34 (1) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_1 = e3 & op(e4, e3) = e3) % 189.60/30.34 (2) ~ (e4 = e3) % 189.60/30.34 (3) all_252_1 = e2 % 189.60/30.34 (4) all_252_0 = e4 % 189.60/30.34 (5) ~ (e3 = e2) % 189.60/30.34 % 189.60/30.34 Begin of proof % 189.60/30.34 | % 189.60/30.34 | BETA: splitting (1) gives: % 189.60/30.34 | % 189.60/30.34 | Case 1: % 189.60/30.34 | | % 189.60/30.34 | | (6) all_252_0 = e3 & op(e4, e4) = e3 % 189.60/30.34 | | % 189.60/30.34 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #235. % 189.60/30.34 | | % 189.60/30.34 | Case 2: % 189.60/30.34 | | % 189.60/30.34 | | (7) all_252_1 = e3 & op(e4, e3) = e3 % 189.60/30.34 | | % 189.60/30.34 | | ALPHA: (7) implies: % 189.60/30.34 | | (8) all_252_1 = e3 % 189.60/30.34 | | % 189.60/30.34 | | COMBINE_EQS: (3), (8) imply: % 189.69/30.34 | | (9) e3 = e2 % 189.69/30.34 | | % 189.69/30.34 | | SIMP: (9) implies: % 189.69/30.34 | | (10) e3 = e2 % 189.69/30.34 | | % 189.69/30.34 | | REDUCE: (5), (10) imply: % 189.69/30.34 | | (11) $false % 189.69/30.34 | | % 189.69/30.34 | | CLOSE: (11) is inconsistent. % 189.69/30.34 | | % 189.69/30.34 | End of split % 189.69/30.34 | % 189.69/30.34 End of proof % 189.69/30.34 % 189.69/30.34 Sub-proof #157 shows that the following formulas are inconsistent: % 189.69/30.34 ---------------------------------------------------------------- % 189.69/30.34 (1) all_252_20 = e2 % 189.69/30.34 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.34 (3) ~ (all_20_2 = e4) % 189.69/30.34 (4) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_18 = e4 & op(e2, e0) = e4) % 189.69/30.34 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.34 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.34 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.34 (6) op(e0, e2) = e4 % 189.69/30.34 (7) op(e3, e1) = all_36_2 % 189.69/30.34 (8) ~ (e2 = e1) % 189.69/30.34 (9) all_252_12 = e0 % 189.69/30.34 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.34 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.34 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.34 (11) op(e2, e1) = e0 % 189.69/30.34 (12) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.34 all_250_23 = e0 % 189.69/30.34 (13) ~ (e4 = e0) % 189.69/30.34 (14) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.69/30.34 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.69/30.34 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.34 (15) ~ (e4 = e3) % 189.69/30.34 (16) ~ (all_36_2 = e2) % 189.69/30.34 (17) all_252_9 = e0 % 189.69/30.34 (18) ~ (all_40_2 = all_34_2) % 189.69/30.34 (19) ~ (all_244_24 = all_20_2) % 189.69/30.34 (20) op(e1, e4) = e0 % 189.69/30.34 (21) ~ (all_20_2 = e3) % 189.69/30.34 (22) op(all_20_2, e4) = e1 % 189.69/30.34 (23) op(e0, e0) = all_244_24 % 189.69/30.34 (24) op(e0, e1) = all_20_2 % 189.69/30.34 (25) all_252_19 = e4 % 189.69/30.34 (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.34 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.34 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.34 (27) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.69/30.34 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.34 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.34 (28) ~ (all_20_2 = e0) % 189.69/30.34 (29) all_252_11 = e3 % 189.69/30.34 (30) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.34 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.34 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.34 (31) all_252_17 = e2 % 189.69/30.34 (32) ~ (all_20_2 = e2) % 189.69/30.34 (33) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.34 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.34 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.34 (34) op(e0, e4) = e2 % 189.69/30.34 (35) ~ (e3 = e0) % 189.69/30.34 (36) ~ (all_20_2 = all_8_1) % 189.69/30.34 (37) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.34 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.34 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.35 (38) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.35 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.35 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.35 (39) ~ (e3 = e2) % 189.69/30.35 (40) all_252_22 = e4 % 189.69/30.35 (41) op(e4, all_20_2) = e0 % 189.69/30.35 (42) op(e0, e3) = all_8_1 % 189.69/30.35 (43) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.35 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.35 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.35 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.35 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.35 op(e0, e1) = e0))) % 189.69/30.35 (44) ~ (e4 = e2) % 189.69/30.35 (45) op(e2, e0) = all_40_2 % 189.69/30.35 (46) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.35 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.35 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.35 (47) ~ (e1 = e0) % 189.69/30.35 (48) all_250_23 = all_20_2 % 189.69/30.35 (49) ~ (e3 = e1) % 189.69/30.35 (50) ~ (e2 = e0) % 189.69/30.35 (51) op(e1, e0) = all_34_2 % 189.69/30.35 (52) ~ (all_34_2 = e2) % 189.69/30.35 (53) ~ (e4 = e1) % 189.69/30.35 (54) op(e2, e0) = e1 % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | BETA: splitting (4) gives: % 189.69/30.35 | % 189.69/30.35 | Case 1: % 189.69/30.35 | | % 189.69/30.35 | | (55) all_252_11 = e4 & op(e2, e1) = e4 % 189.69/30.35 | | % 189.69/30.35 | | ALPHA: (55) implies: % 189.69/30.35 | | (56) all_252_11 = e4 % 189.69/30.35 | | % 189.69/30.35 | | COMBINE_EQS: (29), (56) imply: % 189.69/30.35 | | (57) e4 = e3 % 189.69/30.35 | | % 189.69/30.35 | | REDUCE: (15), (57) imply: % 189.69/30.35 | | (58) $false % 189.69/30.35 | | % 189.69/30.35 | | CLOSE: (58) is inconsistent. % 189.69/30.35 | | % 189.69/30.35 | Case 2: % 189.69/30.35 | | % 189.69/30.35 | | (59) all_252_18 = e4 & op(e2, e0) = e4 % 189.69/30.35 | | % 189.69/30.35 | | ALPHA: (59) implies: % 189.69/30.35 | | (60) all_252_18 = e4 % 189.69/30.35 | | % 189.69/30.35 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 189.69/30.35 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 189.69/30.35 | | (25), (26), (27), (28), (30), (31), (32), (33), (34), (35), (36), % 189.69/30.35 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), % 189.69/30.35 | | (48), (49), (50), (51), (52), (53), (54), (60) are inconsistent % 189.69/30.35 | | by sub-proof #158. % 189.69/30.35 | | % 189.69/30.35 | End of split % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #158 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) all_252_20 = e2 % 189.69/30.35 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.35 (3) ~ (all_20_2 = e4) % 189.69/30.35 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.35 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.35 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.35 (5) op(e0, e2) = e4 % 189.69/30.35 (6) op(e3, e1) = all_36_2 % 189.69/30.35 (7) ~ (e2 = e1) % 189.69/30.35 (8) all_252_12 = e0 % 189.69/30.35 (9) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.35 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.35 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.35 (10) op(e2, e1) = e0 % 189.69/30.35 (11) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.35 all_250_23 = e0 % 189.69/30.35 (12) ~ (e4 = e0) % 189.69/30.35 (13) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.69/30.35 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.69/30.35 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.35 (14) ~ (e4 = e3) % 189.69/30.35 (15) ~ (all_36_2 = e2) % 189.69/30.35 (16) all_252_9 = e0 % 189.69/30.35 (17) ~ (all_40_2 = all_34_2) % 189.69/30.35 (18) ~ (all_244_24 = all_20_2) % 189.69/30.35 (19) op(e1, e4) = e0 % 189.69/30.35 (20) ~ (all_20_2 = e3) % 189.69/30.35 (21) op(all_20_2, e4) = e1 % 189.69/30.35 (22) op(e0, e0) = all_244_24 % 189.69/30.35 (23) op(e0, e1) = all_20_2 % 189.69/30.35 (24) all_252_19 = e4 % 189.69/30.35 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.35 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.35 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.35 (26) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.69/30.35 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.35 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.35 (27) ~ (all_20_2 = e0) % 189.69/30.35 (28) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.35 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.35 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.35 (29) all_252_17 = e2 % 189.69/30.35 (30) ~ (all_20_2 = e2) % 189.69/30.35 (31) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.35 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.35 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.35 (32) op(e0, e4) = e2 % 189.69/30.35 (33) ~ (e3 = e0) % 189.69/30.35 (34) ~ (all_20_2 = all_8_1) % 189.69/30.35 (35) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.35 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.35 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.35 (36) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.35 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.35 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.35 (37) ~ (e3 = e2) % 189.69/30.35 (38) all_252_22 = e4 % 189.69/30.35 (39) op(e4, all_20_2) = e0 % 189.69/30.35 (40) op(e0, e3) = all_8_1 % 189.69/30.35 (41) all_252_18 = e4 % 189.69/30.35 (42) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.35 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.35 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.35 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.35 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.35 op(e0, e1) = e0))) % 189.69/30.35 (43) ~ (e4 = e2) % 189.69/30.35 (44) op(e2, e0) = all_40_2 % 189.69/30.35 (45) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.35 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.35 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.35 (46) ~ (e1 = e0) % 189.69/30.35 (47) all_250_23 = all_20_2 % 189.69/30.35 (48) ~ (e3 = e1) % 189.69/30.35 (49) ~ (e2 = e0) % 189.69/30.35 (50) op(e1, e0) = all_34_2 % 189.69/30.35 (51) ~ (all_34_2 = e2) % 189.69/30.35 (52) ~ (e4 = e1) % 189.69/30.35 (53) op(e2, e0) = e1 % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | BETA: splitting (26) gives: % 189.69/30.35 | % 189.69/30.35 | Case 1: % 189.69/30.35 | | % 189.69/30.35 | | (54) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) % 189.69/30.35 | | = e3) % 189.69/30.35 | | % 189.69/30.35 | | BETA: splitting (54) gives: % 189.69/30.35 | | % 189.69/30.35 | | Case 1: % 189.69/30.35 | | | % 189.69/30.35 | | | (55) all_252_16 = e3 & op(e4, e0) = e3 % 189.69/30.35 | | | % 189.69/30.35 | | | REF_CLOSE: (2), (7), (12), (13), (24), (29), (33), (41), (42), (46), (48), % 189.69/30.35 | | | (49), (52), (55) are inconsistent by sub-proof #160. % 189.69/30.35 | | | % 189.69/30.35 | | Case 2: % 189.69/30.35 | | | % 189.69/30.35 | | | (56) all_252_17 = e3 & op(e3, e0) = e3 % 189.69/30.35 | | | % 189.69/30.35 | | | REF_CLOSE: (29), (37), (56) are inconsistent by sub-proof #159. % 189.69/30.35 | | | % 189.69/30.35 | | End of split % 189.69/30.35 | | % 189.69/30.35 | Case 2: % 189.69/30.35 | | % 189.69/30.35 | | (57) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) % 189.69/30.35 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.35 | | % 189.69/30.35 | | BETA: splitting (57) gives: % 189.69/30.35 | | % 189.69/30.35 | | Case 1: % 189.69/30.35 | | | % 189.69/30.35 | | | (58) all_252_18 = e3 & op(e2, e0) = e3 % 189.69/30.35 | | | % 189.69/30.35 | | | REF_CLOSE: (14), (41), (58) are inconsistent by sub-proof #355. % 189.69/30.35 | | | % 189.69/30.35 | | Case 2: % 189.69/30.35 | | | % 189.69/30.35 | | | (59) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, % 189.69/30.35 | | | e0) = e3) % 189.69/30.35 | | | % 189.69/30.35 | | | BETA: splitting (59) gives: % 189.69/30.35 | | | % 189.69/30.35 | | | Case 1: % 189.69/30.35 | | | | % 189.69/30.35 | | | | (60) all_252_19 = e3 & op(e1, e0) = e3 % 189.69/30.35 | | | | % 189.69/30.35 | | | | REF_CLOSE: (14), (24), (60) are inconsistent by sub-proof #177. % 189.69/30.35 | | | | % 189.69/30.35 | | | Case 2: % 189.69/30.35 | | | | % 189.69/30.35 | | | | (61) all_252_24 = e3 & op(e0, e0) = e3 % 189.69/30.35 | | | | % 189.69/30.35 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), % 189.69/30.35 | | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), % 189.69/30.35 | | | | (24), (25), (27), (28), (30), (31), (32), (33), (34), (35), % 189.69/30.35 | | | | (36), (37), (38), (39), (40), (42), (43), (44), (45), (47), % 189.69/30.35 | | | | (49), (50), (51), (53), (61) are inconsistent by sub-proof % 189.69/30.35 | | | | #169. % 189.69/30.35 | | | | % 189.69/30.35 | | | End of split % 189.69/30.35 | | | % 189.69/30.35 | | End of split % 189.69/30.35 | | % 189.69/30.35 | End of split % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #159 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) all_252_17 = e3 & op(e3, e0) = e3 % 189.69/30.35 (2) all_252_17 = e2 % 189.69/30.35 (3) ~ (e3 = e2) % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | ALPHA: (1) implies: % 189.69/30.35 | (4) all_252_17 = e3 % 189.69/30.35 | % 189.69/30.35 | COMBINE_EQS: (2), (4) imply: % 189.69/30.35 | (5) e3 = e2 % 189.69/30.35 | % 189.69/30.35 | SIMP: (5) implies: % 189.69/30.35 | (6) e3 = e2 % 189.69/30.35 | % 189.69/30.35 | REDUCE: (3), (6) imply: % 189.69/30.35 | (7) $false % 189.69/30.35 | % 189.69/30.35 | CLOSE: (7) is inconsistent. % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #160 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.35 (2) ~ (e2 = e1) % 189.69/30.35 (3) ~ (e4 = e0) % 189.69/30.35 (4) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 189.69/30.35 | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0) = % 189.69/30.35 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.35 (5) all_252_19 = e4 % 189.69/30.35 (6) all_252_17 = e2 % 189.69/30.35 (7) ~ (e3 = e0) % 189.69/30.35 (8) all_252_18 = e4 % 189.69/30.35 (9) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.35 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.35 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.35 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.35 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.35 op(e0, e1) = e0))) % 189.69/30.35 (10) ~ (e1 = e0) % 189.69/30.35 (11) all_252_16 = e3 & op(e4, e0) = e3 % 189.69/30.35 (12) ~ (e3 = e1) % 189.69/30.35 (13) ~ (e2 = e0) % 189.69/30.35 (14) ~ (e4 = e1) % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | ALPHA: (11) implies: % 189.69/30.35 | (15) op(e4, e0) = e3 % 189.69/30.35 | % 189.69/30.35 | BETA: splitting (4) gives: % 189.69/30.35 | % 189.69/30.35 | Case 1: % 189.69/30.35 | | % 189.69/30.35 | | (16) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) % 189.69/30.35 | | = e1) % 189.69/30.35 | | % 189.69/30.35 | | BETA: splitting (16) gives: % 189.69/30.35 | | % 189.69/30.35 | | Case 1: % 189.69/30.35 | | | % 189.69/30.35 | | | (17) all_252_16 = e1 & op(e4, e0) = e1 % 189.69/30.35 | | | % 189.69/30.35 | | | ALPHA: (17) implies: % 189.69/30.35 | | | (18) op(e4, e0) = e1 % 189.69/30.35 | | | % 189.69/30.35 | | | REF_CLOSE: (1), (12), (15), (18) are inconsistent by sub-proof #387. % 189.69/30.35 | | | % 189.69/30.35 | | Case 2: % 189.69/30.35 | | | % 189.69/30.35 | | | (19) all_252_17 = e1 & op(e3, e0) = e1 % 189.69/30.35 | | | % 189.69/30.35 | | | REF_CLOSE: (2), (6), (19) are inconsistent by sub-proof #162. % 189.69/30.35 | | | % 189.69/30.35 | | End of split % 189.69/30.35 | | % 189.69/30.35 | Case 2: % 189.69/30.35 | | % 189.69/30.35 | | (20) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, e0) % 189.69/30.35 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.35 | | % 189.69/30.35 | | BETA: splitting (20) gives: % 189.69/30.35 | | % 189.69/30.35 | | Case 1: % 189.69/30.35 | | | % 189.69/30.35 | | | (21) all_252_18 = e1 & op(e2, e0) = e1 % 189.69/30.35 | | | % 189.69/30.35 | | | REF_CLOSE: (8), (14), (21) are inconsistent by sub-proof #246. % 189.69/30.35 | | | % 189.69/30.35 | | Case 2: % 189.69/30.35 | | | % 189.69/30.35 | | | (22) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, % 189.69/30.35 | | | e0) = e1) % 189.69/30.35 | | | % 189.69/30.35 | | | BETA: splitting (22) gives: % 189.69/30.35 | | | % 189.69/30.35 | | | Case 1: % 189.69/30.35 | | | | % 189.69/30.35 | | | | (23) all_252_19 = e1 & op(e1, e0) = e1 % 189.69/30.35 | | | | % 189.69/30.35 | | | | ALPHA: (23) implies: % 189.69/30.35 | | | | (24) all_252_19 = e1 % 189.69/30.35 | | | | % 189.69/30.35 | | | | COMBINE_EQS: (5), (24) imply: % 189.69/30.35 | | | | (25) e4 = e1 % 189.69/30.35 | | | | % 189.69/30.35 | | | | SIMP: (25) implies: % 189.69/30.35 | | | | (26) e4 = e1 % 189.69/30.35 | | | | % 189.69/30.35 | | | | REDUCE: (14), (26) imply: % 189.69/30.35 | | | | (27) $false % 189.69/30.35 | | | | % 189.69/30.35 | | | | CLOSE: (27) is inconsistent. % 189.69/30.35 | | | | % 189.69/30.35 | | | Case 2: % 189.69/30.35 | | | | % 189.69/30.35 | | | | (28) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.35 | | | | % 189.69/30.35 | | | | ALPHA: (28) implies: % 189.69/30.35 | | | | (29) all_252_24 = e1 % 189.69/30.35 | | | | % 189.69/30.35 | | | | BETA: splitting (9) gives: % 189.69/30.35 | | | | % 189.69/30.35 | | | | Case 1: % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | (30) all_252_24 = e0 & op(e0, e0) = e0 % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | ALPHA: (30) implies: % 189.69/30.35 | | | | | (31) all_252_24 = e0 % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | COMBINE_EQS: (29), (31) imply: % 189.69/30.35 | | | | | (32) e1 = e0 % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | REDUCE: (10), (32) imply: % 189.69/30.35 | | | | | (33) $false % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | CLOSE: (33) is inconsistent. % 189.69/30.35 | | | | | % 189.69/30.35 | | | | Case 2: % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | (34) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & % 189.69/30.35 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | % 189.69/30.35 | | | | | (all_252_19 = e0 & op(e1, e0) = e0)) & ((all_252_20 = e0 & % 189.69/30.35 | | | | | op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) | % 189.69/30.35 | | | | | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.35 | | | | | op(e0, e1) = e0)) % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | ALPHA: (34) implies: % 189.69/30.35 | | | | | (35) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & % 189.69/30.35 | | | | | op(e3, e0) = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | % 189.69/30.35 | | | | | (all_252_19 = e0 & op(e1, e0) = e0) % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | BETA: splitting (35) gives: % 189.69/30.35 | | | | | % 189.69/30.35 | | | | | Case 1: % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | | (36) (all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & % 189.69/30.35 | | | | | | op(e3, e0) = e0) % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | | BETA: splitting (36) gives: % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | | Case 1: % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | (37) all_252_16 = e0 & op(e4, e0) = e0 % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | REF_CLOSE: (1), (7), (15), (37) are inconsistent by sub-proof % 189.69/30.35 | | | | | | | #342. % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | Case 2: % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | (38) all_252_17 = e0 & op(e3, e0) = e0 % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | ALPHA: (38) implies: % 189.69/30.35 | | | | | | | (39) all_252_17 = e0 % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | COMBINE_EQS: (6), (39) imply: % 189.69/30.35 | | | | | | | (40) e2 = e0 % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | REDUCE: (13), (40) imply: % 189.69/30.35 | | | | | | | (41) $false % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | CLOSE: (41) is inconsistent. % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | End of split % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | Case 2: % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | | (42) (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & % 189.69/30.35 | | | | | | op(e1, e0) = e0) % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | | BETA: splitting (42) gives: % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | | Case 1: % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | (43) all_252_18 = e0 & op(e2, e0) = e0 % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | REF_CLOSE: (3), (8), (43) are inconsistent by sub-proof #359. % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | Case 2: % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | (44) all_252_19 = e0 & op(e1, e0) = e0 % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | | REF_CLOSE: (3), (5), (44) are inconsistent by sub-proof #161. % 189.69/30.35 | | | | | | | % 189.69/30.35 | | | | | | End of split % 189.69/30.35 | | | | | | % 189.69/30.35 | | | | | End of split % 189.69/30.35 | | | | | % 189.69/30.35 | | | | End of split % 189.69/30.35 | | | | % 189.69/30.35 | | | End of split % 189.69/30.35 | | | % 189.69/30.35 | | End of split % 189.69/30.35 | | % 189.69/30.35 | End of split % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #161 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) all_252_19 = e0 & op(e1, e0) = e0 % 189.69/30.35 (2) all_252_19 = e4 % 189.69/30.35 (3) ~ (e4 = e0) % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | ALPHA: (1) implies: % 189.69/30.35 | (4) all_252_19 = e0 % 189.69/30.35 | % 189.69/30.35 | COMBINE_EQS: (2), (4) imply: % 189.69/30.35 | (5) e4 = e0 % 189.69/30.35 | % 189.69/30.35 | SIMP: (5) implies: % 189.69/30.35 | (6) e4 = e0 % 189.69/30.35 | % 189.69/30.35 | REDUCE: (3), (6) imply: % 189.69/30.35 | (7) $false % 189.69/30.35 | % 189.69/30.35 | CLOSE: (7) is inconsistent. % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #162 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) all_252_17 = e1 & op(e3, e0) = e1 % 189.69/30.35 (2) all_252_17 = e2 % 189.69/30.35 (3) ~ (e2 = e1) % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | ALPHA: (1) implies: % 189.69/30.35 | (4) all_252_17 = e1 % 189.69/30.35 | % 189.69/30.35 | COMBINE_EQS: (2), (4) imply: % 189.69/30.35 | (5) e2 = e1 % 189.69/30.35 | % 189.69/30.35 | REDUCE: (3), (5) imply: % 189.69/30.35 | (6) $false % 189.69/30.35 | % 189.69/30.35 | CLOSE: (6) is inconsistent. % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #163 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) all_252_8 = e4 % 189.69/30.35 (2) all_252_8 = e2 % 189.69/30.35 (3) ~ (e4 = e2) % 189.69/30.35 % 189.69/30.35 Begin of proof % 189.69/30.35 | % 189.69/30.35 | COMBINE_EQS: (1), (2) imply: % 189.69/30.35 | (4) e4 = e2 % 189.69/30.35 | % 189.69/30.35 | SIMP: (4) implies: % 189.69/30.35 | (5) e4 = e2 % 189.69/30.35 | % 189.69/30.35 | REDUCE: (3), (5) imply: % 189.69/30.35 | (6) $false % 189.69/30.35 | % 189.69/30.35 | CLOSE: (6) is inconsistent. % 189.69/30.35 | % 189.69/30.35 End of proof % 189.69/30.35 % 189.69/30.35 Sub-proof #164 shows that the following formulas are inconsistent: % 189.69/30.35 ---------------------------------------------------------------- % 189.69/30.35 (1) all_252_20 = e2 % 189.69/30.35 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.69/30.35 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.69/30.35 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.69/30.35 (3) all_252_10 = e4 % 189.69/30.35 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.69/30.35 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.69/30.35 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.69/30.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.35 (6) ~ (all_20_2 = e4) % 189.69/30.35 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.35 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.35 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.35 (8) op(e0, e2) = e4 % 189.69/30.35 (9) op(e3, e1) = all_36_2 % 189.69/30.35 (10) ~ (e2 = e1) % 189.69/30.35 (11) all_252_12 = e0 % 189.69/30.35 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.35 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.35 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.35 (13) op(e2, e1) = e0 % 189.69/30.35 (14) all_252_7 = e0 % 189.69/30.35 (15) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.35 all_250_23 = e0 % 189.69/30.35 (16) ~ (e4 = e0) % 189.69/30.35 (17) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) = e4) % 189.69/30.35 | (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) = % 189.69/30.35 e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.69/30.35 (18) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & op(e3, e0) = % 189.69/30.35 e1) | (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & op(e1, % 189.69/30.35 e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.35 (19) ~ (e4 = e3) % 189.69/30.35 (20) ~ (all_36_2 = e2) % 189.69/30.35 (21) all_252_9 = e0 % 189.69/30.35 (22) ~ (all_40_2 = all_34_2) % 189.69/30.35 (23) ~ (all_244_24 = all_20_2) % 189.69/30.35 (24) op(e1, e4) = e0 % 189.69/30.35 (25) ~ (all_6_2 = e4) % 189.69/30.35 (26) ~ (all_20_2 = e3) % 189.69/30.35 (27) op(all_20_2, e4) = e1 % 189.69/30.35 (28) op(e0, e0) = all_244_24 % 189.69/30.35 (29) op(e0, e1) = all_20_2 % 189.69/30.35 (30) all_252_19 = e4 % 189.69/30.35 (31) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.35 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.35 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.35 (32) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.69/30.35 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.35 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.35 (33) ~ (all_20_2 = e0) % 189.69/30.36 (34) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.36 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.36 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.36 (35) all_252_17 = e2 % 189.69/30.36 (36) ~ (all_20_2 = e2) % 189.69/30.36 (37) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.36 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.36 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.36 (38) all_252_1 = e2 % 189.69/30.36 (39) op(e0, e4) = e2 % 189.69/30.36 (40) ~ (e3 = e0) % 189.69/30.36 (41) ~ (all_20_2 = all_8_1) % 189.69/30.36 (42) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.36 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.36 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.36 (43) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.36 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.36 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.36 (44) ~ (e3 = e2) % 189.69/30.36 (45) all_252_22 = e4 % 189.69/30.36 (46) op(e4, all_20_2) = e0 % 189.69/30.36 (47) op(e0, e3) = all_8_1 % 189.69/30.36 (48) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_7 = e4 & op(e2, e3) = e4) % 189.69/30.36 (49) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.36 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.36 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.36 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.36 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.36 op(e0, e1) = e0))) % 189.69/30.36 (50) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.69/30.36 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.69/30.36 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.69/30.36 (51) ~ (e4 = e2) % 189.69/30.36 (52) op(e2, e0) = all_40_2 % 189.69/30.36 (53) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.36 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.36 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.36 (54) ~ (e1 = e0) % 189.69/30.36 (55) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 189.69/30.36 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 189.69/30.36 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 189.69/30.36 (56) op(e0, e4) = all_12_2 % 189.69/30.36 (57) all_250_23 = all_20_2 % 189.69/30.36 (58) ~ (e3 = e1) % 189.69/30.36 (59) ~ (e2 = e0) % 189.69/30.36 (60) op(e1, e0) = all_34_2 % 189.69/30.36 (61) ~ (all_244_24 = e1) % 189.69/30.36 (62) ~ (all_12_2 = e3) % 189.69/30.36 (63) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.69/30.36 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.69/30.36 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.69/30.36 (64) ~ (all_34_2 = e2) % 189.69/30.36 (65) op(e4, e2) = all_6_2 % 189.69/30.36 (66) all_252_5 = e0 % 189.69/30.36 (67) ~ (e4 = e1) % 189.69/30.36 (68) op(e2, e0) = e1 % 189.69/30.36 % 189.69/30.36 Begin of proof % 189.69/30.36 | % 189.69/30.36 | BETA: splitting (48) gives: % 189.69/30.36 | % 189.69/30.36 | Case 1: % 189.69/30.36 | | % 189.69/30.36 | | (69) all_252_6 = e4 & op(e2, e4) = e4 % 189.69/30.36 | | % 189.69/30.36 | | ALPHA: (69) implies: % 189.69/30.36 | | (70) all_252_6 = e4 % 189.69/30.36 | | % 189.69/30.36 | | BETA: splitting (17) gives: % 189.69/30.36 | | % 189.69/30.36 | | Case 1: % 189.69/30.36 | | | % 189.69/30.36 | | | (71) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_1 = e4 & op(e4, e3) % 189.69/30.36 | | | = e4) % 189.69/30.36 | | | % 189.69/30.36 | | | BETA: splitting (71) gives: % 189.69/30.36 | | | % 189.69/30.36 | | | Case 1: % 189.69/30.36 | | | | % 189.69/30.36 | | | | (72) all_252_0 = e4 & op(e4, e4) = e4 % 189.69/30.36 | | | | % 189.69/30.36 | | | | ALPHA: (72) implies: % 189.69/30.36 | | | | (73) all_252_0 = e4 % 189.69/30.36 | | | | % 189.69/30.36 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (10), (11), (16), (19), (35), (39), % 189.69/30.36 | | | | (40), (44), (50), (51), (54), (55), (56), (58), (59), (62), % 189.69/30.36 | | | | (63), (66), (67), (70), (73) are inconsistent by sub-proof % 189.69/30.36 | | | | #213. % 189.69/30.36 | | | | % 189.69/30.36 | | | Case 2: % 189.69/30.36 | | | | % 189.69/30.36 | | | | (74) all_252_1 = e4 & op(e4, e3) = e4 % 189.69/30.36 | | | | % 189.69/30.36 | | | | REF_CLOSE: (1), (2), (4), (5), (10), (11), (16), (19), (38), (39), (40), % 189.69/30.36 | | | | (44), (50), (51), (54), (56), (58), (59), (62), (63), (67), % 189.69/30.36 | | | | (70), (74) are inconsistent by sub-proof #212. % 189.69/30.36 | | | | % 189.69/30.36 | | | End of split % 189.69/30.36 | | | % 189.69/30.36 | | Case 2: % 189.69/30.36 | | | % 189.69/30.36 | | | (75) (all_252_4 = e4 & op(e4, e2) = e4) | (all_252_9 = e4 & op(e4, e1) % 189.69/30.36 | | | = e4) | (all_252_16 = e4 & op(e4, e0) = e4) % 189.69/30.36 | | | % 189.69/30.36 | | | BETA: splitting (75) gives: % 189.69/30.36 | | | % 189.69/30.36 | | | Case 1: % 189.69/30.36 | | | | % 189.69/30.36 | | | | (76) all_252_4 = e4 & op(e4, e2) = e4 % 189.69/30.36 | | | | % 189.69/30.36 | | | | REF_CLOSE: (5), (25), (65), (76) are inconsistent by sub-proof #388. % 189.69/30.36 | | | | % 189.69/30.36 | | | Case 2: % 189.69/30.36 | | | | % 189.69/30.36 | | | | (77) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_16 = e4 & op(e4, % 189.69/30.36 | | | | e0) = e4) % 189.69/30.36 | | | | % 189.69/30.36 | | | | BETA: splitting (77) gives: % 189.69/30.36 | | | | % 189.69/30.36 | | | | Case 1: % 189.69/30.36 | | | | | % 189.69/30.36 | | | | | (78) all_252_9 = e4 & op(e4, e1) = e4 % 189.69/30.36 | | | | | % 189.69/30.36 | | | | | REF_CLOSE: (16), (21), (78) are inconsistent by sub-proof #211. % 189.69/30.36 | | | | | % 189.69/30.36 | | | | Case 2: % 189.69/30.36 | | | | | % 189.69/30.36 | | | | | (79) all_252_16 = e4 & op(e4, e0) = e4 % 189.69/30.36 | | | | | % 189.69/30.36 | | | | | ALPHA: (79) implies: % 189.69/30.36 | | | | | (80) all_252_16 = e4 % 189.69/30.36 | | | | | (81) op(e4, e0) = e4 % 189.69/30.36 | | | | | % 189.69/30.36 | | | | | BETA: splitting (18) gives: % 189.69/30.36 | | | | | % 189.69/30.36 | | | | | Case 1: % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | | (82) (all_252_16 = e1 & op(e4, e0) = e1) | (all_252_17 = e1 & % 189.69/30.36 | | | | | | op(e3, e0) = e1) % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | | BETA: splitting (82) gives: % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | | Case 1: % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | (83) all_252_16 = e1 & op(e4, e0) = e1 % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | REF_CLOSE: (67), (80), (83) are inconsistent by sub-proof #538. % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | Case 2: % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | (84) all_252_17 = e1 & op(e3, e0) = e1 % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | REF_CLOSE: (10), (35), (84) are inconsistent by sub-proof #247. % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | End of split % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | Case 2: % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | | (85) (all_252_18 = e1 & op(e2, e0) = e1) | (all_252_19 = e1 & % 189.69/30.36 | | | | | | op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | | BETA: splitting (85) gives: % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | | Case 1: % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | (86) all_252_18 = e1 & op(e2, e0) = e1 % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | ALPHA: (86) implies: % 189.69/30.36 | | | | | | | (87) all_252_18 = e1 % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), % 189.69/30.36 | | | | | | | (12), (13), (15), (16), (19), (20), (21), (22), (23), % 189.69/30.36 | | | | | | | (24), (26), (27), (28), (29), (30), (31), (32), (33), % 189.69/30.36 | | | | | | | (34), (35), (36), (37), (39), (40), (41), (42), (43), % 189.69/30.36 | | | | | | | (44), (45), (46), (47), (49), (50), (51), (52), (53), % 189.69/30.36 | | | | | | | (54), (56), (57), (58), (59), (60), (62), (63), (64), % 189.69/30.36 | | | | | | | (67), (68), (70), (81), (87) are inconsistent by % 189.69/30.36 | | | | | | | sub-proof #167. % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | Case 2: % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | (88) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & % 189.69/30.36 | | | | | | | op(e0, e0) = e1) % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | | REF_CLOSE: (5), (22), (28), (52), (60), (61), (68), (88) are % 189.69/30.36 | | | | | | | inconsistent by sub-proof #166. % 189.69/30.36 | | | | | | | % 189.69/30.36 | | | | | | End of split % 189.69/30.36 | | | | | | % 189.69/30.36 | | | | | End of split % 189.69/30.36 | | | | | % 189.69/30.36 | | | | End of split % 189.69/30.36 | | | | % 189.69/30.36 | | | End of split % 189.69/30.36 | | | % 189.69/30.36 | | End of split % 189.69/30.36 | | % 189.69/30.36 | Case 2: % 189.69/30.36 | | % 189.69/30.36 | | (89) all_252_7 = e4 & op(e2, e3) = e4 % 189.69/30.36 | | % 189.69/30.36 | | REF_CLOSE: (14), (16), (89) are inconsistent by sub-proof #165. % 189.69/30.36 | | % 189.69/30.36 | End of split % 189.69/30.36 | % 189.69/30.36 End of proof % 189.69/30.36 % 189.69/30.36 Sub-proof #165 shows that the following formulas are inconsistent: % 189.69/30.36 ---------------------------------------------------------------- % 189.69/30.36 (1) all_252_7 = e4 & op(e2, e3) = e4 % 189.69/30.36 (2) all_252_7 = e0 % 189.69/30.36 (3) ~ (e4 = e0) % 189.69/30.36 % 189.69/30.36 Begin of proof % 189.69/30.36 | % 189.69/30.36 | ALPHA: (1) implies: % 189.69/30.36 | (4) all_252_7 = e4 % 189.69/30.36 | % 189.69/30.36 | COMBINE_EQS: (2), (4) imply: % 189.69/30.36 | (5) e4 = e0 % 189.69/30.36 | % 189.69/30.36 | REDUCE: (3), (5) imply: % 189.69/30.36 | (6) $false % 189.69/30.36 | % 189.69/30.36 | CLOSE: (6) is inconsistent. % 189.69/30.36 | % 189.69/30.36 End of proof % 189.69/30.36 % 189.69/30.36 Sub-proof #166 shows that the following formulas are inconsistent: % 189.69/30.36 ---------------------------------------------------------------- % 189.69/30.36 (1) (all_252_19 = e1 & op(e1, e0) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.36 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.36 (3) ~ (all_40_2 = all_34_2) % 189.69/30.36 (4) op(e0, e0) = all_244_24 % 189.69/30.36 (5) op(e2, e0) = all_40_2 % 189.69/30.36 (6) op(e1, e0) = all_34_2 % 189.69/30.36 (7) ~ (all_244_24 = e1) % 189.69/30.36 (8) op(e2, e0) = e1 % 189.69/30.36 % 189.69/30.36 Begin of proof % 189.69/30.36 | % 189.69/30.36 | BETA: splitting (1) gives: % 189.69/30.36 | % 189.69/30.36 | Case 1: % 189.69/30.36 | | % 189.69/30.36 | | (9) all_252_19 = e1 & op(e1, e0) = e1 % 189.69/30.36 | | % 189.69/30.36 | | ALPHA: (9) implies: % 189.69/30.36 | | (10) op(e1, e0) = e1 % 189.69/30.36 | | % 189.69/30.36 | | REF_CLOSE: (2), (3), (5), (6), (8), (10) are inconsistent by sub-proof #352. % 189.69/30.36 | | % 189.69/30.36 | Case 2: % 189.69/30.36 | | % 189.69/30.36 | | (11) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.36 | | % 189.69/30.36 | | ALPHA: (11) implies: % 189.69/30.36 | | (12) op(e0, e0) = e1 % 189.69/30.36 | | % 189.69/30.36 | | REF_CLOSE: (2), (4), (7), (12) are inconsistent by sub-proof #474. % 189.69/30.36 | | % 189.69/30.36 | End of split % 189.69/30.36 | % 189.69/30.36 End of proof % 189.69/30.36 % 189.69/30.36 Sub-proof #167 shows that the following formulas are inconsistent: % 189.69/30.36 ---------------------------------------------------------------- % 189.69/30.36 (1) all_252_20 = e2 % 189.69/30.36 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.69/30.36 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.69/30.36 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.69/30.36 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.69/30.36 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.69/30.36 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.69/30.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.36 (5) all_252_18 = e1 % 189.69/30.36 (6) ~ (all_20_2 = e4) % 189.69/30.36 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.36 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.36 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.36 (8) op(e0, e2) = e4 % 189.69/30.36 (9) op(e3, e1) = all_36_2 % 189.69/30.36 (10) ~ (e2 = e1) % 189.69/30.36 (11) all_252_12 = e0 % 189.69/30.36 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.36 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.36 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.36 (13) op(e2, e1) = e0 % 189.69/30.36 (14) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.36 all_250_23 = e0 % 189.69/30.36 (15) ~ (e4 = e0) % 189.69/30.36 (16) ~ (e4 = e3) % 189.69/30.36 (17) ~ (all_36_2 = e2) % 189.69/30.36 (18) all_252_9 = e0 % 189.69/30.36 (19) ~ (all_40_2 = all_34_2) % 189.69/30.36 (20) ~ (all_244_24 = all_20_2) % 189.69/30.36 (21) op(e1, e4) = e0 % 189.69/30.36 (22) ~ (all_20_2 = e3) % 189.69/30.36 (23) op(all_20_2, e4) = e1 % 189.69/30.36 (24) op(e0, e0) = all_244_24 % 189.69/30.36 (25) op(e0, e1) = all_20_2 % 189.69/30.36 (26) all_252_19 = e4 % 189.69/30.36 (27) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.36 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.36 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.36 (28) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.69/30.36 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.36 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.36 (29) ~ (all_20_2 = e0) % 189.69/30.36 (30) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.36 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.36 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.36 (31) all_252_17 = e2 % 189.69/30.36 (32) ~ (all_20_2 = e2) % 189.69/30.36 (33) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.36 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.36 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.36 (34) op(e0, e4) = e2 % 189.69/30.36 (35) ~ (e3 = e0) % 189.69/30.36 (36) ~ (all_20_2 = all_8_1) % 189.69/30.36 (37) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.36 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.36 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.36 (38) all_252_6 = e4 % 189.69/30.36 (39) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.36 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.36 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.36 (40) ~ (e3 = e2) % 189.69/30.36 (41) op(e4, e0) = e4 % 189.69/30.36 (42) all_252_22 = e4 % 189.69/30.36 (43) op(e4, all_20_2) = e0 % 189.69/30.36 (44) op(e0, e3) = all_8_1 % 189.69/30.36 (45) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.36 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.36 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.36 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.36 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.36 op(e0, e1) = e0))) % 189.69/30.36 (46) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.69/30.36 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.69/30.36 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.69/30.36 (47) ~ (e4 = e2) % 189.69/30.36 (48) op(e2, e0) = all_40_2 % 189.69/30.36 (49) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.36 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.36 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.36 (50) ~ (e1 = e0) % 189.69/30.36 (51) op(e0, e4) = all_12_2 % 189.69/30.36 (52) all_250_23 = all_20_2 % 189.69/30.36 (53) ~ (e3 = e1) % 189.69/30.36 (54) ~ (e2 = e0) % 189.69/30.36 (55) op(e1, e0) = all_34_2 % 189.69/30.36 (56) ~ (all_12_2 = e3) % 189.69/30.36 (57) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.69/30.36 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.69/30.36 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.69/30.36 (58) ~ (all_34_2 = e2) % 189.69/30.36 (59) ~ (e4 = e1) % 189.69/30.36 (60) op(e2, e0) = e1 % 189.69/30.36 % 189.69/30.36 Begin of proof % 189.69/30.36 | % 189.69/30.36 | BETA: splitting (28) gives: % 189.69/30.36 | % 189.69/30.36 | Case 1: % 189.69/30.36 | | % 189.69/30.36 | | (61) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) % 189.69/30.36 | | = e3) % 189.69/30.36 | | % 189.69/30.36 | | BETA: splitting (61) gives: % 189.69/30.36 | | % 189.69/30.36 | | Case 1: % 189.69/30.36 | | | % 189.69/30.36 | | | (62) all_252_16 = e3 & op(e4, e0) = e3 % 189.69/30.36 | | | % 189.69/30.36 | | | REF_CLOSE: (4), (16), (41), (62) are inconsistent by sub-proof #210. % 189.69/30.36 | | | % 189.69/30.36 | | Case 2: % 189.69/30.36 | | | % 189.69/30.36 | | | (63) all_252_17 = e3 & op(e3, e0) = e3 % 189.69/30.36 | | | % 189.69/30.36 | | | REF_CLOSE: (31), (40), (63) are inconsistent by sub-proof #249. % 189.69/30.36 | | | % 189.69/30.36 | | End of split % 189.69/30.36 | | % 189.69/30.36 | Case 2: % 189.69/30.36 | | % 189.69/30.36 | | (64) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) % 189.69/30.36 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.36 | | % 189.69/30.36 | | BETA: splitting (64) gives: % 189.69/30.36 | | % 189.69/30.36 | | Case 1: % 189.69/30.36 | | | % 189.69/30.36 | | | (65) all_252_18 = e3 & op(e2, e0) = e3 % 189.69/30.36 | | | % 189.69/30.36 | | | REF_CLOSE: (5), (53), (65) are inconsistent by sub-proof #209. % 189.69/30.36 | | | % 189.69/30.36 | | Case 2: % 189.69/30.36 | | | % 189.69/30.36 | | | (66) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, % 189.69/30.36 | | | e0) = e3) % 189.69/30.36 | | | % 189.69/30.36 | | | BETA: splitting (66) gives: % 189.69/30.36 | | | % 189.69/30.36 | | | Case 1: % 189.69/30.36 | | | | % 189.69/30.36 | | | | (67) all_252_19 = e3 & op(e1, e0) = e3 % 189.69/30.36 | | | | % 189.69/30.36 | | | | ALPHA: (67) implies: % 189.69/30.36 | | | | (68) all_252_19 = e3 % 189.69/30.36 | | | | % 189.69/30.36 | | | | COMBINE_EQS: (26), (68) imply: % 189.69/30.36 | | | | (69) e4 = e3 % 189.69/30.36 | | | | % 189.69/30.36 | | | | SIMP: (69) implies: % 189.69/30.36 | | | | (70) e4 = e3 % 189.69/30.36 | | | | % 189.69/30.36 | | | | COMBINE_EQS: (38), (70) imply: % 189.69/30.36 | | | | (71) all_252_6 = e3 % 189.69/30.36 | | | | % 189.69/30.36 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), % 189.69/30.36 | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), % 189.69/30.36 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), % 189.69/30.36 | | | | (32), (33), (34), (35), (36), (37), (39), (40), (41), (42), % 189.69/30.36 | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52), % 189.69/30.36 | | | | (53), (54), (55), (56), (57), (58), (59), (60), (71) are % 189.69/30.36 | | | | inconsistent by sub-proof #168. % 189.69/30.36 | | | | % 189.69/30.36 | | | Case 2: % 189.69/30.36 | | | | % 189.69/30.36 | | | | (72) all_252_24 = e3 & op(e0, e0) = e3 % 189.69/30.36 | | | | % 189.69/30.36 | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15), % 189.69/30.36 | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 189.69/30.36 | | | | (26), (27), (29), (30), (32), (33), (34), (35), (36), (37), % 189.69/30.36 | | | | (39), (40), (42), (43), (44), (45), (47), (48), (49), (52), % 189.69/30.36 | | | | (54), (55), (58), (60), (72) are inconsistent by sub-proof % 189.69/30.36 | | | | #169. % 189.69/30.36 | | | | % 189.69/30.36 | | | End of split % 189.69/30.36 | | | % 189.69/30.36 | | End of split % 189.69/30.36 | | % 189.69/30.36 | End of split % 189.69/30.36 | % 189.69/30.36 End of proof % 189.69/30.36 % 189.69/30.36 Sub-proof #168 shows that the following formulas are inconsistent: % 189.69/30.36 ---------------------------------------------------------------- % 189.69/30.36 (1) all_252_20 = e2 % 189.69/30.36 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.69/30.36 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.69/30.36 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.69/30.36 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.69/30.36 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.69/30.36 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.69/30.36 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.36 (5) all_252_18 = e1 % 189.69/30.36 (6) ~ (all_20_2 = e4) % 189.69/30.36 (7) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.36 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.36 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.36 (8) op(e0, e2) = e4 % 189.69/30.36 (9) op(e3, e1) = all_36_2 % 189.69/30.36 (10) ~ (e2 = e1) % 189.69/30.36 (11) all_252_12 = e0 % 189.69/30.36 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.36 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.36 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.36 (13) op(e2, e1) = e0 % 189.69/30.36 (14) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.36 all_250_23 = e0 % 189.69/30.36 (15) ~ (e4 = e0) % 189.69/30.36 (16) ~ (e4 = e3) % 189.69/30.36 (17) ~ (all_36_2 = e2) % 189.69/30.36 (18) all_252_9 = e0 % 189.69/30.36 (19) ~ (all_40_2 = all_34_2) % 189.69/30.36 (20) ~ (all_244_24 = all_20_2) % 189.69/30.36 (21) op(e1, e4) = e0 % 189.69/30.36 (22) ~ (all_20_2 = e3) % 189.69/30.36 (23) op(all_20_2, e4) = e1 % 189.69/30.36 (24) op(e0, e0) = all_244_24 % 189.69/30.36 (25) op(e0, e1) = all_20_2 % 189.69/30.36 (26) all_252_19 = e4 % 189.69/30.36 (27) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.36 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.36 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.36 (28) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = % 189.69/30.36 e3) | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.36 e0) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.36 (29) ~ (all_20_2 = e0) % 189.69/30.37 (30) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.37 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.37 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.37 (31) all_252_17 = e2 % 189.69/30.37 (32) ~ (all_20_2 = e2) % 189.69/30.37 (33) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.37 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.37 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.37 (34) all_252_6 = e3 % 189.69/30.37 (35) op(e0, e4) = e2 % 189.69/30.37 (36) ~ (e3 = e0) % 189.69/30.37 (37) ~ (all_20_2 = all_8_1) % 189.69/30.37 (38) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.37 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.37 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.37 (39) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.37 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.37 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.37 (40) ~ (e3 = e2) % 189.69/30.37 (41) op(e4, e0) = e4 % 189.69/30.37 (42) all_252_22 = e4 % 189.69/30.37 (43) op(e4, all_20_2) = e0 % 189.69/30.37 (44) op(e0, e3) = all_8_1 % 189.69/30.37 (45) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.37 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.37 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.37 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.37 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.37 op(e0, e1) = e0))) % 189.69/30.37 (46) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.69/30.37 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.69/30.37 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.69/30.37 (47) ~ (e4 = e2) % 189.69/30.37 (48) op(e2, e0) = all_40_2 % 189.69/30.37 (49) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.37 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.37 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.37 (50) ~ (e1 = e0) % 189.69/30.37 (51) op(e0, e4) = all_12_2 % 189.69/30.37 (52) all_250_23 = all_20_2 % 189.69/30.37 (53) ~ (e3 = e1) % 189.69/30.37 (54) ~ (e2 = e0) % 189.69/30.37 (55) op(e1, e0) = all_34_2 % 189.69/30.37 (56) ~ (all_12_2 = e3) % 189.69/30.37 (57) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 189.69/30.37 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 189.69/30.37 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 189.69/30.37 (58) ~ (all_34_2 = e2) % 189.69/30.37 (59) ~ (e4 = e1) % 189.69/30.37 (60) op(e2, e0) = e1 % 189.69/30.37 % 189.69/30.37 Begin of proof % 189.69/30.37 | % 189.69/30.37 | BETA: splitting (28) gives: % 189.69/30.37 | % 189.69/30.37 | Case 1: % 189.69/30.37 | | % 189.69/30.37 | | (61) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) % 189.69/30.37 | | = e3) % 189.69/30.37 | | % 189.69/30.37 | | BETA: splitting (61) gives: % 189.69/30.37 | | % 189.69/30.37 | | Case 1: % 189.69/30.37 | | | % 189.69/30.37 | | | (62) all_252_16 = e3 & op(e4, e0) = e3 % 189.69/30.37 | | | % 189.69/30.37 | | | REF_CLOSE: (4), (16), (41), (62) are inconsistent by sub-proof #210. % 189.69/30.37 | | | % 189.69/30.37 | | Case 2: % 189.69/30.37 | | | % 189.69/30.37 | | | (63) all_252_17 = e3 & op(e3, e0) = e3 % 189.69/30.37 | | | % 189.69/30.37 | | | ALPHA: (63) implies: % 189.69/30.37 | | | (64) all_252_17 = e3 % 189.69/30.37 | | | % 189.69/30.37 | | | COMBINE_EQS: (31), (64) imply: % 189.69/30.37 | | | (65) e3 = e2 % 189.69/30.37 | | | % 189.69/30.37 | | | COMBINE_EQS: (34), (65) imply: % 189.69/30.37 | | | (66) all_252_6 = e2 % 189.69/30.37 | | | % 189.69/30.37 | | | REF_CLOSE: (1), (2), (3), (4), (10), (11), (15), (16), (35), (36), (40), % 189.69/30.37 | | | (46), (47), (50), (51), (53), (54), (56), (57), (59), (66) are % 189.69/30.37 | | | inconsistent by sub-proof #223. % 189.69/30.37 | | | % 189.69/30.37 | | End of split % 189.69/30.37 | | % 189.69/30.37 | Case 2: % 189.69/30.37 | | % 189.69/30.37 | | (67) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) % 189.69/30.37 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 189.69/30.37 | | % 189.69/30.37 | | BETA: splitting (67) gives: % 189.69/30.37 | | % 189.69/30.37 | | Case 1: % 189.69/30.37 | | | % 189.69/30.37 | | | (68) all_252_18 = e3 & op(e2, e0) = e3 % 189.69/30.37 | | | % 189.69/30.37 | | | REF_CLOSE: (5), (53), (68) are inconsistent by sub-proof #209. % 189.69/30.37 | | | % 189.69/30.37 | | Case 2: % 189.69/30.37 | | | % 189.69/30.37 | | | (69) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, % 189.69/30.37 | | | e0) = e3) % 189.69/30.37 | | | % 189.69/30.37 | | | BETA: splitting (69) gives: % 189.69/30.37 | | | % 189.69/30.37 | | | Case 1: % 189.69/30.37 | | | | % 189.69/30.37 | | | | (70) all_252_19 = e3 & op(e1, e0) = e3 % 189.69/30.37 | | | | % 189.69/30.37 | | | | REF_CLOSE: (16), (26), (70) are inconsistent by sub-proof #243. % 189.69/30.37 | | | | % 189.69/30.37 | | | Case 2: % 189.69/30.37 | | | | % 189.69/30.37 | | | | (71) all_252_24 = e3 & op(e0, e0) = e3 % 189.69/30.37 | | | | % 189.69/30.37 | | | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (11), (12), (13), (14), (15), % 189.69/30.37 | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 189.69/30.37 | | | | (26), (27), (29), (30), (32), (33), (35), (36), (37), (38), % 189.69/30.37 | | | | (39), (40), (42), (43), (44), (45), (47), (48), (49), (52), % 189.69/30.37 | | | | (54), (55), (58), (60), (71) are inconsistent by sub-proof % 189.69/30.37 | | | | #169. % 189.69/30.37 | | | | % 189.69/30.37 | | | End of split % 189.69/30.37 | | | % 189.69/30.37 | | End of split % 189.69/30.37 | | % 189.69/30.37 | End of split % 189.69/30.37 | % 189.69/30.37 End of proof % 189.69/30.37 % 189.69/30.37 Sub-proof #169 shows that the following formulas are inconsistent: % 189.69/30.37 ---------------------------------------------------------------- % 189.69/30.37 (1) all_252_20 = e2 % 189.69/30.37 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.37 (3) ~ (all_20_2 = e4) % 189.69/30.37 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.37 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.37 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.37 (5) op(e0, e2) = e4 % 189.69/30.37 (6) op(e3, e1) = all_36_2 % 189.69/30.37 (7) all_252_12 = e0 % 189.69/30.37 (8) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.37 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.37 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.37 (9) op(e2, e1) = e0 % 189.69/30.37 (10) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.37 all_250_23 = e0 % 189.69/30.37 (11) ~ (e4 = e0) % 189.69/30.37 (12) ~ (e4 = e3) % 189.69/30.37 (13) ~ (all_36_2 = e2) % 189.69/30.37 (14) all_252_9 = e0 % 189.69/30.37 (15) ~ (all_40_2 = all_34_2) % 189.69/30.37 (16) ~ (all_244_24 = all_20_2) % 189.69/30.37 (17) op(e1, e4) = e0 % 189.69/30.37 (18) ~ (all_20_2 = e3) % 189.69/30.37 (19) op(all_20_2, e4) = e1 % 189.69/30.37 (20) op(e0, e0) = all_244_24 % 189.69/30.37 (21) op(e0, e1) = all_20_2 % 189.69/30.37 (22) all_252_19 = e4 % 189.69/30.37 (23) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.37 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.37 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.37 (24) ~ (all_20_2 = e0) % 189.69/30.37 (25) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.37 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.37 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.37 (26) ~ (all_20_2 = e2) % 189.69/30.37 (27) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.37 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.37 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.37 (28) all_252_24 = e3 & op(e0, e0) = e3 % 189.69/30.37 (29) op(e0, e4) = e2 % 189.69/30.37 (30) ~ (e3 = e0) % 189.69/30.37 (31) ~ (all_20_2 = all_8_1) % 189.69/30.37 (32) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.37 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.37 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.37 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.37 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.37 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.37 (34) ~ (e3 = e2) % 189.69/30.37 (35) all_252_22 = e4 % 189.69/30.37 (36) op(e4, all_20_2) = e0 % 189.69/30.37 (37) op(e0, e3) = all_8_1 % 189.69/30.37 (38) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 189.69/30.37 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 189.69/30.37 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 189.69/30.37 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 189.69/30.37 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.37 op(e0, e1) = e0))) % 189.69/30.37 (39) ~ (e4 = e2) % 189.69/30.37 (40) op(e2, e0) = all_40_2 % 189.69/30.37 (41) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.37 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.37 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.37 (42) all_250_23 = all_20_2 % 189.69/30.37 (43) ~ (e2 = e0) % 189.69/30.37 (44) op(e1, e0) = all_34_2 % 189.69/30.37 (45) ~ (all_34_2 = e2) % 189.69/30.37 (46) op(e2, e0) = e1 % 189.69/30.37 % 189.69/30.37 Begin of proof % 189.69/30.37 | % 189.69/30.37 | ALPHA: (28) implies: % 189.69/30.37 | (47) all_252_24 = e3 % 189.69/30.37 | % 189.69/30.37 | BETA: splitting (38) gives: % 189.69/30.37 | % 189.69/30.37 | Case 1: % 189.69/30.37 | | % 189.69/30.37 | | (48) all_252_24 = e0 & op(e0, e0) = e0 % 189.69/30.37 | | % 189.69/30.37 | | ALPHA: (48) implies: % 189.69/30.37 | | (49) all_252_24 = e0 % 189.69/30.37 | | % 189.69/30.37 | | REF_CLOSE: (30), (47), (49) are inconsistent by sub-proof #331. % 189.69/30.37 | | % 189.69/30.37 | Case 2: % 189.69/30.37 | | % 189.69/30.37 | | (50) ((all_252_16 = e0 & op(e4, e0) = e0) | (all_252_17 = e0 & op(e3, e0) % 189.69/30.37 | | = e0) | (all_252_18 = e0 & op(e2, e0) = e0) | (all_252_19 = e0 & % 189.69/30.37 | | op(e1, e0) = e0)) & ((all_252_20 = e0 & op(e0, e4) = e0) | % 189.69/30.37 | | (all_252_21 = e0 & op(e0, e3) = e0) | (all_252_22 = e0 & op(e0, % 189.69/30.37 | | e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0)) % 189.69/30.37 | | % 189.69/30.37 | | ALPHA: (50) implies: % 189.69/30.37 | | (51) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 189.69/30.37 | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 189.69/30.37 | | op(e0, e1) = e0) % 189.69/30.37 | | % 189.69/30.37 | | BETA: splitting (51) gives: % 189.69/30.37 | | % 189.69/30.37 | | Case 1: % 189.69/30.37 | | | % 189.69/30.37 | | | (52) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, % 189.69/30.37 | | | e3) = e0) % 189.69/30.37 | | | % 189.69/30.37 | | | BETA: splitting (52) gives: % 189.69/30.37 | | | % 189.69/30.37 | | | Case 1: % 189.69/30.37 | | | | % 189.69/30.37 | | | | (53) all_252_20 = e0 & op(e0, e4) = e0 % 189.69/30.37 | | | | % 189.69/30.37 | | | | REF_CLOSE: (2), (29), (43), (53) are inconsistent by sub-proof #255. % 189.69/30.37 | | | | % 189.69/30.37 | | | Case 2: % 189.69/30.37 | | | | % 189.69/30.37 | | | | (54) all_252_21 = e0 & op(e0, e3) = e0 % 189.69/30.37 | | | | % 189.69/30.37 | | | | ALPHA: (54) implies: % 189.69/30.37 | | | | (55) op(e0, e3) = e0 % 189.69/30.37 | | | | % 189.69/30.37 | | | | BETA: splitting (10) gives: % 189.69/30.37 | | | | % 189.69/30.37 | | | | Case 1: % 189.69/30.37 | | | | | % 189.69/30.37 | | | | | (56) all_250_23 = e4 % 189.69/30.37 | | | | | % 189.69/30.37 | | | | | REF_CLOSE: (3), (42), (56) are inconsistent by sub-proof #489. % 189.69/30.37 | | | | | % 189.69/30.37 | | | | Case 2: % 189.69/30.37 | | | | | % 189.69/30.37 | | | | | (57) ~ (all_250_23 = e4) % 189.69/30.37 | | | | | (58) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.37 | | | | | all_250_23 = e0 % 189.69/30.37 | | | | | % 189.69/30.37 | | | | | BETA: splitting (58) gives: % 189.69/30.37 | | | | | % 189.69/30.37 | | | | | Case 1: % 189.69/30.37 | | | | | | % 189.69/30.37 | | | | | | (59) all_250_23 = e3 % 189.69/30.37 | | | | | | % 189.69/30.37 | | | | | | REF_CLOSE: (18), (42), (59) are inconsistent by sub-proof #488. % 189.69/30.37 | | | | | | % 189.69/30.37 | | | | | Case 2: % 189.69/30.37 | | | | | | % 189.69/30.37 | | | | | | (60) ~ (all_250_23 = e3) % 189.69/30.37 | | | | | | (61) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.69/30.37 | | | | | | % 189.69/30.37 | | | | | | BETA: splitting (61) gives: % 189.69/30.37 | | | | | | % 189.69/30.37 | | | | | | Case 1: % 189.69/30.37 | | | | | | | % 189.69/30.37 | | | | | | | (62) all_250_23 = e2 % 189.69/30.37 | | | | | | | % 189.69/30.37 | | | | | | | REF_CLOSE: (26), (42), (62) are inconsistent by sub-proof #487. % 189.69/30.37 | | | | | | | % 189.69/30.37 | | | | | | Case 2: % 189.69/30.37 | | | | | | | % 189.69/30.37 | | | | | | | (63) ~ (all_250_23 = e2) % 189.69/30.37 | | | | | | | (64) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.37 | | | | | | | % 189.69/30.37 | | | | | | | BETA: splitting (64) gives: % 189.69/30.37 | | | | | | | % 189.69/30.37 | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | (65) all_250_23 = e1 % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | COMBINE_EQS: (42), (65) imply: % 189.69/30.37 | | | | | | | | (66) all_20_2 = e1 % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | SIMP: (66) implies: % 189.69/30.37 | | | | | | | | (67) all_20_2 = e1 % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (16), (67) imply: % 189.69/30.37 | | | | | | | | (68) ~ (all_244_24 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (3), (67) imply: % 189.69/30.37 | | | | | | | | (69) ~ (e4 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | SIMP: (69) implies: % 189.69/30.37 | | | | | | | | (70) ~ (e4 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (18), (67) imply: % 189.69/30.37 | | | | | | | | (71) ~ (e3 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | SIMP: (71) implies: % 189.69/30.37 | | | | | | | | (72) ~ (e3 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (26), (67) imply: % 189.69/30.37 | | | | | | | | (73) ~ (e2 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | SIMP: (73) implies: % 189.69/30.37 | | | | | | | | (74) ~ (e2 = e1) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (24), (67) imply: % 189.69/30.37 | | | | | | | | (75) ~ (e1 = e0) % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (19), (67) imply: % 189.69/30.37 | | | | | | | | (76) op(e1, e4) = e1 % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (36), (67) imply: % 189.69/30.37 | | | | | | | | (77) op(e4, e1) = e0 % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | REDUCE: (21), (67) imply: % 189.69/30.37 | | | | | | | | (78) op(e0, e1) = e1 % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | BETA: splitting (27) gives: % 189.69/30.37 | | | | | | | | % 189.69/30.37 | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | | (79) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 % 189.69/30.37 | | | | | | | | | & op(e3, e1) = e4) % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | | BETA: splitting (79) gives: % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | (80) all_252_9 = e4 & op(e4, e1) = e4 % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | REF_CLOSE: (11), (14), (80) are inconsistent by sub-proof % 189.69/30.37 | | | | | | | | | | #220. % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | (81) all_252_10 = e4 & op(e3, e1) = e4 % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | ALPHA: (81) implies: % 189.69/30.37 | | | | | | | | | | (82) all_252_10 = e4 % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | BETA: splitting (4) gives: % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | (83) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 189.69/30.37 | | | | | | | | | | | e2 & op(e3, e1) = e2) % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | REF_CLOSE: (2), (6), (13), (14), (43), (83) are inconsistent % 189.69/30.37 | | | | | | | | | | | by sub-proof #207. % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | (84) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 189.69/30.37 | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 189.69/30.37 | | | | | | | | | | | op(e0, e1) = e2) % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | BETA: splitting (84) gives: % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | (85) all_252_11 = e2 & op(e2, e1) = e2 % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | ALPHA: (85) implies: % 189.69/30.37 | | | | | | | | | | | | (86) all_252_11 = e2 % 189.69/30.37 | | | | | | | | | | | | (87) op(e2, e1) = e2 % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), % 189.69/30.37 | | | | | | | | | | | | (12), (13), (16), (17), (18), (20), (21), (23), % 189.69/30.37 | | | | | | | | | | | | (24), (26), (27), (29), (30), (31), (33), (34), % 189.69/30.37 | | | | | | | | | | | | (37), (39), (42), (43), (55), (64), (68), (70), % 189.69/30.37 | | | | | | | | | | | | (72), (74), (75), (76), (77), (86), (87) are % 189.69/30.37 | | | | | | | | | | | | inconsistent by sub-proof #190. % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | (88) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 189.69/30.37 | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | BETA: splitting (88) gives: % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | (89) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | ALPHA: (89) implies: % 189.69/30.37 | | | | | | | | | | | | | (90) all_252_15 = e2 % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | BETA: splitting (8) gives: % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | (91) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = % 189.69/30.37 | | | | | | | | | | | | | | e3 & op(e3, e1) = e3) % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (30), (77), (82), (91) are inconsistent % 189.69/30.37 | | | | | | | | | | | | | | by sub-proof #218. % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | (92) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 % 189.69/30.37 | | | | | | | | | | | | | | = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 189.69/30.37 | | | | | | | | | | | | | | op(e0, e1) = e3) % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | BETA: splitting (92) gives: % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | (93) all_252_11 = e3 & op(e2, e1) = e3 % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | ALPHA: (93) implies: % 189.69/30.37 | | | | | | | | | | | | | | | (94) all_252_11 = e3 % 189.69/30.37 | | | | | | | | | | | | | | | (95) op(e2, e1) = e3 % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), % 189.69/30.37 | | | | | | | | | | | | | | | (12), (13), (16), (17), (18), (20), (21), (23), % 189.69/30.37 | | | | | | | | | | | | | | | (24), (26), (27), (29), (30), (31), (33), (34), % 189.69/30.37 | | | | | | | | | | | | | | | (37), (39), (42), (43), (55), (64), (68), (70), % 189.69/30.37 | | | | | | | | | | | | | | | (72), (74), (75), (76), (77), (94), (95) are % 189.69/30.37 | | | | | | | | | | | | | | | inconsistent by sub-proof #189. % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | (96) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 % 189.69/30.37 | | | | | | | | | | | | | | | = e3 & op(e0, e1) = e3) % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | BETA: splitting (96) gives: % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | (97) all_252_15 = e3 & op(e1, e1) = e3 % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | REF_CLOSE: (34), (90), (97) are inconsistent by sub-proof % 189.69/30.37 | | | | | | | | | | | | | | | | #188. % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | (98) all_252_23 = e3 & op(e0, e1) = e3 % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | ALPHA: (98) implies: % 189.69/30.37 | | | | | | | | | | | | | | | | (99) all_252_23 = e3 % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | BETA: splitting (38) gives: % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | | (100) all_252_24 = e0 & op(e0, e0) = e0 % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | | ALPHA: (100) implies: % 189.69/30.37 | | | | | | | | | | | | | | | | | (101) all_252_24 = e0 % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (47), (101) are inconsistent by sub-proof % 189.69/30.37 | | | | | | | | | | | | | | | | | #331. % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (11), (20), (23), (30), (35), (43), % 189.69/30.37 | | | | | | | | | | | | | | | | | (51), (68), (70), (72), (74), (75), (99) are % 189.69/30.37 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186. % 189.69/30.37 | | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | (102) all_252_23 = e2 & op(e0, e1) = e2 % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (23), (37), (47), (55), (70), (72), % 189.69/30.37 | | | | | | | | | | | | | (74), (75), (102) are inconsistent by sub-proof % 189.69/30.37 | | | | | | | | | | | | | #185. % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | End of split % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | | (103) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = % 189.69/30.37 | | | | | | | | | e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, % 189.69/30.37 | | | | | | | | | e1) = e4) % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | | BETA: splitting (103) gives: % 189.69/30.37 | | | | | | | | | % 189.69/30.37 | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | (104) all_252_11 = e4 & op(e2, e1) = e4 % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | ALPHA: (104) implies: % 189.69/30.37 | | | | | | | | | | (105) all_252_11 = e4 % 189.69/30.37 | | | | | | | | | | (106) op(e2, e1) = e4 % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | BETA: splitting (23) gives: % 189.69/30.37 | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | (107) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 189.69/30.37 | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | REF_CLOSE: (2), (29), (37), (55), (74), (75), (107) are % 189.69/30.37 | | | | | | | | | | | inconsistent by sub-proof #205. % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | (108) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 189.69/30.37 | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 189.69/30.37 | | | | | | | | | | | op(e0, e0) = e1) % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | BETA: splitting (108) gives: % 189.69/30.37 | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | (109) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | ALPHA: (109) implies: % 189.69/30.37 | | | | | | | | | | | | (110) op(e0, e2) = e1 % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | REF_CLOSE: (2), (5), (70), (110) are inconsistent by % 189.69/30.37 | | | | | | | | | | | | sub-proof #256. % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | (111) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 189.69/30.37 | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | BETA: splitting (111) gives: % 189.69/30.37 | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | Case 1: % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | (112) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), % 189.69/30.37 | | | | | | | | | | | | | (12), (13), (16), (17), (18), (20), (21), (23), % 189.69/30.37 | | | | | | | | | | | | | (24), (26), (27), (30), (31), (33), (34), (37), % 189.69/30.37 | | | | | | | | | | | | | (39), (42), (43), (64), (70), (72), (74), (75), % 189.69/30.37 | | | | | | | | | | | | | (76), (77), (78), (105), (106) are inconsistent by % 189.69/30.37 | | | | | | | | | | | | | sub-proof #184. % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.37 | | | | | | | | | | | | Case 2: % 189.69/30.37 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | (113) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | ALPHA: (113) implies: % 189.69/30.38 | | | | | | | | | | | | | (114) op(e0, e0) = e1 % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | REF_CLOSE: (2), (20), (68), (114) are inconsistent by % 189.69/30.38 | | | | | | | | | | | | | sub-proof #474. % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | % 189.69/30.38 | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | (115) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = % 189.69/30.38 | | | | | | | | | | e4 & op(e0, e1) = e4) % 189.69/30.38 | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | BETA: splitting (115) gives: % 189.69/30.38 | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | (116) all_252_15 = e4 & op(e1, e1) = e4 % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | ALPHA: (116) implies: % 189.69/30.38 | | | | | | | | | | | (117) all_252_15 = e4 % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | BETA: splitting (4) gives: % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | (118) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = % 189.69/30.38 | | | | | | | | | | | | e2 & op(e3, e1) = e2) % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | REF_CLOSE: (2), (6), (13), (14), (43), (118) are inconsistent % 189.69/30.38 | | | | | | | | | | | | by sub-proof #207. % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | (119) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 % 189.69/30.38 | | | | | | | | | | | | = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 189.69/30.38 | | | | | | | | | | | | op(e0, e1) = e2) % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | BETA: splitting (119) gives: % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | (120) all_252_11 = e2 & op(e2, e1) = e2 % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | ALPHA: (120) implies: % 189.69/30.38 | | | | | | | | | | | | | (121) all_252_11 = e2 % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | BETA: splitting (23) gives: % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | (122) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 % 189.69/30.38 | | | | | | | | | | | | | | = e1 & op(e0, e3) = e1) % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | REF_CLOSE: (2), (29), (37), (55), (74), (75), (122) are % 189.69/30.38 | | | | | | | | | | | | | | inconsistent by sub-proof #205. % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | (123) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 % 189.69/30.38 | | | | | | | | | | | | | | = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 189.69/30.38 | | | | | | | | | | | | | | op(e0, e0) = e1) % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | BETA: splitting (123) gives: % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | (124) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | ALPHA: (124) implies: % 189.69/30.38 | | | | | | | | | | | | | | | (125) op(e0, e2) = e1 % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (70), (125) are inconsistent by % 189.69/30.38 | | | | | | | | | | | | | | | sub-proof #256. % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | (126) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 % 189.69/30.38 | | | | | | | | | | | | | | | = e1 & op(e0, e0) = e1) % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | BETA: splitting (126) gives: % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | | (127) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | | ALPHA: (127) implies: % 189.69/30.38 | | | | | | | | | | | | | | | | (128) all_252_23 = e1 % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), % 189.69/30.38 | | | | | | | | | | | | | | | | (12), (13), (15), (16), (17), (18), (20), (21), % 189.69/30.38 | | | | | | | | | | | | | | | | (22), (23), (24), (25), (26), (27), (30), (31), % 189.69/30.38 | | | | | | | | | | | | | | | | (32), (33), (34), (37), (39), (40), (41), (42), % 189.69/30.38 | | | | | | | | | | | | | | | | (43), (44), (45), (46), (64), (70), (72), (74), % 189.69/30.38 | | | | | | | | | | | | | | | | (75), (76), (77), (78), (117), (121), (128) are % 189.69/30.38 | | | | | | | | | | | | | | | | inconsistent by sub-proof #173. % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | | (129) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | | ALPHA: (129) implies: % 189.69/30.38 | | | | | | | | | | | | | | | | (130) op(e0, e0) = e1 % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (20), (68), (130) are inconsistent by % 189.69/30.38 | | | | | | | | | | | | | | | | sub-proof #474. % 189.69/30.38 | | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | (131) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 % 189.69/30.38 | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | BETA: splitting (131) gives: % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | Case 1: % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | (132) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | REF_CLOSE: (39), (117), (132) are inconsistent by sub-proof % 189.69/30.38 | | | | | | | | | | | | | | #396. % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | (133) all_252_23 = e2 & op(e0, e1) = e2 % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (23), (37), (47), (55), (70), (72), % 189.69/30.38 | | | | | | | | | | | | | | (74), (75), (133) are inconsistent by sub-proof % 189.69/30.38 | | | | | | | | | | | | | | #185. % 189.69/30.38 | | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | (134) all_252_23 = e4 & op(e0, e1) = e4 % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | ALPHA: (134) implies: % 189.69/30.38 | | | | | | | | | | | (135) op(e0, e1) = e4 % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | | REF_CLOSE: (2), (21), (70), (78), (135) are inconsistent by % 189.69/30.38 | | | | | | | | | | | sub-proof #401. % 189.69/30.38 | | | | | | | | | | | % 189.69/30.38 | | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | | % 189.69/30.38 | | | | | | | | | End of split % 189.69/30.38 | | | | | | | | | % 189.69/30.38 | | | | | | | | End of split % 189.69/30.38 | | | | | | | | % 189.69/30.38 | | | | | | | Case 2: % 189.69/30.38 | | | | | | | | % 189.69/30.38 | | | | | | | | (136) all_250_23 = e0 % 189.69/30.38 | | | | | | | | % 189.69/30.38 | | | | | | | | REF_CLOSE: (24), (42), (136) are inconsistent by sub-proof #486. % 189.69/30.38 | | | | | | | | % 189.69/30.38 | | | | | | | End of split % 189.69/30.38 | | | | | | | % 189.69/30.38 | | | | | | End of split % 189.69/30.38 | | | | | | % 189.69/30.38 | | | | | End of split % 189.69/30.38 | | | | | % 189.69/30.38 | | | | End of split % 189.69/30.38 | | | | % 189.69/30.38 | | | End of split % 189.69/30.38 | | | % 189.69/30.38 | | Case 2: % 189.69/30.38 | | | % 189.69/30.38 | | | (137) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, % 189.69/30.38 | | | e1) = e0) % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (1), (2), (3), (5), (10), (11), (16), (18), (20), (23), (24), % 189.69/30.38 | | | (26), (31), (37), (42), (137) are inconsistent by sub-proof % 189.69/30.38 | | | #170. % 189.69/30.38 | | | % 189.69/30.38 | | End of split % 189.69/30.38 | | % 189.69/30.38 | End of split % 189.69/30.38 | % 189.69/30.38 End of proof % 189.69/30.38 % 189.69/30.38 Sub-proof #170 shows that the following formulas are inconsistent: % 189.69/30.38 ---------------------------------------------------------------- % 189.69/30.38 (1) all_252_20 = e2 % 189.69/30.38 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.38 (3) ~ (all_20_2 = e4) % 189.69/30.38 (4) op(e0, e2) = e4 % 189.69/30.38 (5) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.38 all_250_23 = e0 % 189.69/30.38 (6) ~ (e4 = e0) % 189.69/30.38 (7) ~ (all_244_24 = all_20_2) % 189.69/30.38 (8) ~ (all_20_2 = e3) % 189.69/30.38 (9) op(e0, e0) = all_244_24 % 189.69/30.38 (10) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.38 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.38 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.38 (11) ~ (all_20_2 = e0) % 189.69/30.38 (12) ~ (all_20_2 = e2) % 189.69/30.38 (13) ~ (all_20_2 = all_8_1) % 189.69/30.38 (14) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) = % 189.69/30.38 e0) % 189.69/30.38 (15) op(e0, e3) = all_8_1 % 189.69/30.38 (16) all_250_23 = all_20_2 % 189.69/30.38 % 189.69/30.38 Begin of proof % 189.69/30.38 | % 189.69/30.38 | BETA: splitting (14) gives: % 189.69/30.38 | % 189.69/30.38 | Case 1: % 189.69/30.38 | | % 189.69/30.38 | | (17) all_252_22 = e0 & op(e0, e2) = e0 % 189.69/30.38 | | % 189.69/30.38 | | ALPHA: (17) implies: % 189.69/30.38 | | (18) op(e0, e2) = e0 % 189.69/30.38 | | % 189.69/30.38 | | REF_CLOSE: (2), (4), (6), (18) are inconsistent by sub-proof #520. % 189.69/30.38 | | % 189.69/30.38 | Case 2: % 189.69/30.38 | | % 189.69/30.38 | | (19) all_252_23 = e0 & op(e0, e1) = e0 % 189.69/30.38 | | % 189.69/30.38 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), % 189.69/30.38 | | (15), (16), (19) are inconsistent by sub-proof #171. % 189.69/30.38 | | % 189.69/30.38 | End of split % 189.69/30.38 | % 189.69/30.38 End of proof % 189.69/30.38 % 189.69/30.38 Sub-proof #171 shows that the following formulas are inconsistent: % 189.69/30.38 ---------------------------------------------------------------- % 189.69/30.38 (1) all_252_20 = e2 % 189.69/30.38 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.38 (3) ~ (all_20_2 = e4) % 189.69/30.38 (4) op(e0, e2) = e4 % 189.69/30.38 (5) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 189.69/30.38 all_250_23 = e0 % 189.69/30.38 (6) ~ (all_244_24 = all_20_2) % 189.69/30.38 (7) ~ (all_20_2 = e3) % 189.69/30.38 (8) op(e0, e0) = all_244_24 % 189.69/30.38 (9) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.38 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.69/30.38 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.38 (10) ~ (all_20_2 = e0) % 189.69/30.38 (11) all_252_23 = e0 & op(e0, e1) = e0 % 189.69/30.38 (12) ~ (all_20_2 = e2) % 189.69/30.38 (13) ~ (all_20_2 = all_8_1) % 189.69/30.38 (14) op(e0, e3) = all_8_1 % 189.69/30.38 (15) all_250_23 = all_20_2 % 189.69/30.38 % 189.69/30.38 Begin of proof % 189.69/30.38 | % 189.69/30.38 | ALPHA: (11) implies: % 189.69/30.38 | (16) all_252_23 = e0 % 189.69/30.38 | % 189.69/30.38 | BETA: splitting (5) gives: % 189.69/30.38 | % 189.69/30.38 | Case 1: % 189.69/30.38 | | % 189.69/30.38 | | (17) all_250_23 = e4 % 189.69/30.38 | | % 189.69/30.38 | | REF_CLOSE: (3), (15), (17) are inconsistent by sub-proof #489. % 189.69/30.38 | | % 189.69/30.38 | Case 2: % 189.69/30.38 | | % 189.69/30.38 | | (18) ~ (all_250_23 = e4) % 189.69/30.38 | | (19) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 189.69/30.38 | | e0 % 189.69/30.38 | | % 189.69/30.38 | | BETA: splitting (19) gives: % 189.69/30.38 | | % 189.69/30.38 | | Case 1: % 189.69/30.38 | | | % 189.69/30.38 | | | (20) all_250_23 = e3 % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (7), (15), (20) are inconsistent by sub-proof #488. % 189.69/30.38 | | | % 189.69/30.38 | | Case 2: % 189.69/30.38 | | | % 189.69/30.38 | | | (21) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13), (14), % 189.69/30.38 | | | (15), (16), (21) are inconsistent by sub-proof #172. % 189.69/30.38 | | | % 189.69/30.38 | | End of split % 189.69/30.38 | | % 189.69/30.38 | End of split % 189.69/30.38 | % 189.69/30.38 End of proof % 189.69/30.38 % 189.69/30.38 Sub-proof #172 shows that the following formulas are inconsistent: % 189.69/30.38 ---------------------------------------------------------------- % 189.69/30.38 (1) all_252_20 = e2 % 189.69/30.38 (2) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 189.69/30.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.38 (4) ~ (all_20_2 = e4) % 189.69/30.38 (5) op(e0, e2) = e4 % 189.69/30.38 (6) ~ (all_244_24 = all_20_2) % 189.69/30.38 (7) op(e0, e0) = all_244_24 % 189.69/30.38 (8) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.38 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.69/30.38 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.38 (9) ~ (all_20_2 = e0) % 189.69/30.38 (10) ~ (all_20_2 = e2) % 189.69/30.38 (11) ~ (all_20_2 = all_8_1) % 189.69/30.38 (12) op(e0, e3) = all_8_1 % 189.69/30.38 (13) all_250_23 = all_20_2 % 189.69/30.38 (14) all_252_23 = e0 % 189.69/30.38 % 189.69/30.38 Begin of proof % 189.69/30.38 | % 189.69/30.38 | BETA: splitting (2) gives: % 189.69/30.38 | % 189.69/30.38 | Case 1: % 189.69/30.38 | | % 189.69/30.38 | | (15) all_250_23 = e2 % 189.69/30.38 | | % 189.69/30.38 | | COMBINE_EQS: (13), (15) imply: % 189.69/30.38 | | (16) all_20_2 = e2 % 189.69/30.38 | | % 189.69/30.38 | | REDUCE: (10), (16) imply: % 189.69/30.38 | | (17) $false % 189.69/30.38 | | % 189.69/30.38 | | CLOSE: (17) is inconsistent. % 189.69/30.38 | | % 189.69/30.38 | Case 2: % 189.69/30.38 | | % 189.69/30.38 | | (18) ~ (all_250_23 = e2) % 189.69/30.38 | | (19) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.38 | | % 189.69/30.38 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 189.69/30.38 | | (14), (19) are inconsistent by sub-proof #192. % 189.69/30.38 | | % 189.69/30.38 | End of split % 189.69/30.38 | % 189.69/30.38 End of proof % 189.69/30.38 % 189.69/30.38 Sub-proof #173 shows that the following formulas are inconsistent: % 189.69/30.38 ---------------------------------------------------------------- % 189.69/30.38 (1) all_252_20 = e2 % 189.69/30.38 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.38 (3) ~ (all_20_2 = e4) % 189.69/30.38 (4) all_252_15 = e4 % 189.69/30.38 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.38 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.38 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.38 (6) op(e0, e2) = e4 % 189.69/30.38 (7) op(e3, e1) = all_36_2 % 189.69/30.38 (8) ~ (e2 = e1) % 189.69/30.38 (9) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.38 (10) all_252_12 = e0 % 189.69/30.38 (11) op(e4, e1) = e0 % 189.69/30.38 (12) all_252_11 = e2 % 189.69/30.38 (13) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.38 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.38 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.38 (14) ~ (e4 = e0) % 189.69/30.38 (15) ~ (e4 = e3) % 189.69/30.38 (16) ~ (all_36_2 = e2) % 189.69/30.38 (17) ~ (all_40_2 = all_34_2) % 189.69/30.38 (18) ~ (all_244_24 = all_20_2) % 189.69/30.38 (19) op(e1, e4) = e0 % 189.69/30.38 (20) all_252_23 = e1 % 189.69/30.38 (21) ~ (all_20_2 = e3) % 189.69/30.38 (22) op(e0, e0) = all_244_24 % 189.69/30.38 (23) op(e0, e1) = all_20_2 % 189.69/30.38 (24) all_252_19 = e4 % 189.69/30.38 (25) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.38 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.38 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.38 (26) ~ (all_20_2 = e0) % 189.69/30.38 (27) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = % 189.69/30.38 e2) | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, % 189.69/30.38 e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.38 (28) ~ (all_20_2 = e2) % 189.69/30.38 (29) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.38 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.38 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.38 (30) ~ (e3 = e0) % 189.69/30.38 (31) ~ (all_20_2 = all_8_1) % 189.69/30.38 (32) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.38 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.38 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.38 (33) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.38 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.38 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.38 (34) ~ (e3 = e2) % 189.69/30.38 (35) op(e0, e3) = all_8_1 % 189.69/30.38 (36) op(e1, e4) = e1 % 189.69/30.38 (37) ~ (e4 = e2) % 189.69/30.38 (38) op(e2, e0) = all_40_2 % 189.69/30.38 (39) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.38 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.38 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.38 (40) ~ (e1 = e0) % 189.69/30.38 (41) all_250_23 = all_20_2 % 189.69/30.38 (42) ~ (e3 = e1) % 189.69/30.38 (43) ~ (e2 = e0) % 189.69/30.38 (44) op(e0, e1) = e1 % 189.69/30.38 (45) op(e1, e0) = all_34_2 % 189.69/30.38 (46) ~ (all_34_2 = e2) % 189.69/30.38 (47) ~ (e4 = e1) % 189.69/30.38 (48) op(e2, e0) = e1 % 189.69/30.38 % 189.69/30.38 Begin of proof % 189.69/30.38 | % 189.69/30.38 | BETA: splitting (27) gives: % 189.69/30.38 | % 189.69/30.38 | Case 1: % 189.69/30.38 | | % 189.69/30.38 | | (49) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 189.69/30.38 | | = e2) % 189.69/30.38 | | % 189.69/30.38 | | BETA: splitting (49) gives: % 189.69/30.38 | | % 189.69/30.38 | | Case 1: % 189.69/30.38 | | | % 189.69/30.38 | | | (50) all_252_12 = e2 & op(e1, e4) = e2 % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 189.69/30.38 | | | (14), (15), (16), (18), (19), (21), (22), (23), (25), (26), % 189.69/30.38 | | | (28), (29), (30), (31), (33), (34), (35), (36), (37), (40), % 189.69/30.38 | | | (41), (42), (43), (44), (47), (50) are inconsistent by % 189.69/30.38 | | | sub-proof #183. % 189.69/30.38 | | | % 189.69/30.38 | | Case 2: % 189.69/30.38 | | | % 189.69/30.38 | | | (51) all_252_13 = e2 & op(e1, e3) = e2 % 189.69/30.38 | | | % 189.69/30.38 | | | ALPHA: (51) implies: % 189.69/30.38 | | | (52) all_252_13 = e2 % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (15), (17), (18), % 189.69/30.38 | | | (20), (22), (24), (25), (26), (28), (30), (31), (32), (34), % 189.69/30.38 | | | (35), (38), (39), (41), (42), (45), (47), (48), (52) are % 189.69/30.38 | | | inconsistent by sub-proof #176. % 189.69/30.38 | | | % 189.69/30.38 | | End of split % 189.69/30.38 | | % 189.69/30.38 | Case 2: % 189.69/30.38 | | % 189.69/30.38 | | (53) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) % 189.69/30.38 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 189.69/30.38 | | % 189.69/30.38 | | BETA: splitting (53) gives: % 189.69/30.38 | | % 189.69/30.38 | | Case 1: % 189.69/30.38 | | | % 189.69/30.38 | | | (54) all_252_14 = e2 & op(e1, e2) = e2 % 189.69/30.38 | | | % 189.69/30.38 | | | ALPHA: (54) implies: % 189.69/30.38 | | | (55) all_252_14 = e2 % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (15), (17), (18), % 189.69/30.38 | | | (20), (22), (24), (25), (26), (28), (30), (31), (32), (34), % 189.69/30.38 | | | (35), (38), (39), (41), (42), (45), (47), (48), (55) are % 189.69/30.38 | | | inconsistent by sub-proof #174. % 189.69/30.38 | | | % 189.69/30.38 | | Case 2: % 189.69/30.38 | | | % 189.69/30.38 | | | (56) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, % 189.69/30.38 | | | e0) = e2) % 189.69/30.38 | | | % 189.69/30.38 | | | BETA: splitting (56) gives: % 189.69/30.38 | | | % 189.69/30.38 | | | Case 1: % 189.69/30.38 | | | | % 189.69/30.38 | | | | (57) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.38 | | | | % 189.69/30.38 | | | | REF_CLOSE: (4), (37), (57) are inconsistent by sub-proof #199. % 189.69/30.38 | | | | % 189.69/30.38 | | | Case 2: % 189.69/30.38 | | | | % 189.69/30.38 | | | | (58) all_252_19 = e2 & op(e1, e0) = e2 % 189.69/30.38 | | | | % 189.69/30.38 | | | | REF_CLOSE: (2), (45), (46), (58) are inconsistent by sub-proof #438. % 189.69/30.38 | | | | % 189.69/30.38 | | | End of split % 189.69/30.38 | | | % 189.69/30.38 | | End of split % 189.69/30.38 | | % 189.69/30.38 | End of split % 189.69/30.38 | % 189.69/30.38 End of proof % 189.69/30.38 % 189.69/30.38 Sub-proof #174 shows that the following formulas are inconsistent: % 189.69/30.38 ---------------------------------------------------------------- % 189.69/30.38 (1) all_252_20 = e2 % 189.69/30.38 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.38 (3) ~ (all_20_2 = e4) % 189.69/30.38 (4) all_252_15 = e4 % 189.69/30.38 (5) op(e0, e2) = e4 % 189.69/30.38 (6) ~ (e2 = e1) % 189.69/30.38 (7) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.38 (8) all_252_12 = e0 % 189.69/30.38 (9) all_252_14 = e2 % 189.69/30.38 (10) ~ (e4 = e3) % 189.69/30.38 (11) ~ (all_40_2 = all_34_2) % 189.69/30.38 (12) ~ (all_244_24 = all_20_2) % 189.69/30.38 (13) all_252_23 = e1 % 189.69/30.38 (14) op(e0, e0) = all_244_24 % 189.69/30.38 (15) all_252_19 = e4 % 189.69/30.38 (16) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.38 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.38 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.38 (17) ~ (all_20_2 = e0) % 189.69/30.38 (18) ~ (all_20_2 = e2) % 189.69/30.38 (19) ~ (e3 = e0) % 189.69/30.38 (20) ~ (all_20_2 = all_8_1) % 189.69/30.38 (21) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.38 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.38 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.38 (22) ~ (e3 = e2) % 189.69/30.38 (23) op(e0, e3) = all_8_1 % 189.69/30.38 (24) op(e2, e0) = all_40_2 % 189.69/30.38 (25) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.38 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.38 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.38 (26) all_250_23 = all_20_2 % 189.69/30.38 (27) ~ (e3 = e1) % 189.69/30.38 (28) op(e1, e0) = all_34_2 % 189.69/30.38 (29) ~ (e4 = e1) % 189.69/30.38 (30) op(e2, e0) = e1 % 189.69/30.38 % 189.69/30.38 Begin of proof % 189.69/30.38 | % 189.69/30.38 | BETA: splitting (21) gives: % 189.69/30.38 | % 189.69/30.38 | Case 1: % 189.69/30.38 | | % 189.69/30.38 | | (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) % 189.69/30.38 | | = e3) % 189.69/30.38 | | % 189.69/30.38 | | BETA: splitting (31) gives: % 189.69/30.38 | | % 189.69/30.38 | | Case 1: % 189.69/30.38 | | | % 189.69/30.38 | | | (32) all_252_12 = e3 & op(e1, e4) = e3 % 189.69/30.38 | | | % 189.69/30.38 | | | ALPHA: (32) implies: % 189.69/30.38 | | | (33) all_252_12 = e3 % 189.69/30.38 | | | % 189.69/30.38 | | | REF_CLOSE: (8), (19), (33) are inconsistent by sub-proof #381. % 189.69/30.38 | | | % 189.69/30.38 | | Case 2: % 189.69/30.38 | | | % 189.69/30.38 | | | (34) all_252_13 = e3 & op(e1, e3) = e3 % 189.69/30.38 | | | % 189.69/30.38 | | | ALPHA: (34) implies: % 189.69/30.38 | | | (35) all_252_13 = e3 % 189.69/30.38 | | | % 189.69/30.38 | | | BETA: splitting (25) gives: % 189.69/30.38 | | | % 189.69/30.38 | | | Case 1: % 189.69/30.38 | | | | % 189.69/30.38 | | | | (36) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, % 189.69/30.38 | | | | e3) = e1) % 189.69/30.38 | | | | % 189.69/30.38 | | | | BETA: splitting (36) gives: % 189.69/30.38 | | | | % 189.69/30.38 | | | | Case 1: % 189.69/30.38 | | | | | % 189.69/30.38 | | | | | (37) all_252_12 = e1 & op(e1, e4) = e1 % 189.69/30.38 | | | | | % 189.69/30.38 | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (12), (13), (14), (16), (17), % 189.69/30.38 | | | | | (18), (20), (23), (26), (37) are inconsistent by sub-proof % 189.69/30.38 | | | | | #181. % 189.69/30.38 | | | | | % 189.69/30.38 | | | | Case 2: % 189.69/30.38 | | | | | % 189.69/30.38 | | | | | (38) all_252_13 = e1 & op(e1, e3) = e1 % 189.69/30.38 | | | | | % 189.69/30.38 | | | | | REF_CLOSE: (27), (35), (38) are inconsistent by sub-proof #175. % 189.69/30.38 | | | | | % 189.69/30.38 | | | | End of split % 189.69/30.38 | | | | % 189.69/30.38 | | | Case 2: % 189.69/30.38 | | | | % 189.69/30.39 | | | | (39) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.39 | | | | e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.39 | | | | % 189.69/30.39 | | | | BETA: splitting (39) gives: % 189.69/30.39 | | | | % 189.69/30.39 | | | | Case 1: % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | (40) all_252_14 = e1 & op(e1, e2) = e1 % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | ALPHA: (40) implies: % 189.69/30.39 | | | | | (41) all_252_14 = e1 % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | REF_CLOSE: (6), (9), (41) are inconsistent by sub-proof #391. % 189.69/30.39 | | | | | % 189.69/30.39 | | | | Case 2: % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | (42) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 189.69/30.39 | | | | | op(e1, e0) = e1) % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | REF_CLOSE: (2), (4), (11), (24), (28), (29), (30), (42) are % 189.69/30.39 | | | | | inconsistent by sub-proof #178. % 189.69/30.39 | | | | | % 189.69/30.39 | | | | End of split % 189.69/30.39 | | | | % 189.69/30.39 | | | End of split % 189.69/30.39 | | | % 189.69/30.39 | | End of split % 189.69/30.39 | | % 189.69/30.39 | Case 2: % 189.69/30.39 | | % 189.69/30.39 | | (43) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) % 189.69/30.39 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.39 | | % 189.69/30.39 | | BETA: splitting (43) gives: % 189.69/30.39 | | % 189.69/30.39 | | Case 1: % 189.69/30.39 | | | % 189.69/30.39 | | | (44) all_252_14 = e3 & op(e1, e2) = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | ALPHA: (44) implies: % 189.69/30.39 | | | (45) all_252_14 = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | COMBINE_EQS: (9), (45) imply: % 189.69/30.39 | | | (46) e3 = e2 % 189.69/30.39 | | | % 189.69/30.39 | | | REDUCE: (22), (46) imply: % 189.69/30.39 | | | (47) $false % 189.69/30.39 | | | % 189.69/30.39 | | | CLOSE: (47) is inconsistent. % 189.69/30.39 | | | % 189.69/30.39 | | Case 2: % 189.69/30.39 | | | % 189.69/30.39 | | | (48) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.39 | | | e0) = e3) % 189.69/30.39 | | | % 189.69/30.39 | | | BETA: splitting (48) gives: % 189.69/30.39 | | | % 189.69/30.39 | | | Case 1: % 189.69/30.39 | | | | % 189.69/30.39 | | | | (49) all_252_15 = e3 & op(e1, e1) = e3 % 189.69/30.39 | | | | % 189.69/30.39 | | | | REF_CLOSE: (4), (10), (49) are inconsistent by sub-proof #265. % 189.69/30.39 | | | | % 189.69/30.39 | | | Case 2: % 189.69/30.39 | | | | % 189.69/30.39 | | | | (50) all_252_19 = e3 & op(e1, e0) = e3 % 189.69/30.39 | | | | % 189.69/30.39 | | | | REF_CLOSE: (10), (15), (50) are inconsistent by sub-proof #177. % 189.69/30.39 | | | | % 189.69/30.39 | | | End of split % 189.69/30.39 | | | % 189.69/30.39 | | End of split % 189.69/30.39 | | % 189.69/30.39 | End of split % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #175 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_13 = e1 & op(e1, e3) = e1 % 189.69/30.39 (2) all_252_13 = e3 % 189.69/30.39 (3) ~ (e3 = e1) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | ALPHA: (1) implies: % 189.69/30.39 | (4) all_252_13 = e1 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (2), (4) imply: % 189.69/30.39 | (5) e3 = e1 % 189.69/30.39 | % 189.69/30.39 | SIMP: (5) implies: % 189.69/30.39 | (6) e3 = e1 % 189.69/30.39 | % 189.69/30.39 | REDUCE: (3), (6) imply: % 189.69/30.39 | (7) $false % 189.69/30.39 | % 189.69/30.39 | CLOSE: (7) is inconsistent. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #176 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_13 = e2 % 189.69/30.39 (2) all_252_20 = e2 % 189.69/30.39 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.39 (4) ~ (all_20_2 = e4) % 189.69/30.39 (5) all_252_15 = e4 % 189.69/30.39 (6) op(e0, e2) = e4 % 189.69/30.39 (7) ~ (e2 = e1) % 189.69/30.39 (8) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.39 (9) all_252_12 = e0 % 189.69/30.39 (10) ~ (e4 = e3) % 189.69/30.39 (11) ~ (all_40_2 = all_34_2) % 189.69/30.39 (12) ~ (all_244_24 = all_20_2) % 189.69/30.39 (13) all_252_23 = e1 % 189.69/30.39 (14) op(e0, e0) = all_244_24 % 189.69/30.39 (15) all_252_19 = e4 % 189.69/30.39 (16) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.39 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.39 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.39 (17) ~ (all_20_2 = e0) % 189.69/30.39 (18) ~ (all_20_2 = e2) % 189.69/30.39 (19) ~ (e3 = e0) % 189.69/30.39 (20) ~ (all_20_2 = all_8_1) % 189.69/30.39 (21) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) = % 189.69/30.39 e3) | (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, % 189.69/30.39 e1) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.39 (22) ~ (e3 = e2) % 189.69/30.39 (23) op(e0, e3) = all_8_1 % 189.69/30.39 (24) op(e2, e0) = all_40_2 % 189.69/30.39 (25) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 189.69/30.39 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.39 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.39 (26) all_250_23 = all_20_2 % 189.69/30.39 (27) ~ (e3 = e1) % 189.69/30.39 (28) op(e1, e0) = all_34_2 % 189.69/30.39 (29) ~ (e4 = e1) % 189.69/30.39 (30) op(e2, e0) = e1 % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | BETA: splitting (21) gives: % 189.69/30.39 | % 189.69/30.39 | Case 1: % 189.69/30.39 | | % 189.69/30.39 | | (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_13 = e3 & op(e1, e3) % 189.69/30.39 | | = e3) % 189.69/30.39 | | % 189.69/30.39 | | BETA: splitting (31) gives: % 189.69/30.39 | | % 189.69/30.39 | | Case 1: % 189.69/30.39 | | | % 189.69/30.39 | | | (32) all_252_12 = e3 & op(e1, e4) = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | ALPHA: (32) implies: % 189.69/30.39 | | | (33) all_252_12 = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | REF_CLOSE: (9), (19), (33) are inconsistent by sub-proof #381. % 189.69/30.39 | | | % 189.69/30.39 | | Case 2: % 189.69/30.39 | | | % 189.69/30.39 | | | (34) all_252_13 = e3 & op(e1, e3) = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | REF_CLOSE: (1), (22), (34) are inconsistent by sub-proof #182. % 189.69/30.39 | | | % 189.69/30.39 | | End of split % 189.69/30.39 | | % 189.69/30.39 | Case 2: % 189.69/30.39 | | % 189.69/30.39 | | (35) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_15 = e3 & op(e1, e1) % 189.69/30.39 | | = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 189.69/30.39 | | % 189.69/30.39 | | BETA: splitting (35) gives: % 189.69/30.39 | | % 189.69/30.39 | | Case 1: % 189.69/30.39 | | | % 189.69/30.39 | | | (36) all_252_14 = e3 & op(e1, e2) = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | ALPHA: (36) implies: % 189.69/30.39 | | | (37) all_252_14 = e3 % 189.69/30.39 | | | % 189.69/30.39 | | | BETA: splitting (25) gives: % 189.69/30.39 | | | % 189.69/30.39 | | | Case 1: % 189.69/30.39 | | | | % 189.69/30.39 | | | | (38) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, % 189.69/30.39 | | | | e3) = e1) % 189.69/30.39 | | | | % 189.69/30.39 | | | | BETA: splitting (38) gives: % 189.69/30.39 | | | | % 189.69/30.39 | | | | Case 1: % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | (39) all_252_12 = e1 & op(e1, e4) = e1 % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (12), (13), (14), (16), (17), % 189.69/30.39 | | | | | (18), (20), (23), (26), (39) are inconsistent by sub-proof % 189.69/30.39 | | | | | #181. % 189.69/30.39 | | | | | % 189.69/30.39 | | | | Case 2: % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | (40) all_252_13 = e1 & op(e1, e3) = e1 % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | REF_CLOSE: (1), (7), (40) are inconsistent by sub-proof #180. % 189.69/30.39 | | | | | % 189.69/30.39 | | | | End of split % 189.69/30.39 | | | | % 189.69/30.39 | | | Case 2: % 189.69/30.39 | | | | % 189.69/30.39 | | | | (41) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 189.69/30.39 | | | | e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.39 | | | | % 189.69/30.39 | | | | BETA: splitting (41) gives: % 189.69/30.39 | | | | % 189.69/30.39 | | | | Case 1: % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | (42) all_252_14 = e1 & op(e1, e2) = e1 % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | ALPHA: (42) implies: % 189.69/30.39 | | | | | (43) all_252_14 = e1 % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | REF_CLOSE: (27), (37), (43) are inconsistent by sub-proof #179. % 189.69/30.39 | | | | | % 189.69/30.39 | | | | Case 2: % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | (44) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & % 189.69/30.39 | | | | | op(e1, e0) = e1) % 189.69/30.39 | | | | | % 189.69/30.39 | | | | | REF_CLOSE: (3), (5), (11), (24), (28), (29), (30), (44) are % 189.69/30.39 | | | | | inconsistent by sub-proof #178. % 189.69/30.39 | | | | | % 189.69/30.39 | | | | End of split % 189.69/30.39 | | | | % 189.69/30.39 | | | End of split % 189.69/30.39 | | | % 189.69/30.39 | | Case 2: % 189.69/30.39 | | | % 189.69/30.39 | | | (45) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_19 = e3 & op(e1, % 189.69/30.39 | | | e0) = e3) % 189.69/30.39 | | | % 189.69/30.39 | | | BETA: splitting (45) gives: % 189.69/30.39 | | | % 189.69/30.39 | | | Case 1: % 189.69/30.39 | | | | % 189.69/30.39 | | | | (46) all_252_15 = e3 & op(e1, e1) = e3 % 189.69/30.39 | | | | % 189.69/30.39 | | | | REF_CLOSE: (5), (10), (46) are inconsistent by sub-proof #265. % 189.69/30.39 | | | | % 189.69/30.39 | | | Case 2: % 189.69/30.39 | | | | % 189.69/30.39 | | | | (47) all_252_19 = e3 & op(e1, e0) = e3 % 189.69/30.39 | | | | % 189.69/30.39 | | | | REF_CLOSE: (10), (15), (47) are inconsistent by sub-proof #177. % 189.69/30.39 | | | | % 189.69/30.39 | | | End of split % 189.69/30.39 | | | % 189.69/30.39 | | End of split % 189.69/30.39 | | % 189.69/30.39 | End of split % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #177 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_19 = e3 & op(e1, e0) = e3 % 189.69/30.39 (2) all_252_19 = e4 % 189.69/30.39 (3) ~ (e4 = e3) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | ALPHA: (1) implies: % 189.69/30.39 | (4) all_252_19 = e3 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (2), (4) imply: % 189.69/30.39 | (5) e4 = e3 % 189.69/30.39 | % 189.69/30.39 | SIMP: (5) implies: % 189.69/30.39 | (6) e4 = e3 % 189.69/30.39 | % 189.69/30.39 | REDUCE: (3), (6) imply: % 189.69/30.39 | (7) $false % 189.69/30.39 | % 189.69/30.39 | CLOSE: (7) is inconsistent. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #178 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.39 (2) all_252_15 = e4 % 189.69/30.39 (3) ~ (all_40_2 = all_34_2) % 189.69/30.39 (4) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 189.69/30.39 (5) op(e2, e0) = all_40_2 % 189.69/30.39 (6) op(e1, e0) = all_34_2 % 189.69/30.39 (7) ~ (e4 = e1) % 189.69/30.39 (8) op(e2, e0) = e1 % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | BETA: splitting (4) gives: % 189.69/30.39 | % 189.69/30.39 | Case 1: % 189.69/30.39 | | % 189.69/30.39 | | (9) all_252_15 = e1 & op(e1, e1) = e1 % 189.69/30.39 | | % 189.69/30.39 | | REF_CLOSE: (2), (7), (9) are inconsistent by sub-proof #394. % 189.69/30.39 | | % 189.69/30.39 | Case 2: % 189.69/30.39 | | % 189.69/30.39 | | (10) all_252_19 = e1 & op(e1, e0) = e1 % 189.69/30.39 | | % 189.69/30.39 | | ALPHA: (10) implies: % 189.69/30.39 | | (11) op(e1, e0) = e1 % 189.69/30.39 | | % 189.69/30.39 | | REF_CLOSE: (1), (3), (5), (6), (8), (11) are inconsistent by sub-proof #352. % 189.69/30.39 | | % 189.69/30.39 | End of split % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #179 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_14 = e3 % 189.69/30.39 (2) all_252_14 = e1 % 189.69/30.39 (3) ~ (e3 = e1) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (1), (2) imply: % 189.69/30.39 | (4) e3 = e1 % 189.69/30.39 | % 189.69/30.39 | SIMP: (4) implies: % 189.69/30.39 | (5) e3 = e1 % 189.69/30.39 | % 189.69/30.39 | REDUCE: (3), (5) imply: % 189.69/30.39 | (6) $false % 189.69/30.39 | % 189.69/30.39 | CLOSE: (6) is inconsistent. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #180 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_13 = e1 & op(e1, e3) = e1 % 189.69/30.39 (2) all_252_13 = e2 % 189.69/30.39 (3) ~ (e2 = e1) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | ALPHA: (1) implies: % 189.69/30.39 | (4) all_252_13 = e1 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (2), (4) imply: % 189.69/30.39 | (5) e2 = e1 % 189.69/30.39 | % 189.69/30.39 | SIMP: (5) implies: % 189.69/30.39 | (6) e2 = e1 % 189.69/30.39 | % 189.69/30.39 | REDUCE: (3), (6) imply: % 189.69/30.39 | (7) $false % 189.69/30.39 | % 189.69/30.39 | CLOSE: (7) is inconsistent. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #181 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_20 = e2 % 189.69/30.39 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.39 (3) ~ (all_20_2 = e4) % 189.69/30.39 (4) op(e0, e2) = e4 % 189.69/30.39 (5) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.39 (6) all_252_12 = e0 % 189.69/30.39 (7) all_252_12 = e1 & op(e1, e4) = e1 % 189.69/30.39 (8) ~ (all_244_24 = all_20_2) % 189.69/30.39 (9) all_252_23 = e1 % 189.69/30.39 (10) op(e0, e0) = all_244_24 % 189.69/30.39 (11) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.39 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.39 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.39 (12) ~ (all_20_2 = e0) % 189.69/30.39 (13) ~ (all_20_2 = e2) % 189.69/30.39 (14) ~ (all_20_2 = all_8_1) % 189.69/30.39 (15) op(e0, e3) = all_8_1 % 189.69/30.39 (16) all_250_23 = all_20_2 % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | ALPHA: (7) implies: % 189.69/30.39 | (17) all_252_12 = e1 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (6), (17) imply: % 189.69/30.39 | (18) e1 = e0 % 189.69/30.39 | % 189.69/30.39 | SIMP: (18) implies: % 189.69/30.39 | (19) e1 = e0 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (9), (19) imply: % 189.69/30.39 | (20) all_252_23 = e0 % 189.69/30.39 | % 189.69/30.39 | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (12), (13), (14), (15), % 189.69/30.39 | (16), (20) are inconsistent by sub-proof #192. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #182 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_13 = e3 & op(e1, e3) = e3 % 189.69/30.39 (2) all_252_13 = e2 % 189.69/30.39 (3) ~ (e3 = e2) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | ALPHA: (1) implies: % 189.69/30.39 | (4) all_252_13 = e3 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (2), (4) imply: % 189.69/30.39 | (5) e3 = e2 % 189.69/30.39 | % 189.69/30.39 | REDUCE: (3), (5) imply: % 189.69/30.39 | (6) $false % 189.69/30.39 | % 189.69/30.39 | CLOSE: (6) is inconsistent. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #183 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_20 = e2 % 189.69/30.39 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.39 (3) ~ (all_20_2 = e4) % 189.69/30.39 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.39 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.39 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.39 (5) op(e0, e2) = e4 % 189.69/30.39 (6) op(e3, e1) = all_36_2 % 189.69/30.39 (7) ~ (e2 = e1) % 189.69/30.39 (8) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.39 (9) all_252_12 = e0 % 189.69/30.39 (10) op(e4, e1) = e0 % 189.69/30.39 (11) all_252_11 = e2 % 189.69/30.39 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.39 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.39 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.39 (13) ~ (e4 = e0) % 189.69/30.39 (14) ~ (e4 = e3) % 189.69/30.39 (15) ~ (all_36_2 = e2) % 189.69/30.39 (16) ~ (all_244_24 = all_20_2) % 189.69/30.39 (17) op(e1, e4) = e0 % 189.69/30.39 (18) ~ (all_20_2 = e3) % 189.69/30.39 (19) op(e0, e0) = all_244_24 % 189.69/30.39 (20) op(e0, e1) = all_20_2 % 189.69/30.39 (21) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.39 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.39 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.39 (22) ~ (all_20_2 = e0) % 189.69/30.39 (23) ~ (all_20_2 = e2) % 189.69/30.39 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.39 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.39 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.39 (25) ~ (e3 = e0) % 189.69/30.39 (26) ~ (all_20_2 = all_8_1) % 189.69/30.39 (27) all_252_12 = e2 & op(e1, e4) = e2 % 189.69/30.39 (28) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.39 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.39 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.39 (29) ~ (e3 = e2) % 189.69/30.39 (30) op(e0, e3) = all_8_1 % 189.69/30.39 (31) op(e1, e4) = e1 % 189.69/30.39 (32) ~ (e4 = e2) % 189.69/30.39 (33) ~ (e1 = e0) % 189.69/30.39 (34) all_250_23 = all_20_2 % 189.69/30.39 (35) ~ (e3 = e1) % 189.69/30.39 (36) ~ (e2 = e0) % 189.69/30.39 (37) op(e0, e1) = e1 % 189.69/30.39 (38) ~ (e4 = e1) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | ALPHA: (27) implies: % 189.69/30.39 | (39) all_252_12 = e2 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (9), (39) imply: % 189.69/30.39 | (40) e2 = e0 % 189.69/30.39 | % 189.69/30.39 | SIMP: (40) implies: % 189.69/30.39 | (41) e2 = e0 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (11), (41) imply: % 189.69/30.39 | (42) all_252_11 = e0 % 189.69/30.39 | % 189.69/30.39 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (13), (14), % 189.69/30.39 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), % 189.69/30.39 | (26), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 189.69/30.39 | (38), (42) are inconsistent by sub-proof #191. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #184 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) op(e2, e1) = e4 % 189.69/30.39 (2) all_252_20 = e2 % 189.69/30.39 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.39 (4) ~ (all_20_2 = e4) % 189.69/30.39 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.39 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.39 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.39 (6) op(e0, e2) = e4 % 189.69/30.39 (7) op(e3, e1) = all_36_2 % 189.69/30.39 (8) ~ (e2 = e1) % 189.69/30.39 (9) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.39 (10) op(e4, e1) = e0 % 189.69/30.39 (11) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.39 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.39 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.39 (12) op(e2, e1) = e0 % 189.69/30.39 (13) all_252_11 = e4 % 189.69/30.39 (14) ~ (e4 = e0) % 189.69/30.39 (15) ~ (e4 = e3) % 189.69/30.39 (16) ~ (all_36_2 = e2) % 189.69/30.39 (17) ~ (all_244_24 = all_20_2) % 189.69/30.39 (18) op(e1, e4) = e0 % 189.69/30.39 (19) ~ (all_20_2 = e3) % 189.69/30.39 (20) op(e0, e0) = all_244_24 % 189.69/30.39 (21) op(e0, e1) = all_20_2 % 189.69/30.39 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.39 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.39 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.39 (23) ~ (all_20_2 = e0) % 189.69/30.39 (24) ~ (all_20_2 = e2) % 189.69/30.39 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.39 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.39 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.39 (26) ~ (e3 = e0) % 189.69/30.39 (27) ~ (all_20_2 = all_8_1) % 189.69/30.39 (28) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.39 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.39 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.39 (29) ~ (e3 = e2) % 189.69/30.39 (30) op(e0, e3) = all_8_1 % 189.69/30.39 (31) op(e1, e4) = e1 % 189.69/30.39 (32) ~ (e4 = e2) % 189.69/30.39 (33) ~ (e1 = e0) % 189.69/30.39 (34) all_250_23 = all_20_2 % 189.69/30.39 (35) ~ (e3 = e1) % 189.69/30.39 (36) ~ (e2 = e0) % 189.69/30.39 (37) op(e0, e1) = e1 % 189.69/30.39 (38) ~ (e4 = e1) % 189.69/30.39 % 189.69/30.39 Begin of proof % 189.69/30.39 | % 189.69/30.39 | GROUND_INST: instantiating (3) with e0, e4, e1, e2, simplifying with (1), (12) % 189.69/30.39 | gives: % 189.69/30.39 | (39) e4 = e0 % 189.69/30.39 | % 189.69/30.39 | COMBINE_EQS: (13), (39) imply: % 189.69/30.39 | (40) all_252_11 = e0 % 189.69/30.39 | % 189.69/30.39 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (15), % 189.69/30.39 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26), % 189.69/30.39 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), % 189.69/30.39 | (38), (40) are inconsistent by sub-proof #191. % 189.69/30.39 | % 189.69/30.39 End of proof % 189.69/30.39 % 189.69/30.39 Sub-proof #185 shows that the following formulas are inconsistent: % 189.69/30.39 ---------------------------------------------------------------- % 189.69/30.39 (1) all_252_20 = e2 % 189.69/30.39 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.39 (3) op(e0, e2) = e4 % 189.69/30.39 (4) ~ (e2 = e1) % 189.69/30.39 (5) all_252_23 = e2 & op(e0, e1) = e2 % 189.69/30.39 (6) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.39 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.69/30.39 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.39 (7) op(e0, e3) = all_8_1 % 189.69/30.39 (8) ~ (e1 = e0) % 189.69/30.39 (9) op(e0, e3) = e0 % 189.69/30.40 (10) all_252_24 = e3 % 189.69/30.40 (11) ~ (e3 = e1) % 189.69/30.40 (12) ~ (e4 = e1) % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | ALPHA: (5) implies: % 189.69/30.40 | (13) all_252_23 = e2 % 189.69/30.40 | % 189.69/30.40 | BETA: splitting (6) gives: % 189.69/30.40 | % 189.69/30.40 | Case 1: % 189.69/30.40 | | % 189.69/30.40 | | (14) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.69/30.40 | | = e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (14) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (15) all_252_20 = e1 & op(e0, e4) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (1), (4), (15) are inconsistent by sub-proof #242. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (16) all_252_21 = e1 & op(e0, e3) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (7), (8), (9), (16) are inconsistent by sub-proof #206. % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | Case 2: % 189.69/30.40 | | % 189.69/30.40 | | (17) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.69/30.40 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (17) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (18) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (18) implies: % 189.69/30.40 | | | (19) op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (3), (12), (19) are inconsistent by sub-proof #256. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (20) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.69/30.40 | | | e0) = e1) % 189.69/30.40 | | | % 189.69/30.40 | | | BETA: splitting (20) gives: % 189.69/30.40 | | | % 189.69/30.40 | | | Case 1: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (21) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | ALPHA: (21) implies: % 189.69/30.40 | | | | (22) all_252_23 = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | REF_CLOSE: (4), (13), (22) are inconsistent by sub-proof #270. % 189.69/30.40 | | | | % 189.69/30.40 | | | Case 2: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (23) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | ALPHA: (23) implies: % 189.69/30.40 | | | | (24) all_252_24 = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | REF_CLOSE: (10), (11), (24) are inconsistent by sub-proof #245. % 189.69/30.40 | | | | % 189.69/30.40 | | | End of split % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | End of split % 189.69/30.40 | % 189.69/30.40 End of proof % 189.69/30.40 % 189.69/30.40 Sub-proof #186 shows that the following formulas are inconsistent: % 189.69/30.40 ---------------------------------------------------------------- % 189.69/30.40 (1) all_252_20 = e2 % 189.69/30.40 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.40 (3) op(e0, e2) = e4 % 189.69/30.40 (4) ~ (e2 = e1) % 189.69/30.40 (5) ~ (e4 = e0) % 189.69/30.40 (6) op(e0, e0) = all_244_24 % 189.69/30.40 (7) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) % 189.69/30.40 | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) = % 189.69/30.40 e0) % 189.69/30.40 (8) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.40 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.69/30.40 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 (9) ~ (e3 = e0) % 189.69/30.40 (10) all_252_23 = e3 % 189.69/30.40 (11) all_252_22 = e4 % 189.69/30.40 (12) ~ (e1 = e0) % 189.69/30.40 (13) ~ (e3 = e1) % 189.69/30.40 (14) ~ (e2 = e0) % 189.69/30.40 (15) ~ (all_244_24 = e1) % 189.69/30.40 (16) ~ (e4 = e1) % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | BETA: splitting (8) gives: % 189.69/30.40 | % 189.69/30.40 | Case 1: % 189.69/30.40 | | % 189.69/30.40 | | (17) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.69/30.40 | | = e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (17) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (18) all_252_20 = e1 & op(e0, e4) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (18) implies: % 189.69/30.40 | | | (19) all_252_20 = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (1), (4), (19) are inconsistent by sub-proof #228. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (20) all_252_21 = e1 & op(e0, e3) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (20) implies: % 189.69/30.40 | | | (21) all_252_21 = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (1), (5), (7), (9), (10), (11), (12), (14), (21) are % 189.69/30.40 | | | inconsistent by sub-proof #187. % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | Case 2: % 189.69/30.40 | | % 189.69/30.40 | | (22) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.69/30.40 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (22) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (23) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (23) implies: % 189.69/30.40 | | | (24) op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (3), (16), (24) are inconsistent by sub-proof #256. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (25) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.69/30.40 | | | e0) = e1) % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (6), (10), (13), (15), (25) are inconsistent by sub-proof % 189.69/30.40 | | | #436. % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | End of split % 189.69/30.40 | % 189.69/30.40 End of proof % 189.69/30.40 % 189.69/30.40 Sub-proof #187 shows that the following formulas are inconsistent: % 189.69/30.40 ---------------------------------------------------------------- % 189.69/30.40 (1) all_252_20 = e2 % 189.69/30.40 (2) ~ (e4 = e0) % 189.69/30.40 (3) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) % 189.69/30.40 | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) = % 189.69/30.40 e0) % 189.69/30.40 (4) ~ (e3 = e0) % 189.69/30.40 (5) all_252_23 = e3 % 189.69/30.40 (6) all_252_22 = e4 % 189.69/30.40 (7) ~ (e1 = e0) % 189.69/30.40 (8) ~ (e2 = e0) % 189.69/30.40 (9) all_252_21 = e1 % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | BETA: splitting (3) gives: % 189.69/30.40 | % 189.69/30.40 | Case 1: % 189.69/30.40 | | % 189.69/30.40 | | (10) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 189.69/30.40 | | = e0) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (10) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (11) all_252_20 = e0 & op(e0, e4) = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #240. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (12) all_252_21 = e0 & op(e0, e3) = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (12) implies: % 189.69/30.40 | | | (13) all_252_21 = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #333. % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | Case 2: % 189.69/30.40 | | % 189.69/30.40 | | (14) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 189.69/30.40 | | = e0) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (14) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (15) all_252_22 = e0 & op(e0, e2) = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #239. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (16) all_252_23 = e0 & op(e0, e1) = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (16) implies: % 189.69/30.40 | | | (17) all_252_23 = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | COMBINE_EQS: (5), (17) imply: % 189.69/30.40 | | | (18) e3 = e0 % 189.69/30.40 | | | % 189.69/30.40 | | | REDUCE: (4), (18) imply: % 189.69/30.40 | | | (19) $false % 189.69/30.40 | | | % 189.69/30.40 | | | CLOSE: (19) is inconsistent. % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | End of split % 189.69/30.40 | % 189.69/30.40 End of proof % 189.69/30.40 % 189.69/30.40 Sub-proof #188 shows that the following formulas are inconsistent: % 189.69/30.40 ---------------------------------------------------------------- % 189.69/30.40 (1) all_252_15 = e3 & op(e1, e1) = e3 % 189.69/30.40 (2) all_252_15 = e2 % 189.69/30.40 (3) ~ (e3 = e2) % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | ALPHA: (1) implies: % 189.69/30.40 | (4) all_252_15 = e3 % 189.69/30.40 | % 189.69/30.40 | COMBINE_EQS: (2), (4) imply: % 189.69/30.40 | (5) e3 = e2 % 189.69/30.40 | % 189.69/30.40 | REDUCE: (3), (5) imply: % 189.69/30.40 | (6) $false % 189.69/30.40 | % 189.69/30.40 | CLOSE: (6) is inconsistent. % 189.69/30.40 | % 189.69/30.40 End of proof % 189.69/30.40 % 189.69/30.40 Sub-proof #189 shows that the following formulas are inconsistent: % 189.69/30.40 ---------------------------------------------------------------- % 189.69/30.40 (1) all_252_20 = e2 % 189.69/30.40 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.40 (3) ~ (all_20_2 = e4) % 189.69/30.40 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.40 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.40 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.40 (5) op(e0, e2) = e4 % 189.69/30.40 (6) op(e3, e1) = all_36_2 % 189.69/30.40 (7) ~ (e2 = e1) % 189.69/30.40 (8) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.40 (9) op(e4, e1) = e0 % 189.69/30.40 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.40 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.40 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.40 (11) op(e2, e1) = e0 % 189.69/30.40 (12) ~ (e4 = e0) % 189.69/30.40 (13) ~ (e4 = e3) % 189.69/30.40 (14) ~ (all_36_2 = e2) % 189.69/30.40 (15) ~ (all_244_24 = all_20_2) % 189.69/30.40 (16) op(e1, e4) = e0 % 189.69/30.40 (17) ~ (all_20_2 = e3) % 189.69/30.40 (18) op(e0, e0) = all_244_24 % 189.69/30.40 (19) op(e0, e1) = all_20_2 % 189.69/30.40 (20) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.40 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.40 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 (21) ~ (all_20_2 = e0) % 189.69/30.40 (22) all_252_11 = e3 % 189.69/30.40 (23) ~ (all_20_2 = e2) % 189.69/30.40 (24) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.40 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.40 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.40 (25) op(e2, e1) = e3 % 189.69/30.40 (26) op(e0, e4) = e2 % 189.69/30.40 (27) ~ (e3 = e0) % 189.69/30.40 (28) ~ (all_20_2 = all_8_1) % 189.69/30.40 (29) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.40 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.40 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.40 (30) ~ (e3 = e2) % 189.69/30.40 (31) op(e0, e3) = all_8_1 % 189.69/30.40 (32) op(e1, e4) = e1 % 189.69/30.40 (33) ~ (e4 = e2) % 189.69/30.40 (34) ~ (e1 = e0) % 189.69/30.40 (35) op(e0, e3) = e0 % 189.69/30.40 (36) all_250_23 = all_20_2 % 189.69/30.40 (37) ~ (e3 = e1) % 189.69/30.40 (38) ~ (e2 = e0) % 189.69/30.40 (39) ~ (all_244_24 = e1) % 189.69/30.40 (40) ~ (e4 = e1) % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | BETA: splitting (20) gives: % 189.69/30.40 | % 189.69/30.40 | Case 1: % 189.69/30.40 | | % 189.69/30.40 | | (41) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.69/30.40 | | = e1) % 189.69/30.40 | | % 189.69/30.40 | | REF_CLOSE: (2), (7), (26), (31), (34), (35), (41) are inconsistent by % 189.69/30.40 | | sub-proof #205. % 189.69/30.40 | | % 189.69/30.40 | Case 2: % 189.69/30.40 | | % 189.69/30.40 | | (42) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.69/30.40 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (42) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (43) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (43) implies: % 189.69/30.40 | | | (44) op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (5), (40), (44) are inconsistent by sub-proof #256. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (45) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.69/30.40 | | | e0) = e1) % 189.69/30.40 | | | % 189.69/30.40 | | | BETA: splitting (45) gives: % 189.69/30.40 | | | % 189.69/30.40 | | | Case 1: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (46) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | ALPHA: (46) implies: % 189.69/30.40 | | | | (47) op(e0, e1) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | GROUND_INST: instantiating (2) with e0, e3, e1, e2, simplifying with % 189.69/30.40 | | | | (11), (25) gives: % 189.69/30.40 | | | | (48) e3 = e0 % 189.69/30.40 | | | | % 189.69/30.40 | | | | COMBINE_EQS: (22), (48) imply: % 189.69/30.40 | | | | (49) all_252_11 = e0 % 189.69/30.40 | | | | % 189.69/30.40 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), % 189.69/30.40 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), % 189.69/30.40 | | | | (24), (27), (28), (29), (30), (31), (32), (33), (34), (36), % 189.69/30.40 | | | | (37), (38), (40), (47), (49) are inconsistent by sub-proof % 189.69/30.40 | | | | #191. % 189.69/30.40 | | | | % 189.69/30.40 | | | Case 2: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (50) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | ALPHA: (50) implies: % 189.69/30.40 | | | | (51) op(e0, e0) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | REF_CLOSE: (2), (18), (39), (51) are inconsistent by sub-proof #474. % 189.69/30.40 | | | | % 189.69/30.40 | | | End of split % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | End of split % 189.69/30.40 | % 189.69/30.40 End of proof % 189.69/30.40 % 189.69/30.40 Sub-proof #190 shows that the following formulas are inconsistent: % 189.69/30.40 ---------------------------------------------------------------- % 189.69/30.40 (1) all_252_20 = e2 % 189.69/30.40 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.40 (3) ~ (all_20_2 = e4) % 189.69/30.40 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.40 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.40 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.40 (5) op(e0, e2) = e4 % 189.69/30.40 (6) op(e3, e1) = all_36_2 % 189.69/30.40 (7) ~ (e2 = e1) % 189.69/30.40 (8) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.40 (9) op(e2, e1) = e2 % 189.69/30.40 (10) op(e4, e1) = e0 % 189.69/30.40 (11) all_252_11 = e2 % 189.69/30.40 (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.40 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.40 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.40 (13) op(e2, e1) = e0 % 189.69/30.40 (14) ~ (e4 = e0) % 189.69/30.40 (15) ~ (e4 = e3) % 189.69/30.40 (16) ~ (all_36_2 = e2) % 189.69/30.40 (17) ~ (all_244_24 = all_20_2) % 189.69/30.40 (18) op(e1, e4) = e0 % 189.69/30.40 (19) ~ (all_20_2 = e3) % 189.69/30.40 (20) op(e0, e0) = all_244_24 % 189.69/30.40 (21) op(e0, e1) = all_20_2 % 189.69/30.40 (22) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.40 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.40 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 (23) ~ (all_20_2 = e0) % 189.69/30.40 (24) ~ (all_20_2 = e2) % 189.69/30.40 (25) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.40 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.40 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.40 (26) op(e0, e4) = e2 % 189.69/30.40 (27) ~ (e3 = e0) % 189.69/30.40 (28) ~ (all_20_2 = all_8_1) % 189.69/30.40 (29) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.40 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.40 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.40 (30) ~ (e3 = e2) % 189.69/30.40 (31) op(e0, e3) = all_8_1 % 189.69/30.40 (32) op(e1, e4) = e1 % 189.69/30.40 (33) ~ (e4 = e2) % 189.69/30.40 (34) ~ (e1 = e0) % 189.69/30.40 (35) op(e0, e3) = e0 % 189.69/30.40 (36) all_250_23 = all_20_2 % 189.69/30.40 (37) ~ (e3 = e1) % 189.69/30.40 (38) ~ (e2 = e0) % 189.69/30.40 (39) ~ (all_244_24 = e1) % 189.69/30.40 (40) ~ (e4 = e1) % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | BETA: splitting (22) gives: % 189.69/30.40 | % 189.69/30.40 | Case 1: % 189.69/30.40 | | % 189.69/30.40 | | (41) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.69/30.40 | | = e1) % 189.69/30.40 | | % 189.69/30.40 | | REF_CLOSE: (2), (7), (26), (31), (34), (35), (41) are inconsistent by % 189.69/30.40 | | sub-proof #205. % 189.69/30.40 | | % 189.69/30.40 | Case 2: % 189.69/30.40 | | % 189.69/30.40 | | (42) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.69/30.40 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (42) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (43) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (43) implies: % 189.69/30.40 | | | (44) op(e0, e2) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | REF_CLOSE: (2), (5), (40), (44) are inconsistent by sub-proof #256. % 189.69/30.40 | | | % 189.69/30.40 | | Case 2: % 189.69/30.40 | | | % 189.69/30.40 | | | (45) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.69/30.40 | | | e0) = e1) % 189.69/30.40 | | | % 189.69/30.40 | | | BETA: splitting (45) gives: % 189.69/30.40 | | | % 189.69/30.40 | | | Case 1: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (46) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | ALPHA: (46) implies: % 189.69/30.40 | | | | (47) op(e0, e1) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | GROUND_INST: instantiating (2) with e0, e2, e1, e2, simplifying with % 189.69/30.40 | | | | (9), (13) gives: % 189.69/30.40 | | | | (48) e2 = e0 % 189.69/30.40 | | | | % 189.69/30.40 | | | | COMBINE_EQS: (11), (48) imply: % 189.69/30.40 | | | | (49) all_252_11 = e0 % 189.69/30.40 | | | | % 189.69/30.40 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (14), % 189.69/30.40 | | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), % 189.69/30.40 | | | | (25), (27), (28), (29), (30), (31), (32), (33), (34), (36), % 189.69/30.40 | | | | (37), (38), (40), (47), (49) are inconsistent by sub-proof % 189.69/30.40 | | | | #191. % 189.69/30.40 | | | | % 189.69/30.40 | | | Case 2: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (50) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | ALPHA: (50) implies: % 189.69/30.40 | | | | (51) op(e0, e0) = e1 % 189.69/30.40 | | | | % 189.69/30.40 | | | | REF_CLOSE: (2), (20), (39), (51) are inconsistent by sub-proof #474. % 189.69/30.40 | | | | % 189.69/30.40 | | | End of split % 189.69/30.40 | | | % 189.69/30.40 | | End of split % 189.69/30.40 | | % 189.69/30.40 | End of split % 189.69/30.40 | % 189.69/30.40 End of proof % 189.69/30.40 % 189.69/30.40 Sub-proof #191 shows that the following formulas are inconsistent: % 189.69/30.40 ---------------------------------------------------------------- % 189.69/30.40 (1) all_252_20 = e2 % 189.69/30.40 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.40 (3) ~ (all_20_2 = e4) % 189.69/30.40 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.40 | (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = % 189.69/30.40 e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.40 (5) op(e0, e2) = e4 % 189.69/30.40 (6) op(e3, e1) = all_36_2 % 189.69/30.40 (7) ~ (e2 = e1) % 189.69/30.40 (8) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.40 (9) op(e4, e1) = e0 % 189.69/30.40 (10) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 189.69/30.40 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 189.69/30.40 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.40 (11) ~ (e4 = e0) % 189.69/30.40 (12) ~ (e4 = e3) % 189.69/30.40 (13) ~ (all_36_2 = e2) % 189.69/30.40 (14) ~ (all_244_24 = all_20_2) % 189.69/30.40 (15) op(e1, e4) = e0 % 189.69/30.40 (16) ~ (all_20_2 = e3) % 189.69/30.40 (17) all_252_11 = e0 % 189.69/30.40 (18) op(e0, e0) = all_244_24 % 189.69/30.40 (19) op(e0, e1) = all_20_2 % 189.69/30.40 (20) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 189.69/30.40 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.40 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.40 (21) ~ (all_20_2 = e0) % 189.69/30.40 (22) ~ (all_20_2 = e2) % 189.69/30.40 (23) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, e1) = e4) % 189.69/30.40 | (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, e1) = % 189.69/30.40 e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.40 (24) ~ (e3 = e0) % 189.69/30.40 (25) ~ (all_20_2 = all_8_1) % 189.69/30.40 (26) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 189.69/30.40 | (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) = % 189.69/30.40 e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.40 (27) ~ (e3 = e2) % 189.69/30.40 (28) op(e0, e3) = all_8_1 % 189.69/30.40 (29) op(e1, e4) = e1 % 189.69/30.40 (30) ~ (e4 = e2) % 189.69/30.40 (31) ~ (e1 = e0) % 189.69/30.40 (32) all_250_23 = all_20_2 % 189.69/30.40 (33) ~ (e3 = e1) % 189.69/30.40 (34) ~ (e2 = e0) % 189.69/30.40 (35) op(e0, e1) = e1 % 189.69/30.40 (36) ~ (e4 = e1) % 189.69/30.40 % 189.69/30.40 Begin of proof % 189.69/30.40 | % 189.69/30.40 | BETA: splitting (26) gives: % 189.69/30.40 | % 189.69/30.40 | Case 1: % 189.69/30.40 | | % 189.69/30.40 | | (37) (all_252_9 = e1 & op(e4, e1) = e1) | (all_252_10 = e1 & op(e3, e1) = % 189.69/30.40 | | e1) % 189.69/30.40 | | % 189.69/30.40 | | BETA: splitting (37) gives: % 189.69/30.40 | | % 189.69/30.40 | | Case 1: % 189.69/30.40 | | | % 189.69/30.40 | | | (38) all_252_9 = e1 & op(e4, e1) = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | ALPHA: (38) implies: % 189.69/30.40 | | | (39) all_252_9 = e1 % 189.69/30.40 | | | % 189.69/30.40 | | | BETA: splitting (23) gives: % 189.69/30.40 | | | % 189.69/30.40 | | | Case 1: % 189.69/30.40 | | | | % 189.69/30.40 | | | | (40) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, % 189.69/30.40 | | | | e1) = e4) % 189.69/30.40 | | | | % 189.69/30.40 | | | | BETA: splitting (40) gives: % 189.69/30.40 | | | | % 189.69/30.40 | | | | Case 1: % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | (41) all_252_9 = e4 & op(e4, e1) = e4 % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | ALPHA: (41) implies: % 189.69/30.40 | | | | | (42) all_252_9 = e4 % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | REF_CLOSE: (36), (39), (42) are inconsistent by sub-proof #204. % 189.69/30.40 | | | | | % 189.69/30.40 | | | | Case 2: % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | (43) all_252_10 = e4 & op(e3, e1) = e4 % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | ALPHA: (43) implies: % 189.69/30.40 | | | | | (44) all_252_10 = e4 % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | BETA: splitting (10) gives: % 189.69/30.40 | | | | | % 189.69/30.40 | | | | | Case 1: % 189.69/30.40 | | | | | | % 189.69/30.40 | | | | | | (45) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & % 189.69/30.40 | | | | | | op(e3, e1) = e3) % 189.69/30.40 | | | | | | % 189.69/30.40 | | | | | | REF_CLOSE: (2), (9), (12), (24), (44), (45) are inconsistent by % 189.69/30.40 | | | | | | sub-proof #218. % 189.69/30.40 | | | | | | % 189.69/30.40 | | | | | Case 2: % 189.69/30.40 | | | | | | % 189.69/30.40 | | | | | | (46) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 189.69/30.40 | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.40 | | | | | | % 189.69/30.40 | | | | | | BETA: splitting (46) gives: % 189.69/30.40 | | | | | | % 189.69/30.40 | | | | | | Case 1: % 189.69/30.40 | | | | | | | % 189.69/30.40 | | | | | | | (47) all_252_11 = e3 & op(e2, e1) = e3 % 189.69/30.40 | | | | | | | % 189.69/30.40 | | | | | | | ALPHA: (47) implies: % 189.69/30.40 | | | | | | | (48) all_252_11 = e3 % 189.69/30.40 | | | | | | | % 189.69/30.40 | | | | | | | REF_CLOSE: (17), (24), (48) are inconsistent by sub-proof #297. % 189.69/30.40 | | | | | | | % 189.69/30.40 | | | | | | Case 2: % 189.69/30.40 | | | | | | | % 189.69/30.41 | | | | | | | (49) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 189.69/30.41 | | | | | | | op(e0, e1) = e3) % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | BETA: splitting (49) gives: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (50) all_252_15 = e3 & op(e1, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | ALPHA: (50) implies: % 189.69/30.41 | | | | | | | | (51) all_252_15 = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | BETA: splitting (4) gives: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (52) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 % 189.69/30.41 | | | | | | | | | & op(e3, e1) = e2) % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | REF_CLOSE: (2), (6), (7), (13), (39), (52) are inconsistent by % 189.69/30.41 | | | | | | | | | sub-proof #203. % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (53) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 % 189.69/30.41 | | | | | | | | | & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = % 189.69/30.41 | | | | | | | | | e2) % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | REF_CLOSE: (2), (17), (19), (22), (27), (34), (51), (53) are % 189.69/30.41 | | | | | | | | | inconsistent by sub-proof #201. % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | End of split % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (54) all_252_23 = e3 & op(e0, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | ALPHA: (54) implies: % 189.69/30.41 | | | | | | | | (55) op(e0, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | REF_CLOSE: (2), (16), (19), (55) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | #508. % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | End of split % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | End of split % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | End of split % 189.69/30.41 | | | | | % 189.69/30.41 | | | | End of split % 189.69/30.41 | | | | % 189.69/30.41 | | | Case 2: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (56) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, % 189.69/30.41 | | | | e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.41 | | | | % 189.69/30.41 | | | | BETA: splitting (56) gives: % 189.69/30.41 | | | | % 189.69/30.41 | | | | Case 1: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (57) all_252_11 = e4 & op(e2, e1) = e4 % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | REF_CLOSE: (11), (17), (57) are inconsistent by sub-proof #200. % 189.69/30.41 | | | | | % 189.69/30.41 | | | | Case 2: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (58) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 189.69/30.41 | | | | | op(e0, e1) = e4) % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | BETA: splitting (58) gives: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | Case 1: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (59) all_252_15 = e4 & op(e1, e1) = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | ALPHA: (59) implies: % 189.69/30.41 | | | | | | (60) all_252_15 = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | BETA: splitting (4) gives: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | Case 1: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (61) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & % 189.69/30.41 | | | | | | | op(e3, e1) = e2) % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | REF_CLOSE: (2), (6), (7), (13), (39), (61) are inconsistent by % 189.69/30.41 | | | | | | | sub-proof #203. % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | Case 2: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (62) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & % 189.69/30.41 | | | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | BETA: splitting (62) gives: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (63) all_252_11 = e2 & op(e2, e1) = e2 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | REF_CLOSE: (17), (34), (63) are inconsistent by sub-proof #279. % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (64) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 189.69/30.41 | | | | | | | | op(e0, e1) = e2) % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | BETA: splitting (64) gives: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (65) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | REF_CLOSE: (30), (60), (65) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | | #199. % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (66) all_252_23 = e2 & op(e0, e1) = e2 % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | REF_CLOSE: (2), (19), (22), (66) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | | #540. % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | End of split % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | End of split % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | End of split % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | Case 2: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (67) all_252_23 = e4 & op(e0, e1) = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | ALPHA: (67) implies: % 189.69/30.41 | | | | | | (68) op(e0, e1) = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | REF_CLOSE: (2), (19), (35), (36), (68) are inconsistent by sub-proof % 189.69/30.41 | | | | | | #401. % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | End of split % 189.69/30.41 | | | | | % 189.69/30.41 | | | | End of split % 189.69/30.41 | | | | % 189.69/30.41 | | | End of split % 189.69/30.41 | | | % 189.69/30.41 | | Case 2: % 189.69/30.41 | | | % 189.69/30.41 | | | (69) all_252_10 = e1 & op(e3, e1) = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | ALPHA: (69) implies: % 189.69/30.41 | | | (70) all_252_10 = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | BETA: splitting (23) gives: % 189.69/30.41 | | | % 189.69/30.41 | | | Case 1: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (71) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 & op(e3, % 189.69/30.41 | | | | e1) = e4) % 189.69/30.41 | | | | % 189.69/30.41 | | | | BETA: splitting (71) gives: % 189.69/30.41 | | | | % 189.69/30.41 | | | | Case 1: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (72) all_252_9 = e4 & op(e4, e1) = e4 % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | ALPHA: (72) implies: % 189.69/30.41 | | | | | (73) all_252_9 = e4 % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | BETA: splitting (10) gives: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | Case 1: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (74) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & % 189.69/30.41 | | | | | | op(e3, e1) = e3) % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | BETA: splitting (74) gives: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | Case 1: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (75) all_252_9 = e3 & op(e4, e1) = e3 % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | REF_CLOSE: (2), (9), (24), (75) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | #275. % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | Case 2: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (76) all_252_10 = e3 & op(e3, e1) = e3 % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | ALPHA: (76) implies: % 189.69/30.41 | | | | | | | (77) all_252_10 = e3 % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | COMBINE_EQS: (70), (77) imply: % 189.69/30.41 | | | | | | | (78) e3 = e1 % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | REDUCE: (33), (78) imply: % 189.69/30.41 | | | | | | | (79) $false % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | CLOSE: (79) is inconsistent. % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | End of split % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | Case 2: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (80) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 189.69/30.41 | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | BETA: splitting (80) gives: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | Case 1: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (81) all_252_11 = e3 & op(e2, e1) = e3 % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | ALPHA: (81) implies: % 189.69/30.41 | | | | | | | (82) all_252_11 = e3 % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | REF_CLOSE: (17), (24), (82) are inconsistent by sub-proof #297. % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | Case 2: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (83) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & % 189.69/30.41 | | | | | | | op(e0, e1) = e3) % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | BETA: splitting (83) gives: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (84) all_252_15 = e3 & op(e1, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | ALPHA: (84) implies: % 189.69/30.41 | | | | | | | | (85) all_252_15 = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | BETA: splitting (4) gives: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (86) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 % 189.69/30.41 | | | | | | | | | & op(e3, e1) = e2) % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | REF_CLOSE: (2), (6), (13), (30), (73), (86) are inconsistent % 189.69/30.41 | | | | | | | | | by sub-proof #198. % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (87) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 % 189.69/30.41 | | | | | | | | | & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = % 189.69/30.41 | | | | | | | | | e2) % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | REF_CLOSE: (2), (17), (19), (22), (27), (34), (85), (87) are % 189.69/30.41 | | | | | | | | | inconsistent by sub-proof #201. % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | End of split % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (88) all_252_23 = e3 & op(e0, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | ALPHA: (88) implies: % 189.69/30.41 | | | | | | | | (89) op(e0, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | REF_CLOSE: (2), (16), (19), (89) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | #508. % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | End of split % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | End of split % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | End of split % 189.69/30.41 | | | | | % 189.69/30.41 | | | | Case 2: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (90) all_252_10 = e4 & op(e3, e1) = e4 % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | ALPHA: (90) implies: % 189.69/30.41 | | | | | (91) all_252_10 = e4 % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | REF_CLOSE: (36), (70), (91) are inconsistent by sub-proof #197. % 189.69/30.41 | | | | | % 189.69/30.41 | | | | End of split % 189.69/30.41 | | | | % 189.69/30.41 | | | Case 2: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (92) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = e4 & op(e1, % 189.69/30.41 | | | | e1) = e4) | (all_252_23 = e4 & op(e0, e1) = e4) % 189.69/30.41 | | | | % 189.69/30.41 | | | | BETA: splitting (92) gives: % 189.69/30.41 | | | | % 189.69/30.41 | | | | Case 1: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (93) all_252_11 = e4 & op(e2, e1) = e4 % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | REF_CLOSE: (11), (17), (93) are inconsistent by sub-proof #200. % 189.69/30.41 | | | | | % 189.69/30.41 | | | | Case 2: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (94) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = e4 & % 189.69/30.41 | | | | | op(e0, e1) = e4) % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | BETA: splitting (94) gives: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | Case 1: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (95) all_252_15 = e4 & op(e1, e1) = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | ALPHA: (95) implies: % 189.69/30.41 | | | | | | (96) all_252_15 = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | REF_CLOSE: (2), (9), (10), (12), (16), (17), (19), (24), (33), (70), % 189.69/30.41 | | | | | | (96) are inconsistent by sub-proof #263. % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | Case 2: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (97) all_252_23 = e4 & op(e0, e1) = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | ALPHA: (97) implies: % 189.69/30.41 | | | | | | (98) op(e0, e1) = e4 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | REF_CLOSE: (2), (19), (35), (36), (98) are inconsistent by sub-proof % 189.69/30.41 | | | | | | #401. % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | End of split % 189.69/30.41 | | | | | % 189.69/30.41 | | | | End of split % 189.69/30.41 | | | | % 189.69/30.41 | | | End of split % 189.69/30.41 | | | % 189.69/30.41 | | End of split % 189.69/30.41 | | % 189.69/30.41 | Case 2: % 189.69/30.41 | | % 189.69/30.41 | | (99) (all_252_11 = e1 & op(e2, e1) = e1) | (all_252_15 = e1 & op(e1, e1) % 189.69/30.41 | | = e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 189.69/30.41 | | % 189.69/30.41 | | BETA: splitting (99) gives: % 189.69/30.41 | | % 189.69/30.41 | | Case 1: % 189.69/30.41 | | | % 189.69/30.41 | | | (100) all_252_11 = e1 & op(e2, e1) = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | REF_CLOSE: (17), (31), (100) are inconsistent by sub-proof #262. % 189.69/30.41 | | | % 189.69/30.41 | | Case 2: % 189.69/30.41 | | | % 189.69/30.41 | | | (101) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_23 = e1 & op(e0, % 189.69/30.41 | | | e1) = e1) % 189.69/30.41 | | | % 189.69/30.41 | | | BETA: splitting (101) gives: % 189.69/30.41 | | | % 189.69/30.41 | | | Case 1: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (102) all_252_15 = e1 & op(e1, e1) = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | ALPHA: (102) implies: % 189.69/30.41 | | | | (103) all_252_15 = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | BETA: splitting (4) gives: % 189.69/30.41 | | | | % 189.69/30.41 | | | | Case 1: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (104) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & % 189.69/30.41 | | | | | op(e3, e1) = e2) % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | BETA: splitting (104) gives: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | Case 1: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (105) all_252_9 = e2 & op(e4, e1) = e2 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | ALPHA: (105) implies: % 189.69/30.41 | | | | | | (106) all_252_9 = e2 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | BETA: splitting (10) gives: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | Case 1: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (107) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & % 189.69/30.41 | | | | | | | op(e3, e1) = e3) % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | BETA: splitting (107) gives: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (108) all_252_9 = e3 & op(e4, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | REF_CLOSE: (2), (9), (24), (108) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | #275. % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | (109) all_252_10 = e3 & op(e3, e1) = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | ALPHA: (109) implies: % 189.69/30.41 | | | | | | | | (110) all_252_10 = e3 % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | BETA: splitting (23) gives: % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (111) (all_252_9 = e4 & op(e4, e1) = e4) | (all_252_10 = e4 % 189.69/30.41 | | | | | | | | | & op(e3, e1) = e4) % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | BETA: splitting (111) gives: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | (112) all_252_9 = e4 & op(e4, e1) = e4 % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | ALPHA: (112) implies: % 189.69/30.41 | | | | | | | | | | (113) all_252_9 = e4 % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | REF_CLOSE: (30), (106), (113) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | | | #196. % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | (114) all_252_10 = e4 & op(e3, e1) = e4 % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | REF_CLOSE: (12), (110), (114) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | | | #195. % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | End of split % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | (115) (all_252_11 = e4 & op(e2, e1) = e4) | (all_252_15 = % 189.69/30.41 | | | | | | | | | e4 & op(e1, e1) = e4) | (all_252_23 = e4 & op(e0, % 189.69/30.41 | | | | | | | | | e1) = e4) % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | BETA: splitting (115) gives: % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | (116) all_252_11 = e4 & op(e2, e1) = e4 % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | REF_CLOSE: (11), (17), (116) are inconsistent by sub-proof % 189.69/30.41 | | | | | | | | | | #268. % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | (117) (all_252_15 = e4 & op(e1, e1) = e4) | (all_252_23 = % 189.69/30.41 | | | | | | | | | | e4 & op(e0, e1) = e4) % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | BETA: splitting (117) gives: % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | Case 1: % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | (118) all_252_15 = e4 & op(e1, e1) = e4 % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | ALPHA: (118) implies: % 189.69/30.41 | | | | | | | | | | | (119) all_252_15 = e4 % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | COMBINE_EQS: (103), (119) imply: % 189.69/30.41 | | | | | | | | | | | (120) e4 = e1 % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | REDUCE: (36), (120) imply: % 189.69/30.41 | | | | | | | | | | | (121) $false % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | CLOSE: (121) is inconsistent. % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | Case 2: % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | (122) all_252_23 = e4 & op(e0, e1) = e4 % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | ALPHA: (122) implies: % 189.69/30.41 | | | | | | | | | | | (123) op(e0, e1) = e4 % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | | REF_CLOSE: (2), (19), (35), (36), (123) are inconsistent by % 189.69/30.41 | | | | | | | | | | | sub-proof #401. % 189.69/30.41 | | | | | | | | | | | % 189.69/30.41 | | | | | | | | | | End of split % 189.69/30.41 | | | | | | | | | | % 189.69/30.41 | | | | | | | | | End of split % 189.69/30.41 | | | | | | | | | % 189.69/30.41 | | | | | | | | End of split % 189.69/30.41 | | | | | | | | % 189.69/30.41 | | | | | | | End of split % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | Case 2: % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | (124) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & % 189.69/30.41 | | | | | | | op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | | REF_CLOSE: (2), (16), (17), (19), (24), (33), (103), (124) are % 189.69/30.41 | | | | | | | inconsistent by sub-proof #271. % 189.69/30.41 | | | | | | | % 189.69/30.41 | | | | | | End of split % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | Case 2: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (125) all_252_10 = e2 & op(e3, e1) = e2 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | ALPHA: (125) implies: % 189.69/30.41 | | | | | | (126) op(e3, e1) = e2 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | REF_CLOSE: (2), (6), (13), (126) are inconsistent by sub-proof #557. % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | End of split % 189.69/30.41 | | | | | % 189.69/30.41 | | | | Case 2: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | (127) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & % 189.69/30.41 | | | | | op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | BETA: splitting (127) gives: % 189.69/30.41 | | | | | % 189.69/30.41 | | | | | Case 1: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (128) all_252_11 = e2 & op(e2, e1) = e2 % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | REF_CLOSE: (17), (34), (128) are inconsistent by sub-proof #279. % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | Case 2: % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | (129) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & % 189.69/30.41 | | | | | | op(e0, e1) = e2) % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | | REF_CLOSE: (2), (7), (19), (22), (103), (129) are inconsistent by % 189.69/30.41 | | | | | | sub-proof #194. % 189.69/30.41 | | | | | | % 189.69/30.41 | | | | | End of split % 189.69/30.41 | | | | | % 189.69/30.41 | | | | End of split % 189.69/30.41 | | | | % 189.69/30.41 | | | Case 2: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (130) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | ALPHA: (130) implies: % 189.69/30.41 | | | | (131) all_252_23 = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | GROUND_INST: instantiating (2) with e0, e1, e4, e1, simplifying with % 189.69/30.41 | | | | (15), (29) gives: % 189.69/30.41 | | | | (132) e1 = e0 % 189.69/30.41 | | | | % 189.69/30.41 | | | | COMBINE_EQS: (131), (132) imply: % 189.69/30.41 | | | | (133) all_252_23 = e0 % 189.69/30.41 | | | | % 189.69/30.41 | | | | REF_CLOSE: (1), (2), (3), (5), (8), (14), (18), (20), (21), (22), (25), % 189.69/30.41 | | | | (28), (32), (133) are inconsistent by sub-proof #192. % 189.69/30.41 | | | | % 189.69/30.41 | | | End of split % 189.69/30.41 | | | % 189.69/30.41 | | End of split % 189.69/30.41 | | % 189.69/30.41 | End of split % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #192 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.41 (1) all_252_20 = e2 % 189.69/30.41 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.41 (3) ~ (all_20_2 = e4) % 189.69/30.41 (4) op(e0, e2) = e4 % 189.69/30.41 (5) all_250_23 = e1 | all_250_23 = e0 % 189.69/30.41 (6) ~ (all_244_24 = all_20_2) % 189.69/30.41 (7) op(e0, e0) = all_244_24 % 189.69/30.41 (8) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.41 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.69/30.41 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.41 (9) ~ (all_20_2 = e0) % 189.69/30.41 (10) ~ (all_20_2 = e2) % 189.69/30.41 (11) ~ (all_20_2 = all_8_1) % 189.69/30.41 (12) op(e0, e3) = all_8_1 % 189.69/30.41 (13) all_250_23 = all_20_2 % 189.69/30.41 (14) all_252_23 = e0 % 189.69/30.41 % 189.69/30.41 Begin of proof % 189.69/30.41 | % 189.69/30.41 | BETA: splitting (5) gives: % 189.69/30.41 | % 189.69/30.41 | Case 1: % 189.69/30.41 | | % 189.69/30.41 | | (15) all_250_23 = e1 % 189.69/30.41 | | % 189.69/30.41 | | COMBINE_EQS: (13), (15) imply: % 189.69/30.41 | | (16) all_20_2 = e1 % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (6), (16) imply: % 189.69/30.41 | | (17) ~ (all_244_24 = e1) % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (11), (16) imply: % 189.69/30.41 | | (18) ~ (all_8_1 = e1) % 189.69/30.41 | | % 189.69/30.41 | | SIMP: (18) implies: % 189.69/30.41 | | (19) ~ (all_8_1 = e1) % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (3), (16) imply: % 189.69/30.41 | | (20) ~ (e4 = e1) % 189.69/30.41 | | % 189.69/30.41 | | SIMP: (20) implies: % 189.69/30.41 | | (21) ~ (e4 = e1) % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (10), (16) imply: % 189.69/30.41 | | (22) ~ (e2 = e1) % 189.69/30.41 | | % 189.69/30.41 | | SIMP: (22) implies: % 189.69/30.41 | | (23) ~ (e2 = e1) % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (9), (16) imply: % 189.69/30.41 | | (24) ~ (e1 = e0) % 189.69/30.41 | | % 189.69/30.41 | | REF_CLOSE: (1), (2), (4), (7), (8), (12), (14), (17), (19), (21), (23), (24) % 189.69/30.41 | | are inconsistent by sub-proof #193. % 189.69/30.41 | | % 189.69/30.41 | Case 2: % 189.69/30.41 | | % 189.69/30.41 | | (25) all_250_23 = e0 % 189.69/30.41 | | % 189.69/30.41 | | COMBINE_EQS: (13), (25) imply: % 189.69/30.41 | | (26) all_20_2 = e0 % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (9), (26) imply: % 189.69/30.41 | | (27) $false % 189.69/30.41 | | % 189.69/30.41 | | CLOSE: (27) is inconsistent. % 189.69/30.41 | | % 189.69/30.41 | End of split % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #193 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.41 (1) all_252_20 = e2 % 189.69/30.41 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.41 (3) op(e0, e2) = e4 % 189.69/30.41 (4) ~ (e2 = e1) % 189.69/30.41 (5) op(e0, e0) = all_244_24 % 189.69/30.41 (6) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.41 | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = % 189.69/30.41 e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.41 (7) op(e0, e3) = all_8_1 % 189.69/30.41 (8) ~ (e1 = e0) % 189.69/30.41 (9) ~ (all_244_24 = e1) % 189.69/30.41 (10) ~ (all_8_1 = e1) % 189.69/30.41 (11) all_252_23 = e0 % 189.69/30.41 (12) ~ (e4 = e1) % 189.69/30.41 % 189.69/30.41 Begin of proof % 189.69/30.41 | % 189.69/30.41 | BETA: splitting (6) gives: % 189.69/30.41 | % 189.69/30.41 | Case 1: % 189.69/30.41 | | % 189.69/30.41 | | (13) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 189.69/30.41 | | = e1) % 189.69/30.41 | | % 189.69/30.41 | | BETA: splitting (13) gives: % 189.69/30.41 | | % 189.69/30.41 | | Case 1: % 189.69/30.41 | | | % 189.69/30.41 | | | (14) all_252_20 = e1 & op(e0, e4) = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | ALPHA: (14) implies: % 189.69/30.41 | | | (15) all_252_20 = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | REF_CLOSE: (1), (4), (15) are inconsistent by sub-proof #228. % 189.69/30.41 | | | % 189.69/30.41 | | Case 2: % 189.69/30.41 | | | % 189.69/30.41 | | | (16) all_252_21 = e1 & op(e0, e3) = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | REF_CLOSE: (2), (7), (10), (16) are inconsistent by sub-proof #281. % 189.69/30.41 | | | % 189.69/30.41 | | End of split % 189.69/30.41 | | % 189.69/30.41 | Case 2: % 189.69/30.41 | | % 189.69/30.41 | | (17) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 189.69/30.41 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 189.69/30.41 | | % 189.69/30.41 | | BETA: splitting (17) gives: % 189.69/30.41 | | % 189.69/30.41 | | Case 1: % 189.69/30.41 | | | % 189.69/30.41 | | | (18) all_252_22 = e1 & op(e0, e2) = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | ALPHA: (18) implies: % 189.69/30.41 | | | (19) op(e0, e2) = e1 % 189.69/30.41 | | | % 189.69/30.41 | | | REF_CLOSE: (2), (3), (12), (19) are inconsistent by sub-proof #256. % 189.69/30.41 | | | % 189.69/30.41 | | Case 2: % 189.69/30.41 | | | % 189.69/30.41 | | | (20) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 189.69/30.41 | | | e0) = e1) % 189.69/30.41 | | | % 189.69/30.41 | | | BETA: splitting (20) gives: % 189.69/30.41 | | | % 189.69/30.41 | | | Case 1: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (21) all_252_23 = e1 & op(e0, e1) = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | REF_CLOSE: (8), (11), (21) are inconsistent by sub-proof #293. % 189.69/30.41 | | | | % 189.69/30.41 | | | Case 2: % 189.69/30.41 | | | | % 189.69/30.41 | | | | (22) all_252_24 = e1 & op(e0, e0) = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | ALPHA: (22) implies: % 189.69/30.41 | | | | (23) op(e0, e0) = e1 % 189.69/30.41 | | | | % 189.69/30.41 | | | | REF_CLOSE: (2), (5), (9), (23) are inconsistent by sub-proof #474. % 189.69/30.41 | | | | % 189.69/30.41 | | | End of split % 189.69/30.41 | | | % 189.69/30.41 | | End of split % 189.69/30.41 | | % 189.69/30.41 | End of split % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #194 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.41 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.41 (2) ~ (e2 = e1) % 189.69/30.41 (3) all_252_15 = e1 % 189.69/30.41 (4) op(e0, e1) = all_20_2 % 189.69/30.41 (5) ~ (all_20_2 = e2) % 189.69/30.41 (6) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.41 % 189.69/30.41 Begin of proof % 189.69/30.41 | % 189.69/30.41 | BETA: splitting (6) gives: % 189.69/30.41 | % 189.69/30.41 | Case 1: % 189.69/30.41 | | % 189.69/30.41 | | (7) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.41 | | % 189.69/30.41 | | ALPHA: (7) implies: % 189.69/30.41 | | (8) all_252_15 = e2 % 189.69/30.41 | | % 189.69/30.41 | | COMBINE_EQS: (3), (8) imply: % 189.69/30.41 | | (9) e2 = e1 % 189.69/30.41 | | % 189.69/30.41 | | SIMP: (9) implies: % 189.69/30.41 | | (10) e2 = e1 % 189.69/30.41 | | % 189.69/30.41 | | REDUCE: (2), (10) imply: % 189.69/30.41 | | (11) $false % 189.69/30.41 | | % 189.69/30.41 | | CLOSE: (11) is inconsistent. % 189.69/30.41 | | % 189.69/30.41 | Case 2: % 189.69/30.41 | | % 189.69/30.41 | | (12) all_252_23 = e2 & op(e0, e1) = e2 % 189.69/30.41 | | % 189.69/30.41 | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #540. % 189.69/30.41 | | % 189.69/30.41 | End of split % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #195 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.41 (1) all_252_10 = e4 & op(e3, e1) = e4 % 189.69/30.41 (2) all_252_10 = e3 % 189.69/30.41 (3) ~ (e4 = e3) % 189.69/30.41 % 189.69/30.41 Begin of proof % 189.69/30.41 | % 189.69/30.41 | ALPHA: (1) implies: % 189.69/30.41 | (4) all_252_10 = e4 % 189.69/30.41 | % 189.69/30.41 | COMBINE_EQS: (2), (4) imply: % 189.69/30.41 | (5) e4 = e3 % 189.69/30.41 | % 189.69/30.41 | REDUCE: (3), (5) imply: % 189.69/30.41 | (6) $false % 189.69/30.41 | % 189.69/30.41 | CLOSE: (6) is inconsistent. % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #196 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.41 (1) all_252_9 = e4 % 189.69/30.41 (2) all_252_9 = e2 % 189.69/30.41 (3) ~ (e4 = e2) % 189.69/30.41 % 189.69/30.41 Begin of proof % 189.69/30.41 | % 189.69/30.41 | COMBINE_EQS: (1), (2) imply: % 189.69/30.41 | (4) e4 = e2 % 189.69/30.41 | % 189.69/30.41 | SIMP: (4) implies: % 189.69/30.41 | (5) e4 = e2 % 189.69/30.41 | % 189.69/30.41 | REDUCE: (3), (5) imply: % 189.69/30.41 | (6) $false % 189.69/30.41 | % 189.69/30.41 | CLOSE: (6) is inconsistent. % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #197 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.41 (1) all_252_10 = e4 % 189.69/30.41 (2) all_252_10 = e1 % 189.69/30.41 (3) ~ (e4 = e1) % 189.69/30.41 % 189.69/30.41 Begin of proof % 189.69/30.41 | % 189.69/30.41 | COMBINE_EQS: (1), (2) imply: % 189.69/30.41 | (4) e4 = e1 % 189.69/30.41 | % 189.69/30.41 | SIMP: (4) implies: % 189.69/30.41 | (5) e4 = e1 % 189.69/30.41 | % 189.69/30.41 | REDUCE: (3), (5) imply: % 189.69/30.41 | (6) $false % 189.69/30.41 | % 189.69/30.41 | CLOSE: (6) is inconsistent. % 189.69/30.41 | % 189.69/30.41 End of proof % 189.69/30.41 % 189.69/30.41 Sub-proof #198 shows that the following formulas are inconsistent: % 189.69/30.41 ---------------------------------------------------------------- % 189.69/30.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (2) op(e3, e1) = all_36_2 % 189.69/30.42 (3) ~ (all_36_2 = e2) % 189.69/30.42 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.42 (5) ~ (e4 = e2) % 189.69/30.42 (6) all_252_9 = e4 % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | BETA: splitting (4) gives: % 189.69/30.42 | % 189.69/30.42 | Case 1: % 189.69/30.42 | | % 189.69/30.42 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | ALPHA: (7) implies: % 189.69/30.42 | | (8) all_252_9 = e2 % 189.69/30.42 | | % 189.69/30.42 | | COMBINE_EQS: (6), (8) imply: % 189.69/30.42 | | (9) e4 = e2 % 189.69/30.42 | | % 189.69/30.42 | | REDUCE: (5), (9) imply: % 189.69/30.42 | | (10) $false % 189.69/30.42 | | % 189.69/30.42 | | CLOSE: (10) is inconsistent. % 189.69/30.42 | | % 189.69/30.42 | Case 2: % 189.69/30.42 | | % 189.69/30.42 | | (11) all_252_10 = e2 & op(e3, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | ALPHA: (11) implies: % 189.69/30.42 | | (12) op(e3, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (1), (2), (3), (12) are inconsistent by sub-proof #557. % 189.69/30.42 | | % 189.69/30.42 | End of split % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #199 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.42 (2) all_252_15 = e4 % 189.69/30.42 (3) ~ (e4 = e2) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (4) all_252_15 = e2 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (2), (4) imply: % 189.69/30.42 | (5) e4 = e2 % 189.69/30.42 | % 189.69/30.42 | SIMP: (5) implies: % 189.69/30.42 | (6) e4 = e2 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (6) imply: % 189.69/30.42 | (7) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (7) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #200 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_11 = e4 & op(e2, e1) = e4 % 189.69/30.42 (2) all_252_11 = e0 % 189.69/30.42 (3) ~ (e4 = e0) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (4) all_252_11 = e4 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (2), (4) imply: % 189.69/30.42 | (5) e4 = e0 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (5) imply: % 189.69/30.42 | (6) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (6) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #201 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (2) all_252_15 = e3 % 189.69/30.42 (3) (all_252_11 = e2 & op(e2, e1) = e2) | (all_252_15 = e2 & op(e1, e1) = e2) % 189.69/30.42 | (all_252_23 = e2 & op(e0, e1) = e2) % 189.69/30.42 (4) all_252_11 = e0 % 189.69/30.42 (5) op(e0, e1) = all_20_2 % 189.69/30.42 (6) ~ (all_20_2 = e2) % 189.69/30.42 (7) ~ (e3 = e2) % 189.69/30.42 (8) ~ (e2 = e0) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | BETA: splitting (3) gives: % 189.69/30.42 | % 189.69/30.42 | Case 1: % 189.69/30.42 | | % 189.69/30.42 | | (9) all_252_11 = e2 & op(e2, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #279. % 189.69/30.42 | | % 189.69/30.42 | Case 2: % 189.69/30.42 | | % 189.69/30.42 | | (10) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) % 189.69/30.42 | | = e2) % 189.69/30.42 | | % 189.69/30.42 | | BETA: splitting (10) gives: % 189.69/30.42 | | % 189.69/30.42 | | Case 1: % 189.69/30.42 | | | % 189.69/30.42 | | | (11) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.42 | | | % 189.69/30.42 | | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #202. % 189.69/30.42 | | | % 189.69/30.42 | | Case 2: % 189.69/30.42 | | | % 189.69/30.42 | | | (12) all_252_23 = e2 & op(e0, e1) = e2 % 189.69/30.42 | | | % 189.69/30.42 | | | REF_CLOSE: (1), (5), (6), (12) are inconsistent by sub-proof #540. % 189.69/30.42 | | | % 189.69/30.42 | | End of split % 189.69/30.42 | | % 189.69/30.42 | End of split % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #202 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_15 = e2 & op(e1, e1) = e2 % 189.69/30.42 (2) all_252_15 = e3 % 189.69/30.42 (3) ~ (e3 = e2) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (4) all_252_15 = e2 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (2), (4) imply: % 189.69/30.42 | (5) e3 = e2 % 189.69/30.42 | % 189.69/30.42 | SIMP: (5) implies: % 189.69/30.42 | (6) e3 = e2 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (6) imply: % 189.69/30.42 | (7) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (7) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #203 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (2) op(e3, e1) = all_36_2 % 189.69/30.42 (3) ~ (e2 = e1) % 189.69/30.42 (4) ~ (all_36_2 = e2) % 189.69/30.42 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.42 (6) all_252_9 = e1 % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | BETA: splitting (5) gives: % 189.69/30.42 | % 189.69/30.42 | Case 1: % 189.69/30.42 | | % 189.69/30.42 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | ALPHA: (7) implies: % 189.69/30.42 | | (8) all_252_9 = e2 % 189.69/30.42 | | % 189.69/30.42 | | COMBINE_EQS: (6), (8) imply: % 189.69/30.42 | | (9) e2 = e1 % 189.69/30.42 | | % 189.69/30.42 | | SIMP: (9) implies: % 189.69/30.42 | | (10) e2 = e1 % 189.69/30.42 | | % 189.69/30.42 | | REDUCE: (3), (10) imply: % 189.69/30.42 | | (11) $false % 189.69/30.42 | | % 189.69/30.42 | | CLOSE: (11) is inconsistent. % 189.69/30.42 | | % 189.69/30.42 | Case 2: % 189.69/30.42 | | % 189.69/30.42 | | (12) all_252_10 = e2 & op(e3, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | ALPHA: (12) implies: % 189.69/30.42 | | (13) op(e3, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (1), (2), (4), (13) are inconsistent by sub-proof #557. % 189.69/30.42 | | % 189.69/30.42 | End of split % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #204 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_9 = e4 % 189.69/30.42 (2) all_252_9 = e1 % 189.69/30.42 (3) ~ (e4 = e1) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (1), (2) imply: % 189.69/30.42 | (4) e4 = e1 % 189.69/30.42 | % 189.69/30.42 | SIMP: (4) implies: % 189.69/30.42 | (5) e4 = e1 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (5) imply: % 189.69/30.42 | (6) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (6) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #205 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (2) ~ (e2 = e1) % 189.69/30.42 (3) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 189.69/30.42 (4) op(e0, e4) = e2 % 189.69/30.42 (5) op(e0, e3) = all_8_1 % 189.69/30.42 (6) ~ (e1 = e0) % 189.69/30.42 (7) op(e0, e3) = e0 % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | BETA: splitting (3) gives: % 189.69/30.42 | % 189.69/30.42 | Case 1: % 189.69/30.42 | | % 189.69/30.42 | | (8) all_252_20 = e1 & op(e0, e4) = e1 % 189.69/30.42 | | % 189.69/30.42 | | ALPHA: (8) implies: % 189.69/30.42 | | (9) op(e0, e4) = e1 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #323. % 189.69/30.42 | | % 189.69/30.42 | Case 2: % 189.69/30.42 | | % 189.69/30.42 | | (10) all_252_21 = e1 & op(e0, e3) = e1 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (1), (5), (6), (7), (10) are inconsistent by sub-proof #206. % 189.69/30.42 | | % 189.69/30.42 | End of split % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #206 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_21 = e1 & op(e0, e3) = e1 % 189.69/30.42 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (3) op(e0, e3) = all_8_1 % 189.69/30.42 (4) ~ (e1 = e0) % 189.69/30.42 (5) op(e0, e3) = e0 % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (6) op(e0, e3) = e1 % 189.69/30.42 | % 189.69/30.42 | GROUND_INST: instantiating (2) with all_8_1, e0, e3, e0, simplifying with (3), % 189.69/30.42 | (5) gives: % 189.69/30.42 | (7) all_8_1 = e0 % 189.69/30.42 | % 189.69/30.42 | GROUND_INST: instantiating (2) with all_8_1, e1, e3, e0, simplifying with (3), % 189.69/30.42 | (6) gives: % 189.69/30.42 | (8) all_8_1 = e1 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (7), (8) imply: % 189.69/30.42 | (9) e1 = e0 % 189.69/30.42 | % 189.69/30.42 | SIMP: (9) implies: % 189.69/30.42 | (10) e1 = e0 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (4), (10) imply: % 189.69/30.42 | (11) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (11) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #207 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (2) op(e3, e1) = all_36_2 % 189.69/30.42 (3) ~ (all_36_2 = e2) % 189.69/30.42 (4) all_252_9 = e0 % 189.69/30.42 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 189.69/30.42 (6) ~ (e2 = e0) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | BETA: splitting (5) gives: % 189.69/30.42 | % 189.69/30.42 | Case 1: % 189.69/30.42 | | % 189.69/30.42 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #208. % 189.69/30.42 | | % 189.69/30.42 | Case 2: % 189.69/30.42 | | % 189.69/30.42 | | (8) all_252_10 = e2 & op(e3, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | ALPHA: (8) implies: % 189.69/30.42 | | (9) op(e3, e1) = e2 % 189.69/30.42 | | % 189.69/30.42 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #557. % 189.69/30.42 | | % 189.69/30.42 | End of split % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #208 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_9 = e2 & op(e4, e1) = e2 % 189.69/30.42 (2) all_252_9 = e0 % 189.69/30.42 (3) ~ (e2 = e0) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (4) all_252_9 = e2 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (2), (4) imply: % 189.69/30.42 | (5) e2 = e0 % 189.69/30.42 | % 189.69/30.42 | SIMP: (5) implies: % 189.69/30.42 | (6) e2 = e0 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (6) imply: % 189.69/30.42 | (7) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (7) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #209 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_18 = e3 & op(e2, e0) = e3 % 189.69/30.42 (2) all_252_18 = e1 % 189.69/30.42 (3) ~ (e3 = e1) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (4) all_252_18 = e3 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (2), (4) imply: % 189.69/30.42 | (5) e3 = e1 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (5) imply: % 189.69/30.42 | (6) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (6) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #210 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_16 = e3 & op(e4, e0) = e3 % 189.69/30.42 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (3) op(e4, e0) = e4 % 189.69/30.42 (4) ~ (e4 = e3) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (5) op(e4, e0) = e3 % 189.69/30.42 | % 189.69/30.42 | GROUND_INST: instantiating (2) with e3, e4, e0, e4, simplifying with (3), (5) % 189.69/30.42 | gives: % 189.69/30.42 | (6) e4 = e3 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (4), (6) imply: % 189.69/30.42 | (7) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (7) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #211 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_9 = e4 & op(e4, e1) = e4 % 189.69/30.42 (2) all_252_9 = e0 % 189.69/30.42 (3) ~ (e4 = e0) % 189.69/30.42 % 189.69/30.42 Begin of proof % 189.69/30.42 | % 189.69/30.42 | ALPHA: (1) implies: % 189.69/30.42 | (4) all_252_9 = e4 % 189.69/30.42 | % 189.69/30.42 | COMBINE_EQS: (2), (4) imply: % 189.69/30.42 | (5) e4 = e0 % 189.69/30.42 | % 189.69/30.42 | REDUCE: (3), (5) imply: % 189.69/30.42 | (6) $false % 189.69/30.42 | % 189.69/30.42 | CLOSE: (6) is inconsistent. % 189.69/30.42 | % 189.69/30.42 End of proof % 189.69/30.42 % 189.69/30.42 Sub-proof #212 shows that the following formulas are inconsistent: % 189.69/30.42 ---------------------------------------------------------------- % 189.69/30.42 (1) all_252_20 = e2 % 189.69/30.42 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 189.69/30.42 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 189.69/30.42 | (all_252_20 = e3 & op(e0, e4) = e3) % 189.69/30.42 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 189.69/30.42 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 189.69/30.42 | (all_252_20 = e4 & op(e0, e4) = e4) % 189.69/30.42 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 189.69/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 189.69/30.42 (5) ~ (e2 = e1) % 189.69/30.42 (6) all_252_12 = e0 % 189.69/30.42 (7) ~ (e4 = e0) % 189.69/30.42 (8) ~ (e4 = e3) % 189.69/30.42 (9) all_252_1 = e2 % 189.69/30.42 (10) op(e0, e4) = e2 % 189.69/30.42 (11) ~ (e3 = e0) % 189.69/30.42 (12) all_252_6 = e4 % 189.69/30.42 (13) ~ (e3 = e2) % 189.69/30.42 (14) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 189.69/30.42 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 189.69/30.42 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 189.69/30.42 (15) ~ (e4 = e2) % 189.69/30.42 (16) ~ (e1 = e0) % 189.69/30.42 (17) all_252_1 = e4 & op(e4, e3) = e4 % 189.69/30.42 (18) op(e0, e4) = all_12_2 % 190.00/30.42 (19) ~ (e3 = e1) % 190.00/30.42 (20) ~ (e2 = e0) % 190.00/30.42 (21) ~ (all_12_2 = e3) % 190.00/30.42 (22) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 190.00/30.42 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.42 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.42 (23) ~ (e4 = e1) % 190.00/30.42 % 190.00/30.42 Begin of proof % 190.00/30.42 | % 190.00/30.42 | ALPHA: (17) implies: % 190.00/30.42 | (24) all_252_1 = e4 % 190.00/30.42 | % 190.00/30.42 | COMBINE_EQS: (9), (24) imply: % 190.00/30.42 | (25) e4 = e2 % 190.00/30.42 | % 190.00/30.42 | SIMP: (25) implies: % 190.00/30.42 | (26) e4 = e2 % 190.00/30.42 | % 190.00/30.42 | COMBINE_EQS: (12), (26) imply: % 190.00/30.42 | (27) all_252_6 = e2 % 190.00/30.42 | % 190.00/30.42 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14), % 190.00/30.42 | (15), (16), (18), (19), (20), (21), (22), (23), (27) are % 190.00/30.42 | inconsistent by sub-proof #223. % 190.00/30.42 | % 190.00/30.42 End of proof % 190.00/30.42 % 190.00/30.42 Sub-proof #213 shows that the following formulas are inconsistent: % 190.00/30.42 ---------------------------------------------------------------- % 190.00/30.42 (1) all_252_20 = e2 % 190.00/30.42 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 190.00/30.42 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 190.00/30.42 | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.42 (3) all_252_10 = e4 % 190.00/30.42 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 190.00/30.42 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 190.00/30.42 | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.42 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.42 (6) ~ (e2 = e1) % 190.00/30.42 (7) all_252_12 = e0 % 190.00/30.42 (8) ~ (e4 = e0) % 190.00/30.42 (9) ~ (e4 = e3) % 190.00/30.42 (10) all_252_17 = e2 % 190.00/30.42 (11) all_252_0 = e4 % 190.00/30.42 (12) op(e0, e4) = e2 % 190.00/30.42 (13) ~ (e3 = e0) % 190.00/30.42 (14) all_252_6 = e4 % 190.00/30.42 (15) ~ (e3 = e2) % 190.00/30.42 (16) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 190.00/30.42 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 190.00/30.42 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 190.00/30.42 (17) ~ (e4 = e2) % 190.00/30.42 (18) ~ (e1 = e0) % 190.00/30.42 (19) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 190.00/30.42 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 190.00/30.42 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.00/30.42 (20) op(e0, e4) = all_12_2 % 190.00/30.42 (21) ~ (e3 = e1) % 190.00/30.42 (22) ~ (e2 = e0) % 190.00/30.42 (23) ~ (all_12_2 = e3) % 190.00/30.42 (24) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 190.00/30.42 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.42 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.42 (25) all_252_5 = e0 % 190.00/30.42 (26) ~ (e4 = e1) % 190.00/30.42 % 190.00/30.42 Begin of proof % 190.00/30.42 | % 190.00/30.42 | BETA: splitting (24) gives: % 190.00/30.42 | % 190.00/30.42 | Case 1: % 190.00/30.42 | | % 190.00/30.42 | | (27) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = % 190.00/30.42 | | e1) % 190.00/30.42 | | % 190.00/30.42 | | BETA: splitting (27) gives: % 190.00/30.42 | | % 190.00/30.42 | | Case 1: % 190.00/30.42 | | | % 190.00/30.42 | | | (28) all_252_0 = e1 & op(e4, e4) = e1 % 190.00/30.42 | | | % 190.00/30.42 | | | REF_CLOSE: (11), (26), (28) are inconsistent by sub-proof #231. % 190.00/30.42 | | | % 190.00/30.42 | | Case 2: % 190.00/30.42 | | | % 190.00/30.42 | | | (29) all_252_2 = e1 & op(e3, e4) = e1 % 190.00/30.42 | | | % 190.00/30.42 | | | ALPHA: (29) implies: % 190.00/30.42 | | | (30) all_252_2 = e1 % 190.00/30.42 | | | % 190.00/30.42 | | | BETA: splitting (19) gives: % 190.00/30.42 | | | % 190.00/30.42 | | | Case 1: % 190.00/30.42 | | | | % 190.00/30.42 | | | | (31) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, % 190.00/30.42 | | | | e3) = e3) % 190.00/30.42 | | | | % 190.00/30.42 | | | | BETA: splitting (31) gives: % 190.00/30.42 | | | | % 190.00/30.42 | | | | Case 1: % 190.00/30.42 | | | | | % 190.00/30.42 | | | | | (32) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.42 | | | | | % 190.00/30.42 | | | | | REF_CLOSE: (21), (30), (32) are inconsistent by sub-proof #234. % 190.00/30.42 | | | | | % 190.00/30.42 | | | | Case 2: % 190.00/30.42 | | | | | % 190.00/30.42 | | | | | (33) all_252_3 = e3 & op(e3, e3) = e3 % 190.00/30.42 | | | | | % 190.00/30.42 | | | | | ALPHA: (33) implies: % 190.00/30.42 | | | | | (34) all_252_3 = e3 % 190.00/30.42 | | | | | % 190.00/30.42 | | | | | BETA: splitting (2) gives: % 190.00/30.42 | | | | | % 190.00/30.42 | | | | | Case 1: % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | | (35) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & % 190.00/30.42 | | | | | | op(e3, e4) = e3) % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | | BETA: splitting (35) gives: % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | | Case 1: % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | (36) all_252_0 = e3 & op(e4, e4) = e3 % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | REF_CLOSE: (9), (11), (36) are inconsistent by sub-proof #235. % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | Case 2: % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | (37) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | REF_CLOSE: (21), (30), (37) are inconsistent by sub-proof #234. % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | End of split % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | Case 2: % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | | (38) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & % 190.00/30.42 | | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | | BETA: splitting (38) gives: % 190.00/30.42 | | | | | | % 190.00/30.42 | | | | | | Case 1: % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | (39) all_252_6 = e3 & op(e2, e4) = e3 % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | ALPHA: (39) implies: % 190.00/30.42 | | | | | | | (40) all_252_6 = e3 % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | COMBINE_EQS: (14), (40) imply: % 190.00/30.42 | | | | | | | (41) e4 = e3 % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | SIMP: (41) implies: % 190.00/30.42 | | | | | | | (42) e4 = e3 % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | REDUCE: (9), (42) imply: % 190.00/30.42 | | | | | | | (43) $false % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | CLOSE: (43) is inconsistent. % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | Case 2: % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | (44) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 190.00/30.42 | | | | | | | op(e0, e4) = e3) % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | BETA: splitting (44) gives: % 190.00/30.42 | | | | | | | % 190.00/30.42 | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | % 190.00/30.42 | | | | | | | | (45) all_252_12 = e3 & op(e1, e4) = e3 % 190.00/30.42 | | | | | | | | % 190.00/30.42 | | | | | | | | ALPHA: (45) implies: % 190.00/30.42 | | | | | | | | (46) all_252_12 = e3 % 190.00/30.42 | | | | | | | | % 190.00/30.42 | | | | | | | | COMBINE_EQS: (7), (46) imply: % 190.00/30.42 | | | | | | | | (47) e3 = e0 % 190.00/30.42 | | | | | | | | % 190.00/30.42 | | | | | | | | COMBINE_EQS: (34), (47) imply: % 190.00/30.42 | | | | | | | | (48) all_252_3 = e0 % 190.00/30.42 | | | | | | | | % 190.00/30.42 | | | | | | | | BETA: splitting (2) gives: % 190.00/30.42 | | | | | | | | % 190.00/30.42 | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | | (49) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & % 190.00/30.42 | | | | | | | | | op(e3, e4) = e3) % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | | BETA: splitting (49) gives: % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | (50) all_252_0 = e3 & op(e4, e4) = e3 % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | REF_CLOSE: (9), (11), (50) are inconsistent by sub-proof % 190.00/30.42 | | | | | | | | | | #235. % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | Case 2: % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | (51) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | REF_CLOSE: (21), (30), (51) are inconsistent by sub-proof % 190.00/30.42 | | | | | | | | | | #234. % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | End of split % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | Case 2: % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | | BETA: splitting (38) gives: % 190.00/30.42 | | | | | | | | | % 190.00/30.42 | | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | (52) all_252_6 = e3 & op(e2, e4) = e3 % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | ALPHA: (52) implies: % 190.00/30.42 | | | | | | | | | | (53) all_252_6 = e3 % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | BETA: splitting (19) gives: % 190.00/30.42 | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | BETA: splitting (31) gives: % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | (54) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | REF_CLOSE: (21), (30), (54) are inconsistent by sub-proof % 190.00/30.42 | | | | | | | | | | | | #234. % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | Case 2: % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | REF_CLOSE: (13), (33), (48) are inconsistent by sub-proof % 190.00/30.42 | | | | | | | | | | | | #363. % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | End of split % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | Case 2: % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | (55) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = % 190.00/30.42 | | | | | | | | | | | e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 190.00/30.42 | | | | | | | | | | | op(e3, e0) = e3) % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | BETA: splitting (55) gives: % 190.00/30.42 | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | (56) all_252_5 = e3 & op(e3, e2) = e3 % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | REF_CLOSE: (13), (25), (56) are inconsistent by sub-proof % 190.00/30.42 | | | | | | | | | | | | #217. % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | Case 2: % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | (57) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 % 190.00/30.42 | | | | | | | | | | | | = e3 & op(e3, e0) = e3) % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | BETA: splitting (57) gives: % 190.00/30.42 | | | | | | | | | | | | % 190.00/30.42 | | | | | | | | | | | | Case 1: % 190.00/30.42 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | (58) all_252_10 = e3 & op(e3, e1) = e3 % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | REF_CLOSE: (3), (9), (58) are inconsistent by sub-proof #274. % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | Case 2: % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | (59) all_252_17 = e3 & op(e3, e0) = e3 % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | ALPHA: (59) implies: % 190.00/30.43 | | | | | | | | | | | | | (60) all_252_17 = e3 % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | COMBINE_EQS: (10), (60) imply: % 190.00/30.43 | | | | | | | | | | | | | (61) e3 = e2 % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | SIMP: (61) implies: % 190.00/30.43 | | | | | | | | | | | | | (62) e3 = e2 % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | COMBINE_EQS: (53), (62) imply: % 190.00/30.43 | | | | | | | | | | | | | (63) all_252_6 = e2 % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (12), % 190.00/30.43 | | | | | | | | | | | | | (13), (15), (16), (17), (18), (20), (21), (22), % 190.00/30.43 | | | | | | | | | | | | | (23), (24), (26), (30), (63) are inconsistent by % 190.00/30.43 | | | | | | | | | | | | | sub-proof #227. % 190.00/30.43 | | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | | End of split % 190.00/30.43 | | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | End of split % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | End of split % 190.00/30.43 | | | | | | | | | | % 190.00/30.43 | | | | | | | | | Case 2: % 190.00/30.43 | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | BETA: splitting (44) gives: % 190.00/30.43 | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | Case 1: % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | REF_CLOSE: (7), (13), (45) are inconsistent by sub-proof % 190.00/30.43 | | | | | | | | | | | #216. % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | Case 2: % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | (64) all_252_20 = e3 & op(e0, e4) = e3 % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | ALPHA: (64) implies: % 190.00/30.43 | | | | | | | | | | | (65) op(e0, e4) = e3 % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | | REF_CLOSE: (5), (20), (23), (65) are inconsistent by % 190.00/30.43 | | | | | | | | | | | sub-proof #512. % 190.00/30.43 | | | | | | | | | | | % 190.00/30.43 | | | | | | | | | | End of split % 190.00/30.43 | | | | | | | | | | % 190.00/30.43 | | | | | | | | | End of split % 190.00/30.43 | | | | | | | | | % 190.00/30.43 | | | | | | | | End of split % 190.00/30.43 | | | | | | | | % 190.00/30.43 | | | | | | | Case 2: % 190.00/30.43 | | | | | | | | % 190.00/30.43 | | | | | | | | (66) all_252_20 = e3 & op(e0, e4) = e3 % 190.00/30.43 | | | | | | | | % 190.00/30.43 | | | | | | | | ALPHA: (66) implies: % 190.00/30.43 | | | | | | | | (67) op(e0, e4) = e3 % 190.00/30.43 | | | | | | | | % 190.00/30.43 | | | | | | | | REF_CLOSE: (5), (20), (23), (67) are inconsistent by sub-proof % 190.00/30.43 | | | | | | | | #512. % 190.00/30.43 | | | | | | | | % 190.00/30.43 | | | | | | | End of split % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | End of split % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | End of split % 190.00/30.43 | | | | | % 190.00/30.43 | | | | End of split % 190.00/30.43 | | | | % 190.00/30.43 | | | Case 2: % 190.00/30.43 | | | | % 190.00/30.43 | | | | (68) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, % 190.00/30.43 | | | | e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.00/30.43 | | | | % 190.00/30.43 | | | | BETA: splitting (68) gives: % 190.00/30.43 | | | | % 190.00/30.43 | | | | Case 1: % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | (69) all_252_5 = e3 & op(e3, e2) = e3 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | REF_CLOSE: (13), (25), (69) are inconsistent by sub-proof #217. % 190.00/30.43 | | | | | % 190.00/30.43 | | | | Case 2: % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | (70) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 190.00/30.43 | | | | | op(e3, e0) = e3) % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | BETA: splitting (70) gives: % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | Case 1: % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | (71) all_252_10 = e3 & op(e3, e1) = e3 % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | REF_CLOSE: (3), (9), (71) are inconsistent by sub-proof #274. % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | Case 2: % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | (72) all_252_17 = e3 & op(e3, e0) = e3 % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | REF_CLOSE: (10), (15), (72) are inconsistent by sub-proof #249. % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | End of split % 190.00/30.43 | | | | | % 190.00/30.43 | | | | End of split % 190.00/30.43 | | | | % 190.00/30.43 | | | End of split % 190.00/30.43 | | | % 190.00/30.43 | | End of split % 190.00/30.43 | | % 190.00/30.43 | Case 2: % 190.00/30.43 | | % 190.00/30.43 | | (73) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.43 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (5), (6), (7), (12), (14), (18), (26), (73) are inconsistent by % 190.00/30.43 | | sub-proof #214. % 190.00/30.43 | | % 190.00/30.43 | End of split % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #214 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.43 (2) ~ (e2 = e1) % 190.00/30.43 (3) all_252_12 = e0 % 190.00/30.43 (4) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = e1) % 190.00/30.43 | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.43 (5) op(e0, e4) = e2 % 190.00/30.43 (6) all_252_6 = e4 % 190.00/30.43 (7) ~ (e1 = e0) % 190.00/30.43 (8) ~ (e4 = e1) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | BETA: splitting (4) gives: % 190.00/30.43 | % 190.00/30.43 | Case 1: % 190.00/30.43 | | % 190.00/30.43 | | (9) all_252_6 = e1 & op(e2, e4) = e1 % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (6), (8), (9) are inconsistent by sub-proof #215. % 190.00/30.43 | | % 190.00/30.43 | Case 2: % 190.00/30.43 | | % 190.00/30.43 | | (10) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) % 190.00/30.43 | | = e1) % 190.00/30.43 | | % 190.00/30.43 | | BETA: splitting (10) gives: % 190.00/30.43 | | % 190.00/30.43 | | Case 1: % 190.00/30.43 | | | % 190.00/30.43 | | | (11) all_252_12 = e1 & op(e1, e4) = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | ALPHA: (11) implies: % 190.00/30.43 | | | (12) all_252_12 = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | COMBINE_EQS: (3), (12) imply: % 190.00/30.43 | | | (13) e1 = e0 % 190.00/30.43 | | | % 190.00/30.43 | | | SIMP: (13) implies: % 190.00/30.43 | | | (14) e1 = e0 % 190.00/30.43 | | | % 190.00/30.43 | | | REDUCE: (7), (14) imply: % 190.00/30.43 | | | (15) $false % 190.00/30.43 | | | % 190.00/30.43 | | | CLOSE: (15) is inconsistent. % 190.00/30.43 | | | % 190.00/30.43 | | Case 2: % 190.00/30.43 | | | % 190.00/30.43 | | | (16) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | ALPHA: (16) implies: % 190.00/30.43 | | | (17) op(e0, e4) = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | REF_CLOSE: (1), (2), (5), (17) are inconsistent by sub-proof #323. % 190.00/30.43 | | | % 190.00/30.43 | | End of split % 190.00/30.43 | | % 190.00/30.43 | End of split % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #215 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_6 = e1 & op(e2, e4) = e1 % 190.00/30.43 (2) all_252_6 = e4 % 190.00/30.43 (3) ~ (e4 = e1) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | ALPHA: (1) implies: % 190.00/30.43 | (4) all_252_6 = e1 % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (2), (4) imply: % 190.00/30.43 | (5) e4 = e1 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (5) imply: % 190.00/30.43 | (6) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (6) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #216 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_12 = e3 & op(e1, e4) = e3 % 190.00/30.43 (2) all_252_12 = e0 % 190.00/30.43 (3) ~ (e3 = e0) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | ALPHA: (1) implies: % 190.00/30.43 | (4) all_252_12 = e3 % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (2), (4) imply: % 190.00/30.43 | (5) e3 = e0 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (5) imply: % 190.00/30.43 | (6) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (6) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #217 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_5 = e3 & op(e3, e2) = e3 % 190.00/30.43 (2) all_252_5 = e0 % 190.00/30.43 (3) ~ (e3 = e0) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | ALPHA: (1) implies: % 190.00/30.43 | (4) all_252_5 = e3 % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (2), (4) imply: % 190.00/30.43 | (5) e3 = e0 % 190.00/30.43 | % 190.00/30.43 | SIMP: (5) implies: % 190.00/30.43 | (6) e3 = e0 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (6) imply: % 190.00/30.43 | (7) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (7) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #218 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_10 = e4 % 190.00/30.43 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.43 (3) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 190.00/30.43 (4) op(e4, e1) = e0 % 190.00/30.43 (5) ~ (e4 = e3) % 190.00/30.43 (6) ~ (e3 = e0) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | BETA: splitting (3) gives: % 190.00/30.43 | % 190.00/30.43 | Case 1: % 190.00/30.43 | | % 190.00/30.43 | | (7) all_252_9 = e3 & op(e4, e1) = e3 % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #275. % 190.00/30.43 | | % 190.00/30.43 | Case 2: % 190.00/30.43 | | % 190.00/30.43 | | (8) all_252_10 = e3 & op(e3, e1) = e3 % 190.00/30.43 | | % 190.00/30.43 | | ALPHA: (8) implies: % 190.00/30.43 | | (9) all_252_10 = e3 % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #219. % 190.00/30.43 | | % 190.00/30.43 | End of split % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #219 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_10 = e4 % 190.00/30.43 (2) all_252_10 = e3 % 190.00/30.43 (3) ~ (e4 = e3) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (1), (2) imply: % 190.00/30.43 | (4) e4 = e3 % 190.00/30.43 | % 190.00/30.43 | SIMP: (4) implies: % 190.00/30.43 | (5) e4 = e3 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (5) imply: % 190.00/30.43 | (6) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (6) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #220 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_9 = e4 & op(e4, e1) = e4 % 190.00/30.43 (2) all_252_9 = e0 % 190.00/30.43 (3) ~ (e4 = e0) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | ALPHA: (1) implies: % 190.00/30.43 | (4) all_252_9 = e4 % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (2), (4) imply: % 190.00/30.43 | (5) e4 = e0 % 190.00/30.43 | % 190.00/30.43 | SIMP: (5) implies: % 190.00/30.43 | (6) e4 = e0 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (6) imply: % 190.00/30.43 | (7) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (7) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #221 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_20 = e2 % 190.00/30.43 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 190.00/30.43 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 190.00/30.43 | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.43 (3) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_7 = e2 & op(e2, e3) = e2) % 190.00/30.43 (4) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 190.00/30.43 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 190.00/30.43 | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.43 (6) ~ (e2 = e1) % 190.00/30.43 (7) all_252_12 = e0 % 190.00/30.43 (8) all_252_7 = e0 % 190.00/30.43 (9) ~ (e4 = e0) % 190.00/30.43 (10) ~ (e4 = e3) % 190.00/30.43 (11) op(e0, e4) = e2 % 190.00/30.43 (12) ~ (e3 = e0) % 190.00/30.43 (13) ~ (e3 = e2) % 190.00/30.43 (14) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 190.00/30.43 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 190.00/30.43 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 190.00/30.43 (15) ~ (e4 = e2) % 190.00/30.43 (16) ~ (e1 = e0) % 190.00/30.43 (17) op(e0, e4) = all_12_2 % 190.00/30.43 (18) ~ (e3 = e1) % 190.00/30.43 (19) ~ (e2 = e0) % 190.00/30.43 (20) ~ (all_12_2 = e3) % 190.00/30.43 (21) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 190.00/30.43 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.43 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.43 (22) ~ (e4 = e1) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | BETA: splitting (3) gives: % 190.00/30.43 | % 190.00/30.43 | Case 1: % 190.00/30.43 | | % 190.00/30.43 | | (23) all_252_6 = e2 & op(e2, e4) = e2 % 190.00/30.43 | | % 190.00/30.43 | | ALPHA: (23) implies: % 190.00/30.43 | | (24) all_252_6 = e2 % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14), % 190.00/30.43 | | (15), (16), (17), (18), (19), (20), (21), (22), (24) are % 190.00/30.43 | | inconsistent by sub-proof #223. % 190.00/30.43 | | % 190.00/30.43 | Case 2: % 190.00/30.43 | | % 190.00/30.43 | | (25) all_252_7 = e2 & op(e2, e3) = e2 % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (8), (19), (25) are inconsistent by sub-proof #222. % 190.00/30.43 | | % 190.00/30.43 | End of split % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #222 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_7 = e2 & op(e2, e3) = e2 % 190.00/30.43 (2) all_252_7 = e0 % 190.00/30.43 (3) ~ (e2 = e0) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | ALPHA: (1) implies: % 190.00/30.43 | (4) all_252_7 = e2 % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (2), (4) imply: % 190.00/30.43 | (5) e2 = e0 % 190.00/30.43 | % 190.00/30.43 | SIMP: (5) implies: % 190.00/30.43 | (6) e2 = e0 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (6) imply: % 190.00/30.43 | (7) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (7) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #223 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_20 = e2 % 190.00/30.43 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 190.00/30.43 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 190.00/30.43 | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.43 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 190.00/30.43 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 190.00/30.43 | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.43 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.43 (5) ~ (e2 = e1) % 190.00/30.43 (6) all_252_12 = e0 % 190.00/30.43 (7) ~ (e4 = e0) % 190.00/30.43 (8) ~ (e4 = e3) % 190.00/30.43 (9) op(e0, e4) = e2 % 190.00/30.43 (10) ~ (e3 = e0) % 190.00/30.43 (11) ~ (e3 = e2) % 190.00/30.43 (12) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 190.00/30.43 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 190.00/30.43 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 190.00/30.43 (13) ~ (e4 = e2) % 190.00/30.43 (14) ~ (e1 = e0) % 190.00/30.43 (15) op(e0, e4) = all_12_2 % 190.00/30.43 (16) ~ (e3 = e1) % 190.00/30.43 (17) ~ (e2 = e0) % 190.00/30.43 (18) all_252_6 = e2 % 190.00/30.43 (19) ~ (all_12_2 = e3) % 190.00/30.43 (20) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 190.00/30.43 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.43 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.43 (21) ~ (e4 = e1) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | BETA: splitting (20) gives: % 190.00/30.43 | % 190.00/30.43 | Case 1: % 190.00/30.43 | | % 190.00/30.43 | | (22) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = % 190.00/30.43 | | e1) % 190.00/30.43 | | % 190.00/30.43 | | BETA: splitting (22) gives: % 190.00/30.43 | | % 190.00/30.43 | | Case 1: % 190.00/30.43 | | | % 190.00/30.43 | | | (23) all_252_0 = e1 & op(e4, e4) = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | ALPHA: (23) implies: % 190.00/30.43 | | | (24) all_252_0 = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | BETA: splitting (3) gives: % 190.00/30.43 | | | % 190.00/30.43 | | | Case 1: % 190.00/30.43 | | | | % 190.00/30.43 | | | | (25) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, % 190.00/30.43 | | | | e4) = e4) % 190.00/30.43 | | | | % 190.00/30.43 | | | | BETA: splitting (25) gives: % 190.00/30.43 | | | | % 190.00/30.43 | | | | Case 1: % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | (26) all_252_0 = e4 & op(e4, e4) = e4 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | ALPHA: (26) implies: % 190.00/30.43 | | | | | (27) all_252_0 = e4 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | COMBINE_EQS: (24), (27) imply: % 190.00/30.43 | | | | | (28) e4 = e1 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | SIMP: (28) implies: % 190.00/30.43 | | | | | (29) e4 = e1 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | REDUCE: (21), (29) imply: % 190.00/30.43 | | | | | (30) $false % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | CLOSE: (30) is inconsistent. % 190.00/30.43 | | | | | % 190.00/30.43 | | | | Case 2: % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | (31) all_252_2 = e4 & op(e3, e4) = e4 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | ALPHA: (31) implies: % 190.00/30.43 | | | | | (32) all_252_2 = e4 % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | BETA: splitting (2) gives: % 190.00/30.43 | | | | | % 190.00/30.43 | | | | | Case 1: % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | (33) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & % 190.00/30.43 | | | | | | op(e3, e4) = e3) % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | BETA: splitting (33) gives: % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | Case 1: % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | (34) all_252_0 = e3 & op(e4, e4) = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | ALPHA: (34) implies: % 190.00/30.43 | | | | | | | (35) all_252_0 = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | COMBINE_EQS: (24), (35) imply: % 190.00/30.43 | | | | | | | (36) e3 = e1 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | SIMP: (36) implies: % 190.00/30.43 | | | | | | | (37) e3 = e1 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | REDUCE: (16), (37) imply: % 190.00/30.43 | | | | | | | (38) $false % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | CLOSE: (38) is inconsistent. % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | Case 2: % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | (39) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | ALPHA: (39) implies: % 190.00/30.43 | | | | | | | (40) all_252_2 = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | COMBINE_EQS: (32), (40) imply: % 190.00/30.43 | | | | | | | (41) e4 = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | REDUCE: (8), (41) imply: % 190.00/30.43 | | | | | | | (42) $false % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | CLOSE: (42) is inconsistent. % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | End of split % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | Case 2: % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | (43) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & % 190.00/30.43 | | | | | | op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | BETA: splitting (43) gives: % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | | Case 1: % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | (44) all_252_6 = e3 & op(e2, e4) = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | ALPHA: (44) implies: % 190.00/30.43 | | | | | | | (45) all_252_6 = e3 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | COMBINE_EQS: (18), (45) imply: % 190.00/30.43 | | | | | | | (46) e3 = e2 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | SIMP: (46) implies: % 190.00/30.43 | | | | | | | (47) e3 = e2 % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | REDUCE: (11), (47) imply: % 190.00/30.43 | | | | | | | (48) $false % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | CLOSE: (48) is inconsistent. % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | Case 2: % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | (49) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & % 190.00/30.43 | | | | | | | op(e0, e4) = e3) % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | | REF_CLOSE: (4), (6), (10), (15), (19), (49) are inconsistent by % 190.00/30.43 | | | | | | | sub-proof #237. % 190.00/30.43 | | | | | | | % 190.00/30.43 | | | | | | End of split % 190.00/30.43 | | | | | | % 190.00/30.43 | | | | | End of split % 190.00/30.43 | | | | | % 190.00/30.43 | | | | End of split % 190.00/30.43 | | | | % 190.00/30.43 | | | Case 2: % 190.00/30.43 | | | | % 190.00/30.43 | | | | (50) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, % 190.00/30.43 | | | | e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.43 | | | | % 190.00/30.43 | | | | REF_CLOSE: (4), (6), (7), (9), (13), (18), (50) are inconsistent by % 190.00/30.43 | | | | sub-proof #236. % 190.00/30.43 | | | | % 190.00/30.43 | | | End of split % 190.00/30.43 | | | % 190.00/30.43 | | Case 2: % 190.00/30.43 | | | % 190.00/30.43 | | | (51) all_252_2 = e1 & op(e3, e4) = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | ALPHA: (51) implies: % 190.00/30.43 | | | (52) all_252_2 = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), % 190.00/30.43 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (52) are % 190.00/30.43 | | | inconsistent by sub-proof #225. % 190.00/30.43 | | | % 190.00/30.43 | | End of split % 190.00/30.43 | | % 190.00/30.43 | Case 2: % 190.00/30.43 | | % 190.00/30.43 | | (53) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.43 | | e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.43 | | % 190.00/30.43 | | BETA: splitting (53) gives: % 190.00/30.43 | | % 190.00/30.43 | | Case 1: % 190.00/30.43 | | | % 190.00/30.43 | | | (54) all_252_6 = e1 & op(e2, e4) = e1 % 190.00/30.43 | | | % 190.00/30.43 | | | REF_CLOSE: (5), (18), (54) are inconsistent by sub-proof #229. % 190.00/30.43 | | | % 190.00/30.43 | | Case 2: % 190.00/30.43 | | | % 190.00/30.43 | | | (55) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, % 190.00/30.43 | | | e4) = e1) % 190.00/30.43 | | | % 190.00/30.43 | | | BETA: splitting (55) gives: % 190.00/30.43 | | | % 190.00/30.43 | | | Case 1: % 190.00/30.43 | | | | % 190.00/30.43 | | | | (56) all_252_12 = e1 & op(e1, e4) = e1 % 190.00/30.43 | | | | % 190.00/30.43 | | | | REF_CLOSE: (6), (14), (56) are inconsistent by sub-proof #224. % 190.00/30.43 | | | | % 190.00/30.43 | | | Case 2: % 190.00/30.43 | | | | % 190.00/30.43 | | | | (57) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.43 | | | | % 190.00/30.43 | | | | ALPHA: (57) implies: % 190.00/30.43 | | | | (58) op(e0, e4) = e1 % 190.00/30.43 | | | | % 190.00/30.43 | | | | REF_CLOSE: (4), (5), (9), (58) are inconsistent by sub-proof #323. % 190.00/30.43 | | | | % 190.00/30.43 | | | End of split % 190.00/30.43 | | | % 190.00/30.43 | | End of split % 190.00/30.43 | | % 190.00/30.43 | End of split % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #224 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_12 = e1 & op(e1, e4) = e1 % 190.00/30.43 (2) all_252_12 = e0 % 190.00/30.43 (3) ~ (e1 = e0) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | ALPHA: (1) implies: % 190.00/30.43 | (4) all_252_12 = e1 % 190.00/30.43 | % 190.00/30.43 | COMBINE_EQS: (2), (4) imply: % 190.00/30.43 | (5) e1 = e0 % 190.00/30.43 | % 190.00/30.43 | REDUCE: (3), (5) imply: % 190.00/30.43 | (6) $false % 190.00/30.43 | % 190.00/30.43 | CLOSE: (6) is inconsistent. % 190.00/30.43 | % 190.00/30.43 End of proof % 190.00/30.43 % 190.00/30.43 Sub-proof #225 shows that the following formulas are inconsistent: % 190.00/30.43 ---------------------------------------------------------------- % 190.00/30.43 (1) all_252_20 = e2 % 190.00/30.43 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 190.00/30.43 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 190.00/30.43 | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.43 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 190.00/30.43 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 190.00/30.43 | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.43 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.43 (5) ~ (e2 = e1) % 190.00/30.43 (6) all_252_12 = e0 % 190.00/30.43 (7) ~ (e4 = e0) % 190.00/30.43 (8) ~ (e4 = e3) % 190.00/30.43 (9) op(e0, e4) = e2 % 190.00/30.43 (10) all_252_2 = e1 % 190.00/30.43 (11) ~ (e3 = e0) % 190.00/30.43 (12) ~ (e3 = e2) % 190.00/30.43 (13) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 190.00/30.43 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 190.00/30.43 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 190.00/30.43 (14) ~ (e4 = e2) % 190.00/30.43 (15) ~ (e1 = e0) % 190.00/30.43 (16) op(e0, e4) = all_12_2 % 190.00/30.43 (17) ~ (e3 = e1) % 190.00/30.43 (18) ~ (e2 = e0) % 190.00/30.43 (19) all_252_6 = e2 % 190.00/30.43 (20) ~ (all_12_2 = e3) % 190.00/30.43 (21) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 190.00/30.43 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.43 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.43 (22) ~ (e4 = e1) % 190.00/30.43 % 190.00/30.43 Begin of proof % 190.00/30.43 | % 190.00/30.43 | BETA: splitting (3) gives: % 190.00/30.43 | % 190.00/30.43 | Case 1: % 190.00/30.43 | | % 190.00/30.43 | | (23) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = % 190.00/30.43 | | e4) % 190.00/30.43 | | % 190.00/30.43 | | BETA: splitting (23) gives: % 190.00/30.43 | | % 190.00/30.43 | | Case 1: % 190.00/30.43 | | | % 190.00/30.43 | | | (24) all_252_0 = e4 & op(e4, e4) = e4 % 190.00/30.43 | | | % 190.00/30.43 | | | ALPHA: (24) implies: % 190.00/30.43 | | | (25) all_252_0 = e4 % 190.00/30.43 | | | % 190.00/30.43 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), % 190.00/30.43 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (25) are % 190.00/30.43 | | | inconsistent by sub-proof #227. % 190.00/30.43 | | | % 190.00/30.43 | | Case 2: % 190.00/30.43 | | | % 190.00/30.43 | | | (26) all_252_2 = e4 & op(e3, e4) = e4 % 190.00/30.43 | | | % 190.00/30.43 | | | ALPHA: (26) implies: % 190.00/30.43 | | | (27) all_252_2 = e4 % 190.00/30.43 | | | % 190.00/30.43 | | | REF_CLOSE: (10), (22), (27) are inconsistent by sub-proof #226. % 190.00/30.43 | | | % 190.00/30.43 | | End of split % 190.00/30.43 | | % 190.00/30.43 | Case 2: % 190.00/30.43 | | % 190.00/30.43 | | (28) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = % 190.00/30.43 | | e4) | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.43 | | % 190.00/30.43 | | REF_CLOSE: (4), (6), (7), (9), (14), (19), (28) are inconsistent by % 190.00/30.43 | | sub-proof #236. % 190.00/30.43 | | % 190.00/30.43 | End of split % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #226 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_2 = e4 % 190.00/30.44 (2) all_252_2 = e1 % 190.00/30.44 (3) ~ (e4 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (1), (2) imply: % 190.00/30.44 | (4) e4 = e1 % 190.00/30.44 | % 190.00/30.44 | SIMP: (4) implies: % 190.00/30.44 | (5) e4 = e1 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #227 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_20 = e2 % 190.00/30.44 (2) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) | % 190.00/30.44 (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = e3) % 190.00/30.44 | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.44 (3) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & op(e3, e4) = e4) | % 190.00/30.44 (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 190.00/30.44 | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.44 (5) ~ (e2 = e1) % 190.00/30.44 (6) ~ (e4 = e0) % 190.00/30.44 (7) ~ (e4 = e3) % 190.00/30.44 (8) all_252_0 = e4 % 190.00/30.44 (9) op(e0, e4) = e2 % 190.00/30.44 (10) all_252_2 = e1 % 190.00/30.44 (11) ~ (e3 = e0) % 190.00/30.44 (12) ~ (e3 = e2) % 190.00/30.44 (13) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, e4) = e0) % 190.00/30.44 | (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, e4) = % 190.00/30.44 e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 190.00/30.44 (14) ~ (e4 = e2) % 190.00/30.44 (15) ~ (e1 = e0) % 190.00/30.44 (16) op(e0, e4) = all_12_2 % 190.00/30.44 (17) ~ (e3 = e1) % 190.00/30.44 (18) ~ (e2 = e0) % 190.00/30.44 (19) all_252_6 = e2 % 190.00/30.44 (20) ~ (all_12_2 = e3) % 190.00/30.44 (21) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & op(e3, e4) = e1) % 190.00/30.44 | (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & op(e1, e4) = % 190.00/30.44 e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.44 (22) ~ (e4 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | BETA: splitting (2) gives: % 190.00/30.44 | % 190.00/30.44 | Case 1: % 190.00/30.44 | | % 190.00/30.44 | | (23) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = % 190.00/30.44 | | e3) % 190.00/30.44 | | % 190.00/30.44 | | BETA: splitting (23) gives: % 190.00/30.44 | | % 190.00/30.44 | | Case 1: % 190.00/30.44 | | | % 190.00/30.44 | | | (24) all_252_0 = e3 & op(e4, e4) = e3 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (7), (8), (24) are inconsistent by sub-proof #235. % 190.00/30.44 | | | % 190.00/30.44 | | Case 2: % 190.00/30.44 | | | % 190.00/30.44 | | | (25) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (10), (17), (25) are inconsistent by sub-proof #234. % 190.00/30.44 | | | % 190.00/30.44 | | End of split % 190.00/30.44 | | % 190.00/30.44 | Case 2: % 190.00/30.44 | | % 190.00/30.44 | | (26) (all_252_6 = e3 & op(e2, e4) = e3) | (all_252_12 = e3 & op(e1, e4) = % 190.00/30.44 | | e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.44 | | % 190.00/30.44 | | BETA: splitting (26) gives: % 190.00/30.44 | | % 190.00/30.44 | | Case 1: % 190.00/30.44 | | | % 190.00/30.44 | | | (27) all_252_6 = e3 & op(e2, e4) = e3 % 190.00/30.44 | | | % 190.00/30.44 | | | ALPHA: (27) implies: % 190.00/30.44 | | | (28) all_252_6 = e3 % 190.00/30.44 | | | % 190.00/30.44 | | | COMBINE_EQS: (19), (28) imply: % 190.00/30.44 | | | (29) e3 = e2 % 190.00/30.44 | | | % 190.00/30.44 | | | REDUCE: (12), (29) imply: % 190.00/30.44 | | | (30) $false % 190.00/30.44 | | | % 190.00/30.44 | | | CLOSE: (30) is inconsistent. % 190.00/30.44 | | | % 190.00/30.44 | | Case 2: % 190.00/30.44 | | | % 190.00/30.44 | | | (31) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, % 190.00/30.44 | | | e4) = e3) % 190.00/30.44 | | | % 190.00/30.44 | | | BETA: splitting (31) gives: % 190.00/30.44 | | | % 190.00/30.44 | | | Case 1: % 190.00/30.44 | | | | % 190.00/30.44 | | | | (32) all_252_12 = e3 & op(e1, e4) = e3 % 190.00/30.44 | | | | % 190.00/30.44 | | | | ALPHA: (32) implies: % 190.00/30.44 | | | | (33) all_252_12 = e3 % 190.00/30.44 | | | | % 190.00/30.44 | | | | BETA: splitting (13) gives: % 190.00/30.44 | | | | % 190.00/30.44 | | | | Case 1: % 190.00/30.44 | | | | | % 190.00/30.44 | | | | | (34) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_2 = e0 & op(e3, % 190.00/30.44 | | | | | e4) = e0) % 190.00/30.44 | | | | | % 190.00/30.44 | | | | | BETA: splitting (34) gives: % 190.00/30.44 | | | | | % 190.00/30.44 | | | | | Case 1: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | (35) all_252_0 = e0 & op(e4, e4) = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | ALPHA: (35) implies: % 190.00/30.44 | | | | | | (36) all_252_0 = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | BETA: splitting (3) gives: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | Case 1: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | (37) (all_252_0 = e4 & op(e4, e4) = e4) | (all_252_2 = e4 & % 190.00/30.44 | | | | | | | op(e3, e4) = e4) % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | BETA: splitting (37) gives: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (38) all_252_0 = e4 & op(e4, e4) = e4 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | REF_CLOSE: (6), (36), (38) are inconsistent by sub-proof #385. % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (39) all_252_2 = e4 & op(e3, e4) = e4 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | ALPHA: (39) implies: % 190.00/30.44 | | | | | | | | (40) all_252_2 = e4 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | BETA: splitting (21) gives: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | (41) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & % 190.00/30.44 | | | | | | | | | op(e3, e4) = e1) % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | BETA: splitting (41) gives: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | (42) all_252_0 = e1 & op(e4, e4) = e1 % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | REF_CLOSE: (15), (36), (42) are inconsistent by sub-proof % 190.00/30.44 | | | | | | | | | | #233. % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | (43) all_252_2 = e1 & op(e3, e4) = e1 % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | REF_CLOSE: (22), (40), (43) are inconsistent by sub-proof % 190.00/30.44 | | | | | | | | | | #232. % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | End of split % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | (44) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 % 190.00/30.44 | | | | | | | | | & op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = % 190.00/30.44 | | | | | | | | | e1) % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | BETA: splitting (44) gives: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | (45) all_252_6 = e1 & op(e2, e4) = e1 % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | ALPHA: (45) implies: % 190.00/30.44 | | | | | | | | | | (46) all_252_6 = e1 % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | COMBINE_EQS: (19), (46) imply: % 190.00/30.44 | | | | | | | | | | (47) e2 = e1 % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | REDUCE: (5), (47) imply: % 190.00/30.44 | | | | | | | | | | (48) $false % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | CLOSE: (48) is inconsistent. % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | (49) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = % 190.00/30.44 | | | | | | | | | | e1 & op(e0, e4) = e1) % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | BETA: splitting (49) gives: % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | (50) all_252_12 = e1 & op(e1, e4) = e1 % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | REF_CLOSE: (17), (33), (50) are inconsistent by sub-proof % 190.00/30.44 | | | | | | | | | | | #424. % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | (51) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | ALPHA: (51) implies: % 190.00/30.44 | | | | | | | | | | | (52) op(e0, e4) = e1 % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | GROUND_INST: instantiating (4) with e1, e2, e4, e0, simplifying % 190.00/30.44 | | | | | | | | | | | with (9), (52) gives: % 190.00/30.44 | | | | | | | | | | | (53) e2 = e1 % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | REDUCE: (5), (53) imply: % 190.00/30.44 | | | | | | | | | | | (54) $false % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | | CLOSE: (54) is inconsistent. % 190.00/30.44 | | | | | | | | | | | % 190.00/30.44 | | | | | | | | | | End of split % 190.00/30.44 | | | | | | | | | | % 190.00/30.44 | | | | | | | | | End of split % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | End of split % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | End of split % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | Case 2: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | (55) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & % 190.00/30.44 | | | | | | | op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | BETA: splitting (55) gives: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (56) all_252_6 = e4 & op(e2, e4) = e4 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | ALPHA: (56) implies: % 190.00/30.44 | | | | | | | | (57) all_252_6 = e4 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | COMBINE_EQS: (19), (57) imply: % 190.00/30.44 | | | | | | | | (58) e4 = e2 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | REDUCE: (14), (58) imply: % 190.00/30.44 | | | | | | | | (59) $false % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | CLOSE: (59) is inconsistent. % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (60) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & % 190.00/30.44 | | | | | | | | op(e0, e4) = e4) % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | BETA: splitting (60) gives: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | (61) all_252_12 = e4 & op(e1, e4) = e4 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | ALPHA: (61) implies: % 190.00/30.44 | | | | | | | | | (62) all_252_12 = e4 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | COMBINE_EQS: (33), (62) imply: % 190.00/30.44 | | | | | | | | | (63) e4 = e3 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | SIMP: (63) implies: % 190.00/30.44 | | | | | | | | | (64) e4 = e3 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | REDUCE: (7), (64) imply: % 190.00/30.44 | | | | | | | | | (65) $false % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | CLOSE: (65) is inconsistent. % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | (66) all_252_20 = e4 & op(e0, e4) = e4 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | ALPHA: (66) implies: % 190.00/30.44 | | | | | | | | | (67) op(e0, e4) = e4 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | REF_CLOSE: (4), (9), (14), (67) are inconsistent by sub-proof % 190.00/30.44 | | | | | | | | | #426. % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | End of split % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | End of split % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | End of split % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | Case 2: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | (68) all_252_2 = e0 & op(e3, e4) = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | ALPHA: (68) implies: % 190.00/30.44 | | | | | | (69) all_252_2 = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | BETA: splitting (21) gives: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | Case 1: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | (70) (all_252_0 = e1 & op(e4, e4) = e1) | (all_252_2 = e1 & % 190.00/30.44 | | | | | | | op(e3, e4) = e1) % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | BETA: splitting (70) gives: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (71) all_252_0 = e1 & op(e4, e4) = e1 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | REF_CLOSE: (8), (22), (71) are inconsistent by sub-proof #231. % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (72) all_252_2 = e1 & op(e3, e4) = e1 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | REF_CLOSE: (15), (69), (72) are inconsistent by sub-proof #230. % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | End of split % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | Case 2: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | (73) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_12 = e1 & % 190.00/30.44 | | | | | | | op(e1, e4) = e1) | (all_252_20 = e1 & op(e0, e4) = e1) % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | BETA: splitting (73) gives: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (74) all_252_6 = e1 & op(e2, e4) = e1 % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | REF_CLOSE: (5), (19), (74) are inconsistent by sub-proof #229. % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | (75) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_20 = e1 & % 190.00/30.44 | | | | | | | | op(e0, e4) = e1) % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | BETA: splitting (75) gives: % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | | Case 1: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | (76) all_252_12 = e1 & op(e1, e4) = e1 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | REF_CLOSE: (17), (33), (76) are inconsistent by sub-proof % 190.00/30.44 | | | | | | | | | #410. % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | Case 2: % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | (77) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | ALPHA: (77) implies: % 190.00/30.44 | | | | | | | | | (78) all_252_20 = e1 % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | | REF_CLOSE: (1), (5), (78) are inconsistent by sub-proof #228. % 190.00/30.44 | | | | | | | | | % 190.00/30.44 | | | | | | | | End of split % 190.00/30.44 | | | | | | | | % 190.00/30.44 | | | | | | | End of split % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | End of split % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | End of split % 190.00/30.44 | | | | | % 190.00/30.44 | | | | Case 2: % 190.00/30.44 | | | | | % 190.00/30.44 | | | | | (79) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_12 = e0 & op(e1, % 190.00/30.44 | | | | | e4) = e0) | (all_252_20 = e0 & op(e0, e4) = e0) % 190.00/30.44 | | | | | % 190.00/30.44 | | | | | BETA: splitting (79) gives: % 190.00/30.44 | | | | | % 190.00/30.44 | | | | | Case 1: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | (80) all_252_6 = e0 & op(e2, e4) = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | ALPHA: (80) implies: % 190.00/30.44 | | | | | | (81) all_252_6 = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | COMBINE_EQS: (19), (81) imply: % 190.00/30.44 | | | | | | (82) e2 = e0 % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | REDUCE: (18), (82) imply: % 190.00/30.44 | | | | | | (83) $false % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | CLOSE: (83) is inconsistent. % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | Case 2: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | (84) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_20 = e0 & % 190.00/30.44 | | | | | | op(e0, e4) = e0) % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | BETA: splitting (84) gives: % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | | Case 1: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | (85) all_252_12 = e0 & op(e1, e4) = e0 % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | REF_CLOSE: (11), (33), (85) are inconsistent by sub-proof #417. % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | Case 2: % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | (86) all_252_20 = e0 & op(e0, e4) = e0 % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | | REF_CLOSE: (4), (9), (18), (86) are inconsistent by sub-proof % 190.00/30.44 | | | | | | | #255. % 190.00/30.44 | | | | | | | % 190.00/30.44 | | | | | | End of split % 190.00/30.44 | | | | | | % 190.00/30.44 | | | | | End of split % 190.00/30.44 | | | | | % 190.00/30.44 | | | | End of split % 190.00/30.44 | | | | % 190.00/30.44 | | | Case 2: % 190.00/30.44 | | | | % 190.00/30.44 | | | | (87) all_252_20 = e3 & op(e0, e4) = e3 % 190.00/30.44 | | | | % 190.00/30.44 | | | | ALPHA: (87) implies: % 190.00/30.44 | | | | (88) op(e0, e4) = e3 % 190.00/30.44 | | | | % 190.00/30.44 | | | | REF_CLOSE: (4), (16), (20), (88) are inconsistent by sub-proof #512. % 190.00/30.44 | | | | % 190.00/30.44 | | | End of split % 190.00/30.44 | | | % 190.00/30.44 | | End of split % 190.00/30.44 | | % 190.00/30.44 | End of split % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #228 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_20 = e2 % 190.00/30.44 (2) all_252_20 = e1 % 190.00/30.44 (3) ~ (e2 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (1), (2) imply: % 190.00/30.44 | (4) e2 = e1 % 190.00/30.44 | % 190.00/30.44 | SIMP: (4) implies: % 190.00/30.44 | (5) e2 = e1 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #229 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_6 = e1 & op(e2, e4) = e1 % 190.00/30.44 (2) all_252_6 = e2 % 190.00/30.44 (3) ~ (e2 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_6 = e1 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e2 = e1 % 190.00/30.44 | % 190.00/30.44 | SIMP: (5) implies: % 190.00/30.44 | (6) e2 = e1 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (6) imply: % 190.00/30.44 | (7) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (7) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #230 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_2 = e1 & op(e3, e4) = e1 % 190.00/30.44 (2) all_252_2 = e0 % 190.00/30.44 (3) ~ (e1 = e0) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_2 = e1 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e1 = e0 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #231 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_0 = e1 & op(e4, e4) = e1 % 190.00/30.44 (2) all_252_0 = e4 % 190.00/30.44 (3) ~ (e4 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_0 = e1 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e4 = e1 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #232 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_2 = e1 & op(e3, e4) = e1 % 190.00/30.44 (2) all_252_2 = e4 % 190.00/30.44 (3) ~ (e4 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_2 = e1 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e4 = e1 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #233 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_0 = e1 & op(e4, e4) = e1 % 190.00/30.44 (2) all_252_0 = e0 % 190.00/30.44 (3) ~ (e1 = e0) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_0 = e1 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e1 = e0 % 190.00/30.44 | % 190.00/30.44 | SIMP: (5) implies: % 190.00/30.44 | (6) e1 = e0 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (6) imply: % 190.00/30.44 | (7) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (7) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #234 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_2 = e3 & op(e3, e4) = e3 % 190.00/30.44 (2) all_252_2 = e1 % 190.00/30.44 (3) ~ (e3 = e1) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_2 = e3 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e3 = e1 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #235 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_0 = e3 & op(e4, e4) = e3 % 190.00/30.44 (2) all_252_0 = e4 % 190.00/30.44 (3) ~ (e4 = e3) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_0 = e3 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e4 = e3 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (5) imply: % 190.00/30.44 | (6) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (6) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #236 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.44 (2) all_252_12 = e0 % 190.00/30.44 (3) ~ (e4 = e0) % 190.00/30.44 (4) op(e0, e4) = e2 % 190.00/30.44 (5) (all_252_6 = e4 & op(e2, e4) = e4) | (all_252_12 = e4 & op(e1, e4) = e4) % 190.00/30.44 | (all_252_20 = e4 & op(e0, e4) = e4) % 190.00/30.44 (6) ~ (e4 = e2) % 190.00/30.44 (7) all_252_6 = e2 % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | BETA: splitting (5) gives: % 190.00/30.44 | % 190.00/30.44 | Case 1: % 190.00/30.44 | | % 190.00/30.44 | | (8) all_252_6 = e4 & op(e2, e4) = e4 % 190.00/30.44 | | % 190.00/30.44 | | ALPHA: (8) implies: % 190.00/30.44 | | (9) all_252_6 = e4 % 190.00/30.44 | | % 190.00/30.44 | | COMBINE_EQS: (7), (9) imply: % 190.00/30.44 | | (10) e4 = e2 % 190.00/30.44 | | % 190.00/30.44 | | SIMP: (10) implies: % 190.00/30.44 | | (11) e4 = e2 % 190.00/30.44 | | % 190.00/30.44 | | REDUCE: (6), (11) imply: % 190.00/30.44 | | (12) $false % 190.00/30.44 | | % 190.00/30.44 | | CLOSE: (12) is inconsistent. % 190.00/30.44 | | % 190.00/30.44 | Case 2: % 190.00/30.44 | | % 190.00/30.44 | | (13) (all_252_12 = e4 & op(e1, e4) = e4) | (all_252_20 = e4 & op(e0, e4) % 190.00/30.44 | | = e4) % 190.00/30.44 | | % 190.00/30.44 | | BETA: splitting (13) gives: % 190.00/30.44 | | % 190.00/30.44 | | Case 1: % 190.00/30.44 | | | % 190.00/30.44 | | | (14) all_252_12 = e4 & op(e1, e4) = e4 % 190.00/30.44 | | | % 190.00/30.44 | | | ALPHA: (14) implies: % 190.00/30.44 | | | (15) all_252_12 = e4 % 190.00/30.44 | | | % 190.00/30.44 | | | COMBINE_EQS: (2), (15) imply: % 190.00/30.44 | | | (16) e4 = e0 % 190.00/30.44 | | | % 190.00/30.44 | | | REDUCE: (3), (16) imply: % 190.00/30.44 | | | (17) $false % 190.00/30.44 | | | % 190.00/30.44 | | | CLOSE: (17) is inconsistent. % 190.00/30.44 | | | % 190.00/30.44 | | Case 2: % 190.00/30.44 | | | % 190.00/30.44 | | | (18) all_252_20 = e4 & op(e0, e4) = e4 % 190.00/30.44 | | | % 190.00/30.44 | | | ALPHA: (18) implies: % 190.00/30.44 | | | (19) op(e0, e4) = e4 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (1), (4), (6), (19) are inconsistent by sub-proof #426. % 190.00/30.44 | | | % 190.00/30.44 | | End of split % 190.00/30.44 | | % 190.00/30.44 | End of split % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #237 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 190.00/30.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.44 (3) all_252_12 = e0 % 190.00/30.44 (4) ~ (e3 = e0) % 190.00/30.44 (5) op(e0, e4) = all_12_2 % 190.00/30.44 (6) ~ (all_12_2 = e3) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | BETA: splitting (1) gives: % 190.00/30.44 | % 190.00/30.44 | Case 1: % 190.00/30.44 | | % 190.00/30.44 | | (7) all_252_12 = e3 & op(e1, e4) = e3 % 190.00/30.44 | | % 190.00/30.44 | | ALPHA: (7) implies: % 190.00/30.44 | | (8) all_252_12 = e3 % 190.00/30.44 | | % 190.00/30.44 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #381. % 190.00/30.44 | | % 190.00/30.44 | Case 2: % 190.00/30.44 | | % 190.00/30.44 | | (9) all_252_20 = e3 & op(e0, e4) = e3 % 190.00/30.44 | | % 190.00/30.44 | | ALPHA: (9) implies: % 190.00/30.44 | | (10) op(e0, e4) = e3 % 190.00/30.44 | | % 190.00/30.44 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #512. % 190.00/30.44 | | % 190.00/30.44 | End of split % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #238 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_20 = e2 % 190.00/30.44 (2) all_252_21 = e3 % 190.00/30.44 (3) ~ (e4 = e0) % 190.00/30.44 (4) all_252_23 = e1 % 190.00/30.44 (5) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = e0) % 190.00/30.44 | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) = % 190.00/30.44 e0) % 190.00/30.44 (6) ~ (e3 = e0) % 190.00/30.44 (7) all_252_22 = e4 % 190.00/30.44 (8) ~ (e1 = e0) % 190.00/30.44 (9) ~ (e2 = e0) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | BETA: splitting (5) gives: % 190.00/30.44 | % 190.00/30.44 | Case 1: % 190.00/30.44 | | % 190.00/30.44 | | (10) (all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) % 190.00/30.44 | | = e0) % 190.00/30.44 | | % 190.00/30.44 | | BETA: splitting (10) gives: % 190.00/30.44 | | % 190.00/30.44 | | Case 1: % 190.00/30.44 | | | % 190.00/30.44 | | | (11) all_252_20 = e0 & op(e0, e4) = e0 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (1), (9), (11) are inconsistent by sub-proof #240. % 190.00/30.44 | | | % 190.00/30.44 | | Case 2: % 190.00/30.44 | | | % 190.00/30.44 | | | (12) all_252_21 = e0 & op(e0, e3) = e0 % 190.00/30.44 | | | % 190.00/30.44 | | | ALPHA: (12) implies: % 190.00/30.44 | | | (13) all_252_21 = e0 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #334. % 190.00/30.44 | | | % 190.00/30.44 | | End of split % 190.00/30.44 | | % 190.00/30.44 | Case 2: % 190.00/30.44 | | % 190.00/30.44 | | (14) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) % 190.00/30.44 | | = e0) % 190.00/30.44 | | % 190.00/30.44 | | BETA: splitting (14) gives: % 190.00/30.44 | | % 190.00/30.44 | | Case 1: % 190.00/30.44 | | | % 190.00/30.44 | | | (15) all_252_22 = e0 & op(e0, e2) = e0 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (3), (7), (15) are inconsistent by sub-proof #239. % 190.00/30.44 | | | % 190.00/30.44 | | Case 2: % 190.00/30.44 | | | % 190.00/30.44 | | | (16) all_252_23 = e0 & op(e0, e1) = e0 % 190.00/30.44 | | | % 190.00/30.44 | | | REF_CLOSE: (4), (8), (16) are inconsistent by sub-proof #403. % 190.00/30.44 | | | % 190.00/30.44 | | End of split % 190.00/30.44 | | % 190.00/30.44 | End of split % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #239 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_22 = e0 & op(e0, e2) = e0 % 190.00/30.44 (2) all_252_22 = e4 % 190.00/30.44 (3) ~ (e4 = e0) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_22 = e0 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.44 | (5) e4 = e0 % 190.00/30.44 | % 190.00/30.44 | SIMP: (5) implies: % 190.00/30.44 | (6) e4 = e0 % 190.00/30.44 | % 190.00/30.44 | REDUCE: (3), (6) imply: % 190.00/30.44 | (7) $false % 190.00/30.44 | % 190.00/30.44 | CLOSE: (7) is inconsistent. % 190.00/30.44 | % 190.00/30.44 End of proof % 190.00/30.44 % 190.00/30.44 Sub-proof #240 shows that the following formulas are inconsistent: % 190.00/30.44 ---------------------------------------------------------------- % 190.00/30.44 (1) all_252_20 = e0 & op(e0, e4) = e0 % 190.00/30.44 (2) all_252_20 = e2 % 190.00/30.44 (3) ~ (e2 = e0) % 190.00/30.44 % 190.00/30.44 Begin of proof % 190.00/30.44 | % 190.00/30.44 | ALPHA: (1) implies: % 190.00/30.44 | (4) all_252_20 = e0 % 190.00/30.44 | % 190.00/30.44 | COMBINE_EQS: (2), (4) imply: % 190.00/30.45 | (5) e2 = e0 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #241 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_20 = e2 % 190.00/30.45 (2) all_252_21 = e3 % 190.00/30.45 (3) ~ (e2 = e1) % 190.00/30.45 (4) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 190.00/30.45 (5) ~ (e3 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (4) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (6) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #242. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (7) all_252_21 = e1 & op(e0, e3) = e1 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (7) implies: % 190.00/30.45 | | (8) all_252_21 = e1 % 190.00/30.45 | | % 190.00/30.45 | | COMBINE_EQS: (2), (8) imply: % 190.00/30.45 | | (9) e3 = e1 % 190.00/30.45 | | % 190.00/30.45 | | SIMP: (9) implies: % 190.00/30.45 | | (10) e3 = e1 % 190.00/30.45 | | % 190.00/30.45 | | REDUCE: (5), (10) imply: % 190.00/30.45 | | (11) $false % 190.00/30.45 | | % 190.00/30.45 | | CLOSE: (11) is inconsistent. % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #242 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.45 (2) all_252_20 = e2 % 190.00/30.45 (3) ~ (e2 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (4) all_252_20 = e1 % 190.00/30.45 | % 190.00/30.45 | COMBINE_EQS: (2), (4) imply: % 190.00/30.45 | (5) e2 = e1 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #243 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_19 = e3 & op(e1, e0) = e3 % 190.00/30.45 (2) all_252_19 = e4 % 190.00/30.45 (3) ~ (e4 = e3) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (4) all_252_19 = e3 % 190.00/30.45 | % 190.00/30.45 | COMBINE_EQS: (2), (4) imply: % 190.00/30.45 | (5) e4 = e3 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #244 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) ~ (e2 = e1) % 190.00/30.45 (3) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 190.00/30.45 (4) op(e0, e4) = e2 % 190.00/30.45 (5) op(e0, e3) = all_8_1 % 190.00/30.45 (6) ~ (all_8_1 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (3) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (7) all_252_20 = e1 & op(e0, e4) = e1 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (7) implies: % 190.00/30.45 | | (8) op(e0, e4) = e1 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #323. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (9) all_252_21 = e1 & op(e0, e3) = e1 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #281. % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #245 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_24 = e3 % 190.00/30.45 (2) all_252_24 = e1 % 190.00/30.45 (3) ~ (e3 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | COMBINE_EQS: (1), (2) imply: % 190.00/30.45 | (4) e3 = e1 % 190.00/30.45 | % 190.00/30.45 | SIMP: (4) implies: % 190.00/30.45 | (5) e3 = e1 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #246 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_18 = e1 & op(e2, e0) = e1 % 190.00/30.45 (2) all_252_18 = e4 % 190.00/30.45 (3) ~ (e4 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (4) all_252_18 = e1 % 190.00/30.45 | % 190.00/30.45 | COMBINE_EQS: (2), (4) imply: % 190.00/30.45 | (5) e4 = e1 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #247 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_17 = e1 & op(e3, e0) = e1 % 190.00/30.45 (2) all_252_17 = e2 % 190.00/30.45 (3) ~ (e2 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (4) all_252_17 = e1 % 190.00/30.45 | % 190.00/30.45 | COMBINE_EQS: (2), (4) imply: % 190.00/30.45 | (5) e2 = e1 % 190.00/30.45 | % 190.00/30.45 | SIMP: (5) implies: % 190.00/30.45 | (6) e2 = e1 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (6) imply: % 190.00/30.45 | (7) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (7) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #248 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) ~ (all_30_2 = e3) % 190.00/30.45 (3) op(e4, e0) = all_30_2 % 190.00/30.45 (4) all_252_17 = e2 % 190.00/30.45 (5) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.00/30.45 (6) ~ (e3 = e2) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (5) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (7) all_252_16 = e3 & op(e4, e0) = e3 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (7) implies: % 190.00/30.45 | | (8) op(e4, e0) = e3 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #539. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (9) all_252_17 = e3 & op(e3, e0) = e3 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #249. % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #249 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_17 = e3 & op(e3, e0) = e3 % 190.00/30.45 (2) all_252_17 = e2 % 190.00/30.45 (3) ~ (e3 = e2) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (4) all_252_17 = e3 % 190.00/30.45 | % 190.00/30.45 | COMBINE_EQS: (2), (4) imply: % 190.00/30.45 | (5) e3 = e2 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (3), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #250 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) op(e3, e0) = e4 % 190.00/30.45 (3) op(e3, e0) = e2 % 190.00/30.45 (4) ~ (e4 = e2) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | GROUND_INST: instantiating (1) with e2, e4, e0, e3, simplifying with (2), (3) % 190.00/30.45 | gives: % 190.00/30.45 | (5) e4 = e2 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (4), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #251 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_2 = e0 & op(e3, e4) = e0 % 190.00/30.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (3) op(e3, e4) = all_100_2 % 190.00/30.45 (4) ~ (all_100_2 = e0) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (5) op(e3, e4) = e0 % 190.00/30.45 | % 190.00/30.45 | GROUND_INST: instantiating (2) with all_100_2, e0, e4, e3, simplifying with % 190.00/30.45 | (3), (5) gives: % 190.00/30.45 | (6) all_100_2 = e0 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (4), (6) imply: % 190.00/30.45 | (7) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (7) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #252 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) op(all_30_2, e2) = e0 % 190.00/30.45 (3) all_250_4 = e4 | all_250_4 = e3 | all_250_4 = e2 | all_250_4 = e1 | % 190.00/30.45 all_250_4 = e0 % 190.00/30.45 (4) ~ (all_244_0 = all_30_2) % 190.00/30.45 (5) ~ (all_30_2 = e3) % 190.00/30.45 (6) op(e4, e4) = e0 % 190.00/30.45 (7) ~ (all_30_2 = e1) % 190.00/30.45 (8) all_250_4 = all_30_2 % 190.00/30.45 (9) op(e4, e4) = all_244_0 % 190.00/30.45 (10) ~ (all_30_2 = e2) % 190.00/30.45 (11) op(e4, e2) = all_6_2 % 190.00/30.45 (12) ~ (all_244_0 = all_6_2) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | GROUND_INST: instantiating (1) with all_244_0, e0, e4, e4, simplifying with % 190.00/30.45 | (6), (9) gives: % 190.00/30.45 | (13) all_244_0 = e0 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (4), (13) imply: % 190.00/30.45 | (14) ~ (all_30_2 = e0) % 190.00/30.45 | % 190.00/30.45 | SIMP: (14) implies: % 190.00/30.45 | (15) ~ (all_30_2 = e0) % 190.00/30.45 | % 190.00/30.45 | REDUCE: (12), (13) imply: % 190.00/30.45 | (16) ~ (all_6_2 = e0) % 190.00/30.45 | % 190.00/30.45 | SIMP: (16) implies: % 190.00/30.45 | (17) ~ (all_6_2 = e0) % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (3) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (18) all_250_4 = e4 % 190.00/30.45 | | % 190.00/30.45 | | COMBINE_EQS: (8), (18) imply: % 190.00/30.45 | | (19) all_30_2 = e4 % 190.00/30.45 | | % 190.00/30.45 | | REDUCE: (2), (19) imply: % 190.00/30.45 | | (20) op(e4, e2) = e0 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (11), (17), (20) are inconsistent by sub-proof #548. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (21) all_250_4 = e3 | all_250_4 = e2 | all_250_4 = e1 | all_250_4 = e0 % 190.00/30.45 | | % 190.00/30.45 | | BETA: splitting (21) gives: % 190.00/30.45 | | % 190.00/30.45 | | Case 1: % 190.00/30.45 | | | % 190.00/30.45 | | | (22) all_250_4 = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | COMBINE_EQS: (8), (22) imply: % 190.00/30.45 | | | (23) all_30_2 = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | REDUCE: (5), (23) imply: % 190.00/30.45 | | | (24) $false % 190.00/30.45 | | | % 190.00/30.45 | | | CLOSE: (24) is inconsistent. % 190.00/30.45 | | | % 190.00/30.45 | | Case 2: % 190.00/30.45 | | | % 190.00/30.45 | | | (25) all_250_4 = e2 | all_250_4 = e1 | all_250_4 = e0 % 190.00/30.45 | | | % 190.00/30.45 | | | BETA: splitting (25) gives: % 190.00/30.45 | | | % 190.00/30.45 | | | Case 1: % 190.00/30.45 | | | | % 190.00/30.45 | | | | (26) all_250_4 = e2 % 190.00/30.45 | | | | % 190.00/30.45 | | | | COMBINE_EQS: (8), (26) imply: % 190.00/30.45 | | | | (27) all_30_2 = e2 % 190.00/30.45 | | | | % 190.00/30.45 | | | | REDUCE: (10), (27) imply: % 190.00/30.45 | | | | (28) $false % 190.00/30.45 | | | | % 190.00/30.45 | | | | CLOSE: (28) is inconsistent. % 190.00/30.45 | | | | % 190.00/30.45 | | | Case 2: % 190.00/30.45 | | | | % 190.00/30.45 | | | | (29) all_250_4 = e1 | all_250_4 = e0 % 190.00/30.45 | | | | % 190.00/30.45 | | | | BETA: splitting (29) gives: % 190.00/30.45 | | | | % 190.00/30.45 | | | | Case 1: % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | (30) all_250_4 = e1 % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | COMBINE_EQS: (8), (30) imply: % 190.00/30.45 | | | | | (31) all_30_2 = e1 % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | REDUCE: (7), (31) imply: % 190.00/30.45 | | | | | (32) $false % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | CLOSE: (32) is inconsistent. % 190.00/30.45 | | | | | % 190.00/30.45 | | | | Case 2: % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | (33) all_250_4 = e0 % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | COMBINE_EQS: (8), (33) imply: % 190.00/30.45 | | | | | (34) all_30_2 = e0 % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | REDUCE: (15), (34) imply: % 190.00/30.45 | | | | | (35) $false % 190.00/30.45 | | | | | % 190.00/30.45 | | | | | CLOSE: (35) is inconsistent. % 190.00/30.45 | | | | | % 190.00/30.45 | | | | End of split % 190.00/30.45 | | | | % 190.00/30.45 | | | End of split % 190.00/30.45 | | | % 190.00/30.45 | | End of split % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #253 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) op(e3, e0) = all_230_1 & $i(all_230_1) & ( ~ (all_230_1 = e2) | ( ~ % 190.00/30.45 (all_230_0 = e4) & op(e0, e2) = all_230_0 & $i(all_230_0))) % 190.00/30.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (3) op(e0, e2) = e4 % 190.00/30.45 (4) op(e3, e0) = e2 % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (5) op(e3, e0) = all_230_1 % 190.00/30.45 | (6) ~ (all_230_1 = e2) | ( ~ (all_230_0 = e4) & op(e0, e2) = all_230_0 & % 190.00/30.45 | $i(all_230_0)) % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (6) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (7) ~ (all_230_1 = e2) % 190.00/30.45 | | % 190.00/30.45 | | GROUND_INST: instantiating (2) with e2, all_230_1, e0, e3, simplifying with % 190.00/30.45 | | (4), (5) gives: % 190.00/30.45 | | (8) all_230_1 = e2 % 190.00/30.45 | | % 190.00/30.45 | | REDUCE: (7), (8) imply: % 190.00/30.45 | | (9) $false % 190.00/30.45 | | % 190.00/30.45 | | CLOSE: (9) is inconsistent. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (10) ~ (all_230_0 = e4) & op(e0, e2) = all_230_0 & $i(all_230_0) % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (10) implies: % 190.00/30.45 | | (11) ~ (all_230_0 = e4) % 190.00/30.45 | | (12) op(e0, e2) = all_230_0 % 190.00/30.45 | | % 190.00/30.45 | | GROUND_INST: instantiating (2) with e4, all_230_0, e2, e0, simplifying with % 190.00/30.45 | | (3), (12) gives: % 190.00/30.45 | | (13) all_230_0 = e4 % 190.00/30.45 | | % 190.00/30.45 | | REDUCE: (11), (13) imply: % 190.00/30.45 | | (14) $false % 190.00/30.45 | | % 190.00/30.45 | | CLOSE: (14) is inconsistent. % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #254 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) op(e0, e2) = e4 % 190.00/30.45 (3) ~ (e4 = e0) % 190.00/30.45 (4) all_252_23 = e1 % 190.00/30.45 (5) (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.00/30.45 (6) ~ (e1 = e0) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (5) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (7) all_252_22 = e0 & op(e0, e2) = e0 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (7) implies: % 190.00/30.45 | | (8) op(e0, e2) = e0 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #520. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (9) all_252_23 = e0 & op(e0, e1) = e0 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #403. % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #255 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_20 = e0 & op(e0, e4) = e0 % 190.00/30.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (3) op(e0, e4) = e2 % 190.00/30.45 (4) ~ (e2 = e0) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | ALPHA: (1) implies: % 190.00/30.45 | (5) op(e0, e4) = e0 % 190.00/30.45 | % 190.00/30.45 | GROUND_INST: instantiating (2) with e0, e2, e4, e0, simplifying with (3), (5) % 190.00/30.45 | gives: % 190.00/30.45 | (6) e2 = e0 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (4), (6) imply: % 190.00/30.45 | (7) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (7) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #256 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) op(e0, e2) = e4 % 190.00/30.45 (3) op(e0, e2) = e1 % 190.00/30.45 (4) ~ (e4 = e1) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | GROUND_INST: instantiating (1) with e4, e1, e2, e0, simplifying with (2), (3) % 190.00/30.45 | gives: % 190.00/30.45 | (5) e4 = e1 % 190.00/30.45 | % 190.00/30.45 | REDUCE: (4), (5) imply: % 190.00/30.45 | (6) $false % 190.00/30.45 | % 190.00/30.45 | CLOSE: (6) is inconsistent. % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #257 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) all_252_24 = e0 % 190.00/30.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (3) op(e0, e2) = e4 % 190.00/30.45 (4) ~ (e4 = e3) % 190.00/30.45 (5) all_252_21 = e4 % 190.00/30.45 (6) ~ (all_20_2 = e3) % 190.00/30.45 (7) op(e0, e1) = all_20_2 % 190.00/30.45 (8) ~ (e3 = e0) % 190.00/30.45 (9) op(e0, e4) = all_12_2 % 190.00/30.45 (10) ~ (all_12_2 = e3) % 190.00/30.45 (11) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 190.00/30.45 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.00/30.45 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (11) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (12) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) % 190.00/30.45 | | = e3) % 190.00/30.45 | | % 190.00/30.45 | | BETA: splitting (12) gives: % 190.00/30.45 | | % 190.00/30.45 | | Case 1: % 190.00/30.45 | | | % 190.00/30.45 | | | (13) all_252_20 = e3 & op(e0, e4) = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | ALPHA: (13) implies: % 190.00/30.45 | | | (14) op(e0, e4) = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | REF_CLOSE: (2), (9), (10), (14) are inconsistent by sub-proof #512. % 190.00/30.45 | | | % 190.00/30.45 | | Case 2: % 190.00/30.45 | | | % 190.00/30.45 | | | (15) all_252_21 = e3 & op(e0, e3) = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | ALPHA: (15) implies: % 190.00/30.45 | | | (16) all_252_21 = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | COMBINE_EQS: (5), (16) imply: % 190.00/30.45 | | | (17) e4 = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | SIMP: (17) implies: % 190.00/30.45 | | | (18) e4 = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | REDUCE: (4), (18) imply: % 190.00/30.45 | | | (19) $false % 190.00/30.45 | | | % 190.00/30.45 | | | CLOSE: (19) is inconsistent. % 190.00/30.45 | | | % 190.00/30.45 | | End of split % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (20) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) % 190.00/30.45 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.00/30.45 | | % 190.00/30.45 | | BETA: splitting (20) gives: % 190.00/30.45 | | % 190.00/30.45 | | Case 1: % 190.00/30.45 | | | % 190.00/30.45 | | | (21) all_252_22 = e3 & op(e0, e2) = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | ALPHA: (21) implies: % 190.00/30.45 | | | (22) op(e0, e2) = e3 % 190.00/30.45 | | | % 190.00/30.45 | | | REF_CLOSE: (2), (3), (4), (22) are inconsistent by sub-proof #328. % 190.00/30.45 | | | % 190.00/30.45 | | Case 2: % 190.00/30.45 | | | % 190.00/30.45 | | | (23) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, % 190.00/30.45 | | | e0) = e3) % 190.00/30.45 | | | % 190.00/30.45 | | | BETA: splitting (23) gives: % 190.00/30.45 | | | % 190.00/30.45 | | | Case 1: % 190.00/30.45 | | | | % 190.00/30.45 | | | | (24) all_252_23 = e3 & op(e0, e1) = e3 % 190.00/30.45 | | | | % 190.00/30.45 | | | | ALPHA: (24) implies: % 190.00/30.45 | | | | (25) op(e0, e1) = e3 % 190.00/30.45 | | | | % 190.00/30.45 | | | | REF_CLOSE: (2), (6), (7), (25) are inconsistent by sub-proof #508. % 190.00/30.45 | | | | % 190.00/30.45 | | | Case 2: % 190.00/30.45 | | | | % 190.00/30.45 | | | | (26) all_252_24 = e3 & op(e0, e0) = e3 % 190.00/30.45 | | | | % 190.00/30.45 | | | | ALPHA: (26) implies: % 190.00/30.45 | | | | (27) all_252_24 = e3 % 190.00/30.45 | | | | % 190.00/30.45 | | | | COMBINE_EQS: (1), (27) imply: % 190.00/30.45 | | | | (28) e3 = e0 % 190.00/30.45 | | | | % 190.00/30.45 | | | | REDUCE: (8), (28) imply: % 190.00/30.45 | | | | (29) $false % 190.00/30.45 | | | | % 190.00/30.45 | | | | CLOSE: (29) is inconsistent. % 190.00/30.45 | | | | % 190.00/30.45 | | | End of split % 190.00/30.45 | | | % 190.00/30.45 | | End of split % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #258 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) ~ (e4 = e3) % 190.00/30.45 (3) all_252_21 = e4 % 190.00/30.45 (4) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 190.00/30.45 (5) op(e0, e4) = all_12_2 % 190.00/30.45 (6) ~ (all_12_2 = e3) % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (4) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (7) all_252_20 = e3 & op(e0, e4) = e3 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (7) implies: % 190.00/30.45 | | (8) op(e0, e4) = e3 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #512. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (9) all_252_21 = e3 & op(e0, e3) = e3 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (9) implies: % 190.00/30.45 | | (10) all_252_21 = e3 % 190.00/30.45 | | % 190.00/30.45 | | COMBINE_EQS: (3), (10) imply: % 190.00/30.45 | | (11) e4 = e3 % 190.00/30.45 | | % 190.00/30.45 | | REDUCE: (2), (11) imply: % 190.00/30.45 | | (12) $false % 190.00/30.45 | | % 190.00/30.45 | | CLOSE: (12) is inconsistent. % 190.00/30.45 | | % 190.00/30.45 | End of split % 190.00/30.45 | % 190.00/30.45 End of proof % 190.00/30.45 % 190.00/30.45 Sub-proof #259 shows that the following formulas are inconsistent: % 190.00/30.45 ---------------------------------------------------------------- % 190.00/30.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.45 (2) op(e0, e2) = all_28_2 % 190.00/30.45 (3) ~ (all_244_24 = e2) % 190.00/30.45 (4) op(e0, e0) = all_244_24 % 190.00/30.45 (5) ~ (all_28_2 = e0) % 190.00/30.45 (6) op(e2, all_40_2) = e0 % 190.00/30.45 (7) op(e0, e1) = e3 % 190.00/30.45 (8) ~ (e3 = e2) % 190.00/30.45 (9) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 190.00/30.45 | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.45 (10) op(all_28_2, all_40_2) = e2 % 190.00/30.45 % 190.00/30.45 Begin of proof % 190.00/30.45 | % 190.00/30.45 | BETA: splitting (9) gives: % 190.00/30.45 | % 190.00/30.45 | Case 1: % 190.00/30.45 | | % 190.00/30.45 | | (11) all_252_22 = e2 & op(e0, e2) = e2 % 190.00/30.45 | | % 190.00/30.45 | | ALPHA: (11) implies: % 190.00/30.45 | | (12) op(e0, e2) = e2 % 190.00/30.45 | | % 190.00/30.45 | | REF_CLOSE: (1), (2), (5), (6), (10), (12) are inconsistent by sub-proof % 190.00/30.45 | | #288. % 190.00/30.45 | | % 190.00/30.45 | Case 2: % 190.00/30.45 | | % 190.00/30.45 | | (13) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) % 190.00/30.45 | | = e2) % 190.00/30.45 | | % 190.00/30.45 | | BETA: splitting (13) gives: % 190.00/30.45 | | % 190.00/30.45 | | Case 1: % 190.00/30.45 | | | % 190.00/30.46 | | | (14) all_252_23 = e2 & op(e0, e1) = e2 % 190.00/30.46 | | | % 190.00/30.46 | | | ALPHA: (14) implies: % 190.00/30.46 | | | (15) op(e0, e1) = e2 % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (1), (7), (8), (15) are inconsistent by sub-proof #446. % 190.00/30.46 | | | % 190.00/30.46 | | Case 2: % 190.00/30.46 | | | % 190.00/30.46 | | | (16) all_252_24 = e2 & op(e0, e0) = e2 % 190.00/30.46 | | | % 190.00/30.46 | | | ALPHA: (16) implies: % 190.00/30.46 | | | (17) op(e0, e0) = e2 % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (1), (3), (4), (17) are inconsistent by sub-proof #477. % 190.00/30.46 | | | % 190.00/30.46 | | End of split % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #260 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_23 = e2 % 190.00/30.46 (2) all_252_23 = e0 % 190.00/30.46 (3) ~ (e2 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (1), (2) imply: % 190.00/30.46 | (4) e2 = e0 % 190.00/30.46 | % 190.00/30.46 | SIMP: (4) implies: % 190.00/30.46 | (5) e2 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #261 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_11 = e4 & op(e2, e1) = e4 % 190.00/30.46 (2) all_252_11 = e2 % 190.00/30.46 (3) ~ (e4 = e2) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_11 = e4 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e4 = e2 % 190.00/30.46 | % 190.00/30.46 | SIMP: (5) implies: % 190.00/30.46 | (6) e4 = e2 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #262 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_11 = e1 & op(e2, e1) = e1 % 190.00/30.46 (2) all_252_11 = e0 % 190.00/30.46 (3) ~ (e1 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_11 = e1 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e1 = e0 % 190.00/30.46 | % 190.00/30.46 | SIMP: (5) implies: % 190.00/30.46 | (6) e1 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #263 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (2) all_252_15 = e4 % 190.00/30.46 (3) all_252_10 = e1 % 190.00/30.46 (4) op(e4, e1) = e0 % 190.00/30.46 (5) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 190.00/30.46 | (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = % 190.00/30.46 e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 190.00/30.46 (6) ~ (e4 = e3) % 190.00/30.46 (7) ~ (all_20_2 = e3) % 190.00/30.46 (8) all_252_11 = e0 % 190.00/30.46 (9) op(e0, e1) = all_20_2 % 190.00/30.46 (10) ~ (e3 = e0) % 190.00/30.46 (11) ~ (e3 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | BETA: splitting (5) gives: % 190.00/30.46 | % 190.00/30.46 | Case 1: % 190.00/30.46 | | % 190.00/30.46 | | (12) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = % 190.00/30.46 | | e3) % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (1), (3), (4), (10), (11), (12) are inconsistent by sub-proof % 190.00/30.46 | | #266. % 190.00/30.46 | | % 190.00/30.46 | Case 2: % 190.00/30.46 | | % 190.00/30.46 | | (13) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) % 190.00/30.46 | | = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 190.00/30.46 | | % 190.00/30.46 | | BETA: splitting (13) gives: % 190.00/30.46 | | % 190.00/30.46 | | Case 1: % 190.00/30.46 | | | % 190.00/30.46 | | | (14) all_252_11 = e3 & op(e2, e1) = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (8), (10), (14) are inconsistent by sub-proof #273. % 190.00/30.46 | | | % 190.00/30.46 | | Case 2: % 190.00/30.46 | | | % 190.00/30.46 | | | (15) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, % 190.00/30.46 | | | e1) = e3) % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (1), (2), (6), (7), (9), (15) are inconsistent by sub-proof % 190.00/30.46 | | | #264. % 190.00/30.46 | | | % 190.00/30.46 | | End of split % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #264 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (2) all_252_15 = e4 % 190.00/30.46 (3) ~ (e4 = e3) % 190.00/30.46 (4) ~ (all_20_2 = e3) % 190.00/30.46 (5) op(e0, e1) = all_20_2 % 190.00/30.46 (6) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | BETA: splitting (6) gives: % 190.00/30.46 | % 190.00/30.46 | Case 1: % 190.00/30.46 | | % 190.00/30.46 | | (7) all_252_15 = e3 & op(e1, e1) = e3 % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #265. % 190.00/30.46 | | % 190.00/30.46 | Case 2: % 190.00/30.46 | | % 190.00/30.46 | | (8) all_252_23 = e3 & op(e0, e1) = e3 % 190.00/30.46 | | % 190.00/30.46 | | ALPHA: (8) implies: % 190.00/30.46 | | (9) op(e0, e1) = e3 % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #508. % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #265 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_15 = e3 & op(e1, e1) = e3 % 190.00/30.46 (2) all_252_15 = e4 % 190.00/30.46 (3) ~ (e4 = e3) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_15 = e3 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e4 = e3 % 190.00/30.46 | % 190.00/30.46 | SIMP: (5) implies: % 190.00/30.46 | (6) e4 = e3 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #266 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (2) all_252_10 = e1 % 190.00/30.46 (3) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_10 = e3 & op(e3, e1) = e3) % 190.00/30.46 (4) op(e4, e1) = e0 % 190.00/30.46 (5) ~ (e3 = e0) % 190.00/30.46 (6) ~ (e3 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | BETA: splitting (3) gives: % 190.00/30.46 | % 190.00/30.46 | Case 1: % 190.00/30.46 | | % 190.00/30.46 | | (7) all_252_9 = e3 & op(e4, e1) = e3 % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #275. % 190.00/30.46 | | % 190.00/30.46 | Case 2: % 190.00/30.46 | | % 190.00/30.46 | | (8) all_252_10 = e3 & op(e3, e1) = e3 % 190.00/30.46 | | % 190.00/30.46 | | ALPHA: (8) implies: % 190.00/30.46 | | (9) all_252_10 = e3 % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #267. % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #267 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_10 = e3 % 190.00/30.46 (2) all_252_10 = e1 % 190.00/30.46 (3) ~ (e3 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (1), (2) imply: % 190.00/30.46 | (4) e3 = e1 % 190.00/30.46 | % 190.00/30.46 | SIMP: (4) implies: % 190.00/30.46 | (5) e3 = e1 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #268 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_11 = e4 & op(e2, e1) = e4 % 190.00/30.46 (2) all_252_11 = e0 % 190.00/30.46 (3) ~ (e4 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_11 = e4 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e4 = e0 % 190.00/30.46 | % 190.00/30.46 | SIMP: (5) implies: % 190.00/30.46 | (6) e4 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #269 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (2) op(e0, e2) = all_28_2 % 190.00/30.46 (3) ~ (all_244_24 = e2) % 190.00/30.46 (4) ~ (e2 = e1) % 190.00/30.46 (5) ~ (all_12_2 = e2) % 190.00/30.46 (6) op(e0, e0) = all_244_24 % 190.00/30.46 (7) ~ (all_8_1 = e2) % 190.00/30.46 (8) all_252_23 = e1 & op(e0, e1) = e1 % 190.00/30.46 (9) ~ (all_28_2 = e0) % 190.00/30.46 (10) op(e2, all_40_2) = e0 % 190.00/30.46 (11) op(e0, e3) = all_8_1 % 190.00/30.46 (12) op(all_28_2, all_40_2) = e2 % 190.00/30.46 (13) op(e0, e4) = all_12_2 % 190.00/30.46 (14) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.00/30.46 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.00/30.46 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (8) implies: % 190.00/30.46 | (15) all_252_23 = e1 % 190.00/30.46 | % 190.00/30.46 | BETA: splitting (14) gives: % 190.00/30.46 | % 190.00/30.46 | Case 1: % 190.00/30.46 | | % 190.00/30.46 | | (16) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) % 190.00/30.46 | | = e2) % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (1), (5), (7), (11), (13), (16) are inconsistent by sub-proof % 190.00/30.46 | | #285. % 190.00/30.46 | | % 190.00/30.46 | Case 2: % 190.00/30.46 | | % 190.00/30.46 | | (17) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) % 190.00/30.46 | | = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.46 | | % 190.00/30.46 | | BETA: splitting (17) gives: % 190.00/30.46 | | % 190.00/30.46 | | Case 1: % 190.00/30.46 | | | % 190.00/30.46 | | | (18) all_252_22 = e2 & op(e0, e2) = e2 % 190.00/30.46 | | | % 190.00/30.46 | | | ALPHA: (18) implies: % 190.00/30.46 | | | (19) op(e0, e2) = e2 % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (1), (2), (9), (10), (12), (19) are inconsistent by sub-proof % 190.00/30.46 | | | #288. % 190.00/30.46 | | | % 190.00/30.46 | | Case 2: % 190.00/30.46 | | | % 190.00/30.46 | | | (20) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, % 190.00/30.46 | | | e0) = e2) % 190.00/30.46 | | | % 190.00/30.46 | | | BETA: splitting (20) gives: % 190.00/30.46 | | | % 190.00/30.46 | | | Case 1: % 190.00/30.46 | | | | % 190.00/30.46 | | | | (21) all_252_23 = e2 & op(e0, e1) = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | ALPHA: (21) implies: % 190.00/30.46 | | | | (22) all_252_23 = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | REF_CLOSE: (4), (15), (22) are inconsistent by sub-proof #270. % 190.00/30.46 | | | | % 190.00/30.46 | | | Case 2: % 190.00/30.46 | | | | % 190.00/30.46 | | | | (23) all_252_24 = e2 & op(e0, e0) = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | ALPHA: (23) implies: % 190.00/30.46 | | | | (24) op(e0, e0) = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | REF_CLOSE: (1), (3), (6), (24) are inconsistent by sub-proof #477. % 190.00/30.46 | | | | % 190.00/30.46 | | | End of split % 190.00/30.46 | | | % 190.00/30.46 | | End of split % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #270 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_23 = e2 % 190.00/30.46 (2) all_252_23 = e1 % 190.00/30.46 (3) ~ (e2 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (1), (2) imply: % 190.00/30.46 | (4) e2 = e1 % 190.00/30.46 | % 190.00/30.46 | SIMP: (4) implies: % 190.00/30.46 | (5) e2 = e1 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #271 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (2) all_252_15 = e1 % 190.00/30.46 (3) ~ (all_20_2 = e3) % 190.00/30.46 (4) all_252_11 = e0 % 190.00/30.46 (5) op(e0, e1) = all_20_2 % 190.00/30.46 (6) (all_252_11 = e3 & op(e2, e1) = e3) | (all_252_15 = e3 & op(e1, e1) = e3) % 190.00/30.46 | (all_252_23 = e3 & op(e0, e1) = e3) % 190.00/30.46 (7) ~ (e3 = e0) % 190.00/30.46 (8) ~ (e3 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | BETA: splitting (6) gives: % 190.00/30.46 | % 190.00/30.46 | Case 1: % 190.00/30.46 | | % 190.00/30.46 | | (9) all_252_11 = e3 & op(e2, e1) = e3 % 190.00/30.46 | | % 190.00/30.46 | | REF_CLOSE: (4), (7), (9) are inconsistent by sub-proof #273. % 190.00/30.46 | | % 190.00/30.46 | Case 2: % 190.00/30.46 | | % 190.00/30.46 | | (10) (all_252_15 = e3 & op(e1, e1) = e3) | (all_252_23 = e3 & op(e0, e1) % 190.00/30.46 | | = e3) % 190.00/30.46 | | % 190.00/30.46 | | BETA: splitting (10) gives: % 190.00/30.46 | | % 190.00/30.46 | | Case 1: % 190.00/30.46 | | | % 190.00/30.46 | | | (11) all_252_15 = e3 & op(e1, e1) = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (2), (8), (11) are inconsistent by sub-proof #272. % 190.00/30.46 | | | % 190.00/30.46 | | Case 2: % 190.00/30.46 | | | % 190.00/30.46 | | | (12) all_252_23 = e3 & op(e0, e1) = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | ALPHA: (12) implies: % 190.00/30.46 | | | (13) op(e0, e1) = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | REF_CLOSE: (1), (3), (5), (13) are inconsistent by sub-proof #508. % 190.00/30.46 | | | % 190.00/30.46 | | End of split % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #272 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_15 = e3 & op(e1, e1) = e3 % 190.00/30.46 (2) all_252_15 = e1 % 190.00/30.46 (3) ~ (e3 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_15 = e3 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e3 = e1 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #273 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_11 = e3 & op(e2, e1) = e3 % 190.00/30.46 (2) all_252_11 = e0 % 190.00/30.46 (3) ~ (e3 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_11 = e3 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e3 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #274 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_10 = e3 & op(e3, e1) = e3 % 190.00/30.46 (2) all_252_10 = e4 % 190.00/30.46 (3) ~ (e4 = e3) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_10 = e3 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e4 = e3 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #275 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_9 = e3 & op(e4, e1) = e3 % 190.00/30.46 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (3) op(e4, e1) = e0 % 190.00/30.46 (4) ~ (e3 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (5) op(e4, e1) = e3 % 190.00/30.46 | % 190.00/30.46 | GROUND_INST: instantiating (2) with e0, e3, e1, e4, simplifying with (3), (5) % 190.00/30.46 | gives: % 190.00/30.46 | (6) e3 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (4), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #276 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_11 = e1 & op(e2, e1) = e1 % 190.00/30.46 (2) all_252_11 = e0 % 190.00/30.46 (3) ~ (e1 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_11 = e1 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e1 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #277 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_10 = e1 & op(e3, e1) = e1 % 190.00/30.46 (2) all_252_10 = e4 % 190.00/30.46 (3) ~ (e4 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_10 = e1 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e4 = e1 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (5) imply: % 190.00/30.46 | (6) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (6) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #278 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_9 = e1 & op(e4, e1) = e1 % 190.00/30.46 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (3) op(e4, e1) = e0 % 190.00/30.46 (4) ~ (e1 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (5) op(e4, e1) = e1 % 190.00/30.46 | % 190.00/30.46 | GROUND_INST: instantiating (2) with e0, e1, e1, e4, simplifying with (3), (5) % 190.00/30.46 | gives: % 190.00/30.46 | (6) e1 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (4), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #279 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_11 = e2 & op(e2, e1) = e2 % 190.00/30.46 (2) all_252_11 = e0 % 190.00/30.46 (3) ~ (e2 = e0) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (4) all_252_11 = e2 % 190.00/30.46 | % 190.00/30.46 | COMBINE_EQS: (2), (4) imply: % 190.00/30.46 | (5) e2 = e0 % 190.00/30.46 | % 190.00/30.46 | SIMP: (5) implies: % 190.00/30.46 | (6) e2 = e0 % 190.00/30.46 | % 190.00/30.46 | REDUCE: (3), (6) imply: % 190.00/30.46 | (7) $false % 190.00/30.46 | % 190.00/30.46 | CLOSE: (7) is inconsistent. % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #280 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (2) all_250_19 = all_34_2 % 190.00/30.46 (3) op(e0, all_20_2) = e1 % 190.00/30.46 (4) all_30_2 = e1 % 190.00/30.46 (5) all_250_19 = e4 | all_250_19 = e3 | all_250_19 = e2 | all_250_19 = e1 | % 190.00/30.46 all_250_19 = e0 % 190.00/30.46 (6) ~ (all_34_2 = all_30_2) % 190.00/30.46 (7) op(all_34_2, all_20_2) = e0 % 190.00/30.46 (8) ~ (all_34_2 = e3) % 190.00/30.46 (9) ~ (all_34_2 = e4) % 190.00/30.46 (10) ~ (all_34_2 = e2) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | REDUCE: (4), (6) imply: % 190.00/30.46 | (11) ~ (all_34_2 = e1) % 190.00/30.46 | % 190.00/30.46 | BETA: splitting (5) gives: % 190.00/30.46 | % 190.00/30.46 | Case 1: % 190.00/30.46 | | % 190.00/30.46 | | (12) all_250_19 = e4 % 190.00/30.46 | | % 190.00/30.46 | | COMBINE_EQS: (2), (12) imply: % 190.00/30.46 | | (13) all_34_2 = e4 % 190.00/30.46 | | % 190.00/30.46 | | SIMP: (13) implies: % 190.00/30.46 | | (14) all_34_2 = e4 % 190.00/30.46 | | % 190.00/30.46 | | REDUCE: (9), (14) imply: % 190.00/30.46 | | (15) $false % 190.00/30.46 | | % 190.00/30.46 | | CLOSE: (15) is inconsistent. % 190.00/30.46 | | % 190.00/30.46 | Case 2: % 190.00/30.46 | | % 190.00/30.46 | | (16) all_250_19 = e3 | all_250_19 = e2 | all_250_19 = e1 | all_250_19 = % 190.00/30.46 | | e0 % 190.00/30.46 | | % 190.00/30.46 | | BETA: splitting (16) gives: % 190.00/30.46 | | % 190.00/30.46 | | Case 1: % 190.00/30.46 | | | % 190.00/30.46 | | | (17) all_250_19 = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | COMBINE_EQS: (2), (17) imply: % 190.00/30.46 | | | (18) all_34_2 = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | SIMP: (18) implies: % 190.00/30.46 | | | (19) all_34_2 = e3 % 190.00/30.46 | | | % 190.00/30.46 | | | REDUCE: (8), (19) imply: % 190.00/30.46 | | | (20) $false % 190.00/30.46 | | | % 190.00/30.46 | | | CLOSE: (20) is inconsistent. % 190.00/30.46 | | | % 190.00/30.46 | | Case 2: % 190.00/30.46 | | | % 190.00/30.46 | | | (21) all_250_19 = e2 | all_250_19 = e1 | all_250_19 = e0 % 190.00/30.46 | | | % 190.00/30.46 | | | BETA: splitting (21) gives: % 190.00/30.46 | | | % 190.00/30.46 | | | Case 1: % 190.00/30.46 | | | | % 190.00/30.46 | | | | (22) all_250_19 = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | COMBINE_EQS: (2), (22) imply: % 190.00/30.46 | | | | (23) all_34_2 = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | SIMP: (23) implies: % 190.00/30.46 | | | | (24) all_34_2 = e2 % 190.00/30.46 | | | | % 190.00/30.46 | | | | REDUCE: (10), (24) imply: % 190.00/30.46 | | | | (25) $false % 190.00/30.46 | | | | % 190.00/30.46 | | | | CLOSE: (25) is inconsistent. % 190.00/30.46 | | | | % 190.00/30.46 | | | Case 2: % 190.00/30.46 | | | | % 190.00/30.46 | | | | (26) all_250_19 = e1 | all_250_19 = e0 % 190.00/30.46 | | | | % 190.00/30.46 | | | | BETA: splitting (26) gives: % 190.00/30.46 | | | | % 190.00/30.46 | | | | Case 1: % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | (27) all_250_19 = e1 % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | COMBINE_EQS: (2), (27) imply: % 190.00/30.46 | | | | | (28) all_34_2 = e1 % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | SIMP: (28) implies: % 190.00/30.46 | | | | | (29) all_34_2 = e1 % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | REDUCE: (11), (29) imply: % 190.00/30.46 | | | | | (30) $false % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | CLOSE: (30) is inconsistent. % 190.00/30.46 | | | | | % 190.00/30.46 | | | | Case 2: % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | (31) all_250_19 = e0 % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | COMBINE_EQS: (2), (31) imply: % 190.00/30.46 | | | | | (32) all_34_2 = e0 % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | SIMP: (32) implies: % 190.00/30.46 | | | | | (33) all_34_2 = e0 % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | REDUCE: (11), (33) imply: % 190.00/30.46 | | | | | (34) ~ (e1 = e0) % 190.00/30.46 | | | | | % 190.00/30.46 | | | | | REF_CLOSE: (1), (3), (7), (33), (34) are inconsistent by sub-proof % 190.00/30.46 | | | | | #345. % 190.00/30.46 | | | | | % 190.00/30.46 | | | | End of split % 190.00/30.46 | | | | % 190.00/30.46 | | | End of split % 190.00/30.46 | | | % 190.00/30.46 | | End of split % 190.00/30.46 | | % 190.00/30.46 | End of split % 190.00/30.46 | % 190.00/30.46 End of proof % 190.00/30.46 % 190.00/30.46 Sub-proof #281 shows that the following formulas are inconsistent: % 190.00/30.46 ---------------------------------------------------------------- % 190.00/30.46 (1) all_252_21 = e1 & op(e0, e3) = e1 % 190.00/30.46 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.46 (3) op(e0, e3) = all_8_1 % 190.00/30.46 (4) ~ (all_8_1 = e1) % 190.00/30.46 % 190.00/30.46 Begin of proof % 190.00/30.46 | % 190.00/30.46 | ALPHA: (1) implies: % 190.00/30.46 | (5) op(e0, e3) = e1 % 190.00/30.46 | % 190.00/30.46 | GROUND_INST: instantiating (2) with all_8_1, e1, e3, e0, simplifying with (3), % 190.00/30.46 | (5) gives: % 190.00/30.47 | (6) all_8_1 = e1 % 190.00/30.47 | % 190.00/30.47 | REDUCE: (4), (6) imply: % 190.00/30.47 | (7) $false % 190.00/30.47 | % 190.00/30.47 | CLOSE: (7) is inconsistent. % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #282 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) ~ (all_16_2 = e2) % 190.00/30.47 (3) op(e1, e3) = all_62_2 % 190.00/30.47 (4) op(e2, all_38_2) = e1 % 190.00/30.47 (5) op(e1, e1) = all_244_15 % 190.00/30.47 (6) ~ (all_4_2 = e1) % 190.00/30.47 (7) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.00/30.47 | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) = % 190.00/30.47 e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.00/30.47 (8) op(all_4_2, all_38_2) = e2 % 190.00/30.47 (9) ~ (all_244_15 = e2) % 190.00/30.47 (10) op(e1, e4) = all_16_2 % 190.00/30.47 (11) ~ (all_62_2 = e2) % 190.00/30.47 (12) op(e1, e0) = all_34_2 % 190.00/30.47 (13) ~ (all_34_2 = e2) % 190.00/30.47 (14) op(e1, e2) = all_4_2 % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | BETA: splitting (7) gives: % 190.00/30.47 | % 190.00/30.47 | Case 1: % 190.00/30.47 | | % 190.00/30.47 | | (15) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 190.00/30.47 | | = e2) % 190.00/30.47 | | % 190.00/30.47 | | BETA: splitting (15) gives: % 190.00/30.47 | | % 190.00/30.47 | | Case 1: % 190.00/30.47 | | | % 190.00/30.47 | | | (16) all_252_12 = e2 & op(e1, e4) = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | ALPHA: (16) implies: % 190.00/30.47 | | | (17) op(e1, e4) = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (1), (2), (10), (17) are inconsistent by sub-proof #573. % 190.00/30.47 | | | % 190.00/30.47 | | Case 2: % 190.00/30.47 | | | % 190.00/30.47 | | | (18) all_252_13 = e2 & op(e1, e3) = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | ALPHA: (18) implies: % 190.00/30.47 | | | (19) op(e1, e3) = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (1), (3), (11), (19) are inconsistent by sub-proof #572. % 190.00/30.47 | | | % 190.00/30.47 | | End of split % 190.00/30.47 | | % 190.00/30.47 | Case 2: % 190.00/30.47 | | % 190.00/30.47 | | (20) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) % 190.00/30.47 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.00/30.47 | | % 190.00/30.47 | | BETA: splitting (20) gives: % 190.00/30.47 | | % 190.00/30.47 | | Case 1: % 190.00/30.47 | | | % 190.00/30.47 | | | (21) all_252_14 = e2 & op(e1, e2) = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | ALPHA: (21) implies: % 190.00/30.47 | | | (22) op(e1, e2) = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e1, simplifying with % 190.00/30.47 | | | (14), (22) gives: % 190.00/30.47 | | | (23) all_4_2 = e2 % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (1), (4), (6), (8), (23) are inconsistent by sub-proof #576. % 190.00/30.47 | | | % 190.00/30.47 | | Case 2: % 190.00/30.47 | | | % 190.00/30.47 | | | (24) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, % 190.00/30.47 | | | e0) = e2) % 190.00/30.47 | | | % 190.00/30.47 | | | BETA: splitting (24) gives: % 190.00/30.47 | | | % 190.00/30.47 | | | Case 1: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (25) all_252_15 = e2 & op(e1, e1) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | ALPHA: (25) implies: % 190.00/30.47 | | | | (26) op(e1, e1) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | GROUND_INST: instantiating (1) with all_244_15, e2, e1, e1, simplifying % 190.00/30.47 | | | | with (5), (26) gives: % 190.00/30.47 | | | | (27) all_244_15 = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | REDUCE: (9), (27) imply: % 190.00/30.47 | | | | (28) $false % 190.00/30.47 | | | | % 190.00/30.47 | | | | CLOSE: (28) is inconsistent. % 190.00/30.47 | | | | % 190.00/30.47 | | | Case 2: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (29) all_252_19 = e2 & op(e1, e0) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | REF_CLOSE: (1), (12), (13), (29) are inconsistent by sub-proof #438. % 190.00/30.47 | | | | % 190.00/30.47 | | | End of split % 190.00/30.47 | | | % 190.00/30.47 | | End of split % 190.00/30.47 | | % 190.00/30.47 | End of split % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #283 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) ~ (all_36_2 = e0) % 190.00/30.47 (3) op(e0, e2) = all_28_2 % 190.00/30.47 (4) ~ (all_244_24 = e2) % 190.00/30.47 (5) op(e3, e1) = all_36_2 % 190.00/30.47 (6) op(e2, all_38_2) = e1 % 190.00/30.47 (7) ~ (all_26_2 = e0) % 190.00/30.47 (8) op(e1, e1) = all_244_15 % 190.00/30.47 (9) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.00/30.47 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.00/30.47 $i(all_38_0)))) % 190.00/30.47 (10) all_58_2 = all_20_2 % 190.00/30.47 (11) ~ (all_12_2 = e2) % 190.00/30.47 (12) op(e0, e0) = all_244_24 % 190.00/30.47 (13) op(e0, e1) = all_20_2 % 190.00/30.47 (14) ~ (all_8_1 = e2) % 190.00/30.47 (15) op(e0, all_20_2) = e1 % 190.00/30.47 (16) op(all_40_2, all_28_2) = e0 % 190.00/30.47 (17) ~ (all_244_15 = all_38_2) % 190.00/30.47 (18) op(e4, e1) = all_26_2 % 190.00/30.47 (19) ~ (all_28_2 = e0) % 190.00/30.47 (20) op(all_244_15, all_244_15) = e1 % 190.00/30.47 (21) op(e2, all_40_2) = e0 % 190.00/30.47 (22) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.00/30.47 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.00/30.47 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.00/30.47 (23) op(e0, e3) = all_8_1 % 190.00/30.47 (24) ~ (all_244_24 = all_28_2) % 190.00/30.47 (25) op(e2, e0) = all_40_2 % 190.00/30.47 (26) op(all_28_2, all_40_2) = e2 % 190.00/30.47 (27) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.00/30.47 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.00/30.47 $i(all_188_0)))) % 190.00/30.47 (28) op(e0, e4) = all_12_2 % 190.00/30.47 (29) ~ (e2 = e0) % 190.00/30.47 (30) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.00/30.47 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.00/30.47 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.47 (31) ~ (all_28_2 = e1) | (op(e1, e0) = all_28_1 & $i(all_28_1) & ( ~ % 190.00/30.47 (all_28_1 = e3) | ( ~ (all_28_0 = e4) & op(e0, e3) = all_28_0 & % 190.00/30.47 $i(all_28_0)))) % 190.00/30.47 (32) all_188_2 = all_38_2 % 190.00/30.47 (33) op(e2, e1) = all_38_2 % 190.00/30.47 (34) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 190.00/30.47 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 190.00/30.47 $i(all_58_0)))) % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | BETA: splitting (31) gives: % 190.00/30.47 | % 190.00/30.47 | Case 1: % 190.00/30.47 | | % 190.00/30.47 | | (35) ~ (all_28_2 = e1) % 190.00/30.47 | | % 190.00/30.47 | | REF_CLOSE: (1), (3), (4), (10), (11), (12), (13), (14), (15), (19), (21), % 190.00/30.47 | | (23), (26), (28), (30), (34), (35) are inconsistent by sub-proof % 190.00/30.47 | | #286. % 190.00/30.47 | | % 190.00/30.47 | Case 2: % 190.00/30.47 | | % 190.00/30.47 | | (36) all_28_2 = e1 % 190.00/30.47 | | % 190.00/30.47 | | REDUCE: (24), (36) imply: % 190.00/30.47 | | (37) ~ (all_244_24 = e1) % 190.00/30.47 | | % 190.00/30.47 | | REDUCE: (16), (36) imply: % 190.00/30.47 | | (38) op(all_40_2, e1) = e0 % 190.00/30.47 | | % 190.00/30.47 | | BETA: splitting (30) gives: % 190.00/30.47 | | % 190.00/30.47 | | Case 1: % 190.00/30.47 | | | % 190.00/30.47 | | | (39) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, % 190.00/30.47 | | | e3) = e2) % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (1), (11), (14), (23), (28), (39) are inconsistent by sub-proof % 190.00/30.47 | | | #285. % 190.00/30.47 | | | % 190.00/30.47 | | Case 2: % 190.00/30.47 | | | % 190.00/30.47 | | | (40) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.00/30.47 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.47 | | | % 190.00/30.47 | | | BETA: splitting (40) gives: % 190.00/30.47 | | | % 190.00/30.47 | | | Case 1: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (41) all_252_22 = e2 & op(e0, e2) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | ALPHA: (41) implies: % 190.00/30.47 | | | | (42) op(e0, e2) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | REF_CLOSE: (1), (3), (19), (21), (26), (42) are inconsistent by % 190.00/30.47 | | | | sub-proof #288. % 190.00/30.47 | | | | % 190.00/30.47 | | | Case 2: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (43) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, % 190.00/30.47 | | | | e0) = e2) % 190.00/30.47 | | | | % 190.00/30.47 | | | | BETA: splitting (43) gives: % 190.00/30.47 | | | | % 190.00/30.47 | | | | Case 1: % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | (44) all_252_23 = e2 & op(e0, e1) = e2 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | ALPHA: (44) implies: % 190.00/30.47 | | | | | (45) all_252_23 = e2 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (12), (17), (18), (20), % 190.00/30.47 | | | | | (22), (25), (27), (29), (32), (33), (37), (38), (45) are % 190.00/30.47 | | | | | inconsistent by sub-proof #284. % 190.00/30.47 | | | | | % 190.00/30.47 | | | | Case 2: % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | (46) all_252_24 = e2 & op(e0, e0) = e2 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | ALPHA: (46) implies: % 190.00/30.47 | | | | | (47) op(e0, e0) = e2 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | REF_CLOSE: (1), (4), (12), (47) are inconsistent by sub-proof #477. % 190.00/30.47 | | | | | % 190.00/30.47 | | | | End of split % 190.00/30.47 | | | | % 190.00/30.47 | | | End of split % 190.00/30.47 | | | % 190.00/30.47 | | End of split % 190.00/30.47 | | % 190.00/30.47 | End of split % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #284 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) ~ (all_36_2 = e0) % 190.00/30.47 (3) op(e3, e1) = all_36_2 % 190.00/30.47 (4) op(e2, all_38_2) = e1 % 190.00/30.47 (5) ~ (all_26_2 = e0) % 190.00/30.47 (6) op(e1, e1) = all_244_15 % 190.00/30.47 (7) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.00/30.47 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.00/30.47 $i(all_38_0)))) % 190.00/30.47 (8) all_252_23 = e2 % 190.00/30.47 (9) op(e0, e0) = all_244_24 % 190.00/30.47 (10) ~ (all_244_15 = all_38_2) % 190.00/30.47 (11) op(e4, e1) = all_26_2 % 190.00/30.47 (12) op(all_40_2, e1) = e0 % 190.00/30.47 (13) op(all_244_15, all_244_15) = e1 % 190.00/30.47 (14) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.00/30.47 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.00/30.47 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.00/30.47 (15) op(e2, e0) = all_40_2 % 190.00/30.47 (16) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.00/30.47 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.00/30.47 $i(all_188_0)))) % 190.00/30.47 (17) ~ (e2 = e0) % 190.00/30.47 (18) all_188_2 = all_38_2 % 190.00/30.47 (19) ~ (all_244_24 = e1) % 190.00/30.47 (20) op(e2, e1) = all_38_2 % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | BETA: splitting (7) gives: % 190.00/30.47 | % 190.00/30.47 | Case 1: % 190.00/30.47 | | % 190.00/30.47 | | (21) ~ (all_38_2 = e0) % 190.00/30.47 | | % 190.00/30.47 | | BETA: splitting (14) gives: % 190.00/30.47 | | % 190.00/30.47 | | Case 1: % 190.00/30.47 | | | % 190.00/30.47 | | | (22) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) % 190.00/30.47 | | | = e0) % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (1), (2), (3), (5), (11), (22) are inconsistent by sub-proof % 190.00/30.47 | | | #451. % 190.00/30.47 | | | % 190.00/30.47 | | Case 2: % 190.00/30.47 | | | % 190.00/30.47 | | | (23) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, % 190.00/30.47 | | | e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.00/30.47 | | | % 190.00/30.47 | | | BETA: splitting (23) gives: % 190.00/30.47 | | | % 190.00/30.47 | | | Case 1: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (24) all_252_11 = e0 & op(e2, e1) = e0 % 190.00/30.47 | | | | % 190.00/30.47 | | | | ALPHA: (24) implies: % 190.00/30.47 | | | | (25) op(e2, e1) = e0 % 190.00/30.47 | | | | % 190.00/30.47 | | | | REF_CLOSE: (1), (20), (21), (25) are inconsistent by sub-proof #549. % 190.00/30.47 | | | | % 190.00/30.47 | | | Case 2: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (26) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, % 190.00/30.47 | | | | e1) = e0) % 190.00/30.47 | | | | % 190.00/30.47 | | | | BETA: splitting (26) gives: % 190.00/30.47 | | | | % 190.00/30.47 | | | | Case 1: % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | (27) all_252_15 = e0 & op(e1, e1) = e0 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | REF_CLOSE: (1), (6), (9), (13), (19), (27) are inconsistent by % 190.00/30.47 | | | | | sub-proof #450. % 190.00/30.47 | | | | | % 190.00/30.47 | | | | Case 2: % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | (28) all_252_23 = e0 & op(e0, e1) = e0 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | ALPHA: (28) implies: % 190.00/30.47 | | | | | (29) all_252_23 = e0 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | COMBINE_EQS: (8), (29) imply: % 190.00/30.47 | | | | | (30) e2 = e0 % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | REDUCE: (17), (30) imply: % 190.00/30.47 | | | | | (31) $false % 190.00/30.47 | | | | | % 190.00/30.47 | | | | | CLOSE: (31) is inconsistent. % 190.00/30.47 | | | | | % 190.00/30.47 | | | | End of split % 190.00/30.47 | | | | % 190.00/30.47 | | | End of split % 190.00/30.47 | | | % 190.00/30.47 | | End of split % 190.00/30.47 | | % 190.00/30.47 | Case 2: % 190.00/30.47 | | % 190.00/30.47 | | (32) all_38_2 = e0 % 190.00/30.47 | | % 190.00/30.47 | | COMBINE_EQS: (18), (32) imply: % 190.00/30.47 | | (33) all_188_2 = e0 % 190.00/30.47 | | % 190.00/30.47 | | REDUCE: (10), (32) imply: % 190.00/30.47 | | (34) ~ (all_244_15 = e0) % 190.00/30.47 | | % 190.00/30.47 | | REDUCE: (4), (32) imply: % 190.00/30.47 | | (35) op(e2, e0) = e1 % 190.00/30.47 | | % 190.00/30.47 | | BETA: splitting (16) gives: % 190.00/30.47 | | % 190.00/30.47 | | Case 1: % 190.00/30.47 | | | % 190.00/30.47 | | | (36) ~ (all_188_2 = e0) % 190.00/30.47 | | | % 190.00/30.47 | | | REDUCE: (33), (36) imply: % 190.00/30.47 | | | (37) $false % 190.00/30.47 | | | % 190.00/30.47 | | | CLOSE: (37) is inconsistent. % 190.00/30.47 | | | % 190.00/30.47 | | Case 2: % 190.00/30.47 | | | % 190.00/30.47 | | | % 190.00/30.47 | | | GROUND_INST: instantiating (1) with all_40_2, e1, e0, e2, simplifying with % 190.00/30.47 | | | (15), (35) gives: % 190.00/30.47 | | | (38) all_40_2 = e1 % 190.00/30.47 | | | % 190.00/30.47 | | | REDUCE: (12), (38) imply: % 190.00/30.47 | | | (39) op(e1, e1) = e0 % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (1), (6), (34), (39) are inconsistent by sub-proof #440. % 190.00/30.47 | | | % 190.00/30.47 | | End of split % 190.00/30.47 | | % 190.00/30.47 | End of split % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #285 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) ~ (all_12_2 = e2) % 190.00/30.47 (3) ~ (all_8_1 = e2) % 190.00/30.47 (4) op(e0, e3) = all_8_1 % 190.00/30.47 (5) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.00/30.47 (6) op(e0, e4) = all_12_2 % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | BETA: splitting (5) gives: % 190.00/30.47 | % 190.00/30.47 | Case 1: % 190.00/30.47 | | % 190.00/30.47 | | (7) all_252_20 = e2 & op(e0, e4) = e2 % 190.00/30.47 | | % 190.00/30.47 | | ALPHA: (7) implies: % 190.00/30.47 | | (8) op(e0, e4) = e2 % 190.00/30.47 | | % 190.00/30.47 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #544. % 190.00/30.47 | | % 190.00/30.47 | Case 2: % 190.00/30.47 | | % 190.00/30.47 | | (9) all_252_21 = e2 & op(e0, e3) = e2 % 190.00/30.47 | | % 190.00/30.47 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #289. % 190.00/30.47 | | % 190.00/30.47 | End of split % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #286 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ~ (all_28_2 = e1) % 190.00/30.47 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (3) op(e0, e2) = all_28_2 % 190.00/30.47 (4) ~ (all_244_24 = e2) % 190.00/30.47 (5) all_58_2 = all_20_2 % 190.00/30.47 (6) ~ (all_12_2 = e2) % 190.00/30.47 (7) op(e0, e0) = all_244_24 % 190.00/30.47 (8) op(e0, e1) = all_20_2 % 190.00/30.47 (9) ~ (all_8_1 = e2) % 190.00/30.47 (10) op(e0, all_20_2) = e1 % 190.00/30.47 (11) ~ (all_28_2 = e0) % 190.00/30.47 (12) op(e2, all_40_2) = e0 % 190.00/30.47 (13) op(e0, e3) = all_8_1 % 190.00/30.47 (14) op(all_28_2, all_40_2) = e2 % 190.00/30.47 (15) op(e0, e4) = all_12_2 % 190.00/30.47 (16) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.00/30.47 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.00/30.47 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.47 (17) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 190.00/30.47 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 190.00/30.47 $i(all_58_0)))) % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | BETA: splitting (17) gives: % 190.00/30.47 | % 190.00/30.47 | Case 1: % 190.00/30.47 | | % 190.00/30.47 | | (18) ~ (all_58_2 = e2) % 190.00/30.47 | | % 190.00/30.47 | | REDUCE: (5), (18) imply: % 190.00/30.47 | | (19) ~ (all_20_2 = e2) % 190.00/30.47 | | % 190.00/30.47 | | BETA: splitting (16) gives: % 190.00/30.47 | | % 190.00/30.47 | | Case 1: % 190.00/30.47 | | | % 190.00/30.47 | | | (20) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, % 190.00/30.47 | | | e3) = e2) % 190.00/30.47 | | | % 190.00/30.47 | | | BETA: splitting (20) gives: % 190.00/30.47 | | | % 190.00/30.47 | | | Case 1: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (21) all_252_20 = e2 & op(e0, e4) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | ALPHA: (21) implies: % 190.00/30.47 | | | | (22) op(e0, e4) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | GROUND_INST: instantiating (2) with all_12_2, e2, e4, e0, simplifying % 190.00/30.47 | | | | with (15), (22) gives: % 190.00/30.47 | | | | (23) all_12_2 = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | REDUCE: (6), (23) imply: % 190.00/30.47 | | | | (24) $false % 190.00/30.47 | | | | % 190.00/30.47 | | | | CLOSE: (24) is inconsistent. % 190.00/30.47 | | | | % 190.00/30.47 | | | Case 2: % 190.00/30.47 | | | | % 190.00/30.47 | | | | (25) all_252_21 = e2 & op(e0, e3) = e2 % 190.00/30.47 | | | | % 190.00/30.47 | | | | REF_CLOSE: (2), (9), (13), (25) are inconsistent by sub-proof #289. % 190.00/30.47 | | | | % 190.00/30.47 | | | End of split % 190.00/30.47 | | | % 190.00/30.47 | | Case 2: % 190.00/30.47 | | | % 190.00/30.47 | | | (26) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.00/30.47 | | | e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.47 | | | % 190.00/30.47 | | | REF_CLOSE: (2), (3), (4), (7), (8), (11), (12), (14), (19), (26) are % 190.00/30.47 | | | inconsistent by sub-proof #287. % 190.00/30.47 | | | % 190.00/30.47 | | End of split % 190.00/30.47 | | % 190.00/30.47 | Case 2: % 190.00/30.47 | | % 190.00/30.47 | | (27) all_58_2 = e2 % 190.00/30.47 | | % 190.00/30.47 | | REF_CLOSE: (1), (2), (3), (5), (10), (27) are inconsistent by sub-proof % 190.00/30.47 | | #501. % 190.00/30.47 | | % 190.00/30.47 | End of split % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #287 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) op(e0, e2) = all_28_2 % 190.00/30.47 (3) ~ (all_244_24 = e2) % 190.00/30.47 (4) op(e0, e0) = all_244_24 % 190.00/30.47 (5) op(e0, e1) = all_20_2 % 190.00/30.47 (6) ~ (all_20_2 = e2) % 190.00/30.47 (7) ~ (all_28_2 = e0) % 190.00/30.47 (8) op(e2, all_40_2) = e0 % 190.00/30.47 (9) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 190.00/30.47 | (all_252_24 = e2 & op(e0, e0) = e2) % 190.00/30.47 (10) op(all_28_2, all_40_2) = e2 % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | BETA: splitting (9) gives: % 190.00/30.47 | % 190.00/30.47 | Case 1: % 190.00/30.47 | | % 190.00/30.47 | | (11) all_252_22 = e2 & op(e0, e2) = e2 % 190.00/30.47 | | % 190.00/30.47 | | ALPHA: (11) implies: % 190.00/30.47 | | (12) op(e0, e2) = e2 % 190.00/30.47 | | % 190.00/30.47 | | REF_CLOSE: (1), (2), (7), (8), (10), (12) are inconsistent by sub-proof % 190.00/30.47 | | #288. % 190.00/30.47 | | % 190.00/30.47 | Case 2: % 190.00/30.47 | | % 190.00/30.47 | | (13) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) % 190.00/30.47 | | = e2) % 190.00/30.47 | | % 190.00/30.47 | | REF_CLOSE: (1), (3), (4), (5), (6), (13) are inconsistent by sub-proof #327. % 190.00/30.47 | | % 190.00/30.47 | End of split % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #288 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) op(e0, e2) = all_28_2 % 190.00/30.47 (3) op(e0, e2) = e2 % 190.00/30.47 (4) ~ (all_28_2 = e0) % 190.00/30.47 (5) op(e2, all_40_2) = e0 % 190.00/30.47 (6) op(all_28_2, all_40_2) = e2 % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | GROUND_INST: instantiating (1) with all_28_2, e2, e2, e0, simplifying with % 190.00/30.47 | (2), (3) gives: % 190.00/30.47 | (7) all_28_2 = e2 % 190.00/30.47 | % 190.00/30.47 | REDUCE: (4), (7) imply: % 190.00/30.47 | (8) ~ (e2 = e0) % 190.00/30.47 | % 190.00/30.47 | REDUCE: (6), (7) imply: % 190.00/30.47 | (9) op(e2, all_40_2) = e2 % 190.00/30.47 | % 190.00/30.47 | GROUND_INST: instantiating (1) with e0, e2, all_40_2, e2, simplifying with % 190.00/30.47 | (5), (9) gives: % 190.00/30.47 | (10) e2 = e0 % 190.00/30.47 | % 190.00/30.47 | REDUCE: (8), (10) imply: % 190.00/30.47 | (11) $false % 190.00/30.47 | % 190.00/30.47 | CLOSE: (11) is inconsistent. % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #289 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) all_252_21 = e2 & op(e0, e3) = e2 % 190.00/30.47 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (3) op(e0, e3) = all_8_1 % 190.00/30.47 (4) ~ (all_8_1 = e2) % 190.00/30.47 % 190.00/30.47 Begin of proof % 190.00/30.47 | % 190.00/30.47 | ALPHA: (1) implies: % 190.00/30.47 | (5) op(e0, e3) = e2 % 190.00/30.47 | % 190.00/30.47 | GROUND_INST: instantiating (2) with all_8_1, e2, e3, e0, simplifying with (3), % 190.00/30.47 | (5) gives: % 190.00/30.47 | (6) all_8_1 = e2 % 190.00/30.47 | % 190.00/30.47 | REDUCE: (4), (6) imply: % 190.00/30.47 | (7) $false % 190.00/30.47 | % 190.00/30.47 | CLOSE: (7) is inconsistent. % 190.00/30.47 | % 190.00/30.47 End of proof % 190.00/30.47 % 190.00/30.47 Sub-proof #290 shows that the following formulas are inconsistent: % 190.00/30.47 ---------------------------------------------------------------- % 190.00/30.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.00/30.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.00/30.47 (2) op(e2, e1) = e3 % 190.00/30.47 (3) op(e2, e1) = e1 % 190.00/30.47 (4) ~ (e3 = e1) % 190.00/30.48 (5) op(e2, e1) = all_38_2 % 190.00/30.48 % 190.00/30.48 Begin of proof % 190.00/30.48 | % 190.00/30.48 | GROUND_INST: instantiating (1) with all_38_2, e1, e1, e2, simplifying with % 190.00/30.48 | (3), (5) gives: % 190.00/30.48 | (6) all_38_2 = e1 % 190.00/30.48 | % 190.00/30.48 | GROUND_INST: instantiating (1) with all_38_2, e3, e1, e2, simplifying with % 190.00/30.48 | (2), (5) gives: % 190.00/30.48 | (7) all_38_2 = e3 % 190.00/30.48 | % 190.00/30.48 | COMBINE_EQS: (6), (7) imply: % 190.00/30.48 | (8) e3 = e1 % 190.00/30.48 | % 190.00/30.48 | SIMP: (8) implies: % 190.00/30.48 | (9) e3 = e1 % 190.00/30.48 | % 190.00/30.48 | REDUCE: (4), (9) imply: % 190.00/30.48 | (10) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (10) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #291 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_19 = e3 & op(e1, e0) = e3 % 190.22/30.48 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (3) op(e1, e0) = e4 % 190.22/30.48 (4) ~ (e4 = e3) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (1) implies: % 190.22/30.48 | (5) op(e1, e0) = e3 % 190.22/30.48 | % 190.22/30.48 | GROUND_INST: instantiating (2) with e3, e4, e0, e1, simplifying with (3), (5) % 190.22/30.48 | gives: % 190.22/30.48 | (6) e4 = e3 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (4), (6) imply: % 190.22/30.48 | (7) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (7) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #292 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) ~ (all_36_2 = e0) % 190.22/30.48 (3) all_250_8 = e1 | all_250_8 = e0 % 190.22/30.48 (4) all_250_8 = all_36_2 % 190.22/30.48 (5) ~ (all_36_2 = e3) % 190.22/30.48 (6) op(all_36_2, all_62_2) = e1 % 190.22/30.48 (7) op(e1, all_62_2) = e3 % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | BETA: splitting (3) gives: % 190.22/30.48 | % 190.22/30.48 | Case 1: % 190.22/30.48 | | % 190.22/30.48 | | (8) all_250_8 = e1 % 190.22/30.48 | | % 190.22/30.48 | | COMBINE_EQS: (4), (8) imply: % 190.22/30.48 | | (9) all_36_2 = e1 % 190.22/30.48 | | % 190.22/30.48 | | REDUCE: (5), (9) imply: % 190.22/30.48 | | (10) ~ (e3 = e1) % 190.22/30.48 | | % 190.22/30.48 | | SIMP: (10) implies: % 190.22/30.48 | | (11) ~ (e3 = e1) % 190.22/30.48 | | % 190.22/30.48 | | REDUCE: (6), (9) imply: % 190.22/30.48 | | (12) op(e1, all_62_2) = e1 % 190.22/30.48 | | % 190.22/30.48 | | GROUND_INST: instantiating (1) with e3, e1, all_62_2, e1, simplifying with % 190.22/30.48 | | (7), (12) gives: % 190.22/30.48 | | (13) e3 = e1 % 190.22/30.48 | | % 190.22/30.48 | | REDUCE: (11), (13) imply: % 190.22/30.48 | | (14) $false % 190.22/30.48 | | % 190.22/30.48 | | CLOSE: (14) is inconsistent. % 190.22/30.48 | | % 190.22/30.48 | Case 2: % 190.22/30.48 | | % 190.22/30.48 | | (15) all_250_8 = e0 % 190.22/30.48 | | % 190.22/30.48 | | COMBINE_EQS: (4), (15) imply: % 190.22/30.48 | | (16) all_36_2 = e0 % 190.22/30.48 | | % 190.22/30.48 | | REDUCE: (2), (16) imply: % 190.22/30.48 | | (17) $false % 190.22/30.48 | | % 190.22/30.48 | | CLOSE: (17) is inconsistent. % 190.22/30.48 | | % 190.22/30.48 | End of split % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #293 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_23 = e1 & op(e0, e1) = e1 % 190.22/30.48 (2) all_252_23 = e0 % 190.22/30.48 (3) ~ (e1 = e0) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (1) implies: % 190.22/30.48 | (4) all_252_23 = e1 % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (2), (4) imply: % 190.22/30.48 | (5) e1 = e0 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #294 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_22 = e4 & op(e0, e2) = e4 % 190.22/30.48 (2) all_252_22 = e2 % 190.22/30.48 (3) ~ (e4 = e2) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (1) implies: % 190.22/30.48 | (4) all_252_22 = e4 % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (2), (4) imply: % 190.22/30.48 | (5) e4 = e2 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #295 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) ~ (e4 = e0) % 190.22/30.48 (3) ~ (all_4_2 = e0) % 190.22/30.48 (4) ~ (all_8_2 = e0) % 190.22/30.48 (5) ~ (all_6_2 = e0) % 190.22/30.48 (6) op(e3, e2) = all_8_2 % 190.22/30.48 (7) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) | % 190.22/30.48 (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = e0) % 190.22/30.48 | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.48 (8) all_252_22 = e2 % 190.22/30.48 (9) ~ (e2 = e0) % 190.22/30.48 (10) all_252_8 = e4 & op(e2, e2) = e4 % 190.22/30.48 (11) op(e1, e2) = all_4_2 % 190.22/30.48 (12) op(e4, e2) = all_6_2 % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (10) implies: % 190.22/30.48 | (13) all_252_8 = e4 % 190.22/30.48 | % 190.22/30.48 | BETA: splitting (7) gives: % 190.22/30.48 | % 190.22/30.48 | Case 1: % 190.22/30.48 | | % 190.22/30.48 | | (14) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = % 190.22/30.48 | | e0) % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (1), (4), (5), (6), (12), (14) are inconsistent by sub-proof % 190.22/30.48 | | #546. % 190.22/30.48 | | % 190.22/30.48 | Case 2: % 190.22/30.48 | | % 190.22/30.48 | | (15) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.22/30.48 | | e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.48 | | % 190.22/30.48 | | BETA: splitting (15) gives: % 190.22/30.48 | | % 190.22/30.48 | | Case 1: % 190.22/30.48 | | | % 190.22/30.48 | | | (16) all_252_8 = e0 & op(e2, e2) = e0 % 190.22/30.48 | | | % 190.22/30.48 | | | ALPHA: (16) implies: % 190.22/30.48 | | | (17) all_252_8 = e0 % 190.22/30.48 | | | % 190.22/30.48 | | | COMBINE_EQS: (13), (17) imply: % 190.22/30.48 | | | (18) e4 = e0 % 190.22/30.48 | | | % 190.22/30.48 | | | SIMP: (18) implies: % 190.22/30.48 | | | (19) e4 = e0 % 190.22/30.48 | | | % 190.22/30.48 | | | REDUCE: (2), (19) imply: % 190.22/30.48 | | | (20) $false % 190.22/30.48 | | | % 190.22/30.48 | | | CLOSE: (20) is inconsistent. % 190.22/30.48 | | | % 190.22/30.48 | | Case 2: % 190.22/30.48 | | | % 190.22/30.48 | | | (21) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, % 190.22/30.48 | | | e2) = e0) % 190.22/30.48 | | | % 190.22/30.48 | | | REF_CLOSE: (1), (3), (8), (9), (11), (21) are inconsistent by sub-proof % 190.22/30.48 | | | #406. % 190.22/30.48 | | | % 190.22/30.48 | | End of split % 190.22/30.48 | | % 190.22/30.48 | End of split % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #296 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_4 = e4 % 190.22/30.48 (2) all_252_4 = e3 % 190.22/30.48 (3) ~ (e4 = e3) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (1), (2) imply: % 190.22/30.48 | (4) e4 = e3 % 190.22/30.48 | % 190.22/30.48 | SIMP: (4) implies: % 190.22/30.48 | (5) e4 = e3 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #297 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_11 = e3 % 190.22/30.48 (2) all_252_11 = e0 % 190.22/30.48 (3) ~ (e3 = e0) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (1), (2) imply: % 190.22/30.48 | (4) e3 = e0 % 190.22/30.48 | % 190.22/30.48 | SIMP: (4) implies: % 190.22/30.48 | (5) e3 = e0 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #298 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) ~ (all_30_2 = e3) % 190.22/30.48 (3) op(e4, e0) = all_30_2 % 190.22/30.48 (4) op(e4, e1) = all_26_2 % 190.22/30.48 (5) ~ (all_26_2 = e3) % 190.22/30.48 (6) (all_252_9 = e3 & op(e4, e1) = e3) | (all_252_16 = e3 & op(e4, e0) = e3) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | BETA: splitting (6) gives: % 190.22/30.48 | % 190.22/30.48 | Case 1: % 190.22/30.48 | | % 190.22/30.48 | | (7) all_252_9 = e3 & op(e4, e1) = e3 % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #299. % 190.22/30.48 | | % 190.22/30.48 | Case 2: % 190.22/30.48 | | % 190.22/30.48 | | (8) all_252_16 = e3 & op(e4, e0) = e3 % 190.22/30.48 | | % 190.22/30.48 | | ALPHA: (8) implies: % 190.22/30.48 | | (9) op(e4, e0) = e3 % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #539. % 190.22/30.48 | | % 190.22/30.48 | End of split % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #299 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_9 = e3 & op(e4, e1) = e3 % 190.22/30.48 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (3) op(e4, e1) = all_26_2 % 190.22/30.48 (4) ~ (all_26_2 = e3) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (1) implies: % 190.22/30.48 | (5) op(e4, e1) = e3 % 190.22/30.48 | % 190.22/30.48 | GROUND_INST: instantiating (2) with all_26_2, e3, e1, e4, simplifying with % 190.22/30.48 | (3), (5) gives: % 190.22/30.48 | (6) all_26_2 = e3 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (4), (6) imply: % 190.22/30.48 | (7) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (7) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #300 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.22/30.48 | (all_252_21 = e2 & op(e0, e3) = e2) % 190.22/30.48 (3) ~ (e2 = e1) % 190.22/30.48 (4) all_252_7 = e1 % 190.22/30.48 (5) op(e0, e3) = all_22_2 % 190.22/30.48 (6) op(e1, e3) = e4 % 190.22/30.48 (7) ~ (all_22_2 = e2) % 190.22/30.48 (8) ~ (e4 = e2) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | BETA: splitting (2) gives: % 190.22/30.48 | % 190.22/30.48 | Case 1: % 190.22/30.48 | | % 190.22/30.48 | | (9) all_252_7 = e2 & op(e2, e3) = e2 % 190.22/30.48 | | % 190.22/30.48 | | ALPHA: (9) implies: % 190.22/30.48 | | (10) all_252_7 = e2 % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #301. % 190.22/30.48 | | % 190.22/30.48 | Case 2: % 190.22/30.48 | | % 190.22/30.48 | | (11) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) % 190.22/30.48 | | = e2) % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (1), (5), (6), (7), (8), (11) are inconsistent by sub-proof #373. % 190.22/30.48 | | % 190.22/30.48 | End of split % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #301 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_7 = e2 % 190.22/30.48 (2) all_252_7 = e1 % 190.22/30.48 (3) ~ (e2 = e1) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (1), (2) imply: % 190.22/30.48 | (4) e2 = e1 % 190.22/30.48 | % 190.22/30.48 | SIMP: (4) implies: % 190.22/30.48 | (5) e2 = e1 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #302 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_7 = e0 & op(e2, e3) = e0 % 190.22/30.48 (2) all_252_7 = e1 % 190.22/30.48 (3) ~ (e1 = e0) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (1) implies: % 190.22/30.48 | (4) all_252_7 = e0 % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (2), (4) imply: % 190.22/30.48 | (5) e1 = e0 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #303 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) op(e4, e3) = all_84_2 % 190.22/30.48 (3) all_252_3 = e2 % 190.22/30.48 (4) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) % 190.22/30.48 (5) ~ (e3 = e0) % 190.22/30.48 (6) ~ (e2 = e0) % 190.22/30.48 (7) op(e4, e3) = e3 % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | BETA: splitting (4) gives: % 190.22/30.48 | % 190.22/30.48 | Case 1: % 190.22/30.48 | | % 190.22/30.48 | | (8) all_252_1 = e0 & op(e4, e3) = e0 % 190.22/30.48 | | % 190.22/30.48 | | ALPHA: (8) implies: % 190.22/30.48 | | (9) op(e4, e3) = e0 % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (1), (2), (5), (7), (9) are inconsistent by sub-proof #431. % 190.22/30.48 | | % 190.22/30.48 | Case 2: % 190.22/30.48 | | % 190.22/30.48 | | (10) all_252_3 = e0 & op(e3, e3) = e0 % 190.22/30.48 | | % 190.22/30.48 | | ALPHA: (10) implies: % 190.22/30.48 | | (11) all_252_3 = e0 % 190.22/30.48 | | % 190.22/30.48 | | COMBINE_EQS: (3), (11) imply: % 190.22/30.48 | | (12) e2 = e0 % 190.22/30.48 | | % 190.22/30.48 | | REDUCE: (6), (12) imply: % 190.22/30.48 | | (13) $false % 190.22/30.48 | | % 190.22/30.48 | | CLOSE: (13) is inconsistent. % 190.22/30.48 | | % 190.22/30.48 | End of split % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #304 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) all_252_1 = e2 & op(e4, e3) = e2 % 190.22/30.48 (2) all_252_1 = e3 % 190.22/30.48 (3) ~ (e3 = e2) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | ALPHA: (1) implies: % 190.22/30.48 | (4) all_252_1 = e2 % 190.22/30.48 | % 190.22/30.48 | COMBINE_EQS: (2), (4) imply: % 190.22/30.48 | (5) e3 = e2 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (3), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #305 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) op(e3, e3) = all_244_3 % 190.22/30.48 (3) op(e3, e3) = e1 % 190.22/30.48 (4) ~ (all_244_3 = e1) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | GROUND_INST: instantiating (1) with all_244_3, e1, e3, e3, simplifying with % 190.22/30.48 | (2), (3) gives: % 190.22/30.48 | (5) all_244_3 = e1 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (4), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #306 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) op(e0, e4) = e3 % 190.22/30.48 (2) op(e2, e2) = all_244_8 % 190.22/30.48 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (4) ~ (all_162_2 = e1) | (op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ % 190.22/30.48 (all_162_1 = e4) | ( ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 190.22/30.48 $i(all_162_0)))) % 190.22/30.48 (5) ~ (e2 = e1) % 190.22/30.48 (6) op(e0, e1) = e2 % 190.22/30.48 (7) ~ (all_4_2 = e0) % 190.22/30.48 (8) ~ (all_244_24 = all_20_2) % 190.22/30.48 (9) ~ (all_8_2 = e0) % 190.22/30.48 (10) op(e0, e0) = all_244_24 % 190.22/30.48 (11) op(e0, e1) = all_20_2 % 190.22/30.48 (12) all_252_20 = e3 % 190.22/30.48 (13) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 190.22/30.48 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 190.22/30.48 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.22/30.48 (14) ~ (all_6_2 = e0) % 190.22/30.48 (15) op(e3, e2) = all_8_2 % 190.22/30.48 (16) op(all_244_8, all_244_8) = e2 % 190.22/30.48 (17) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.22/30.48 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.22/30.48 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.48 (18) ~ (e1 = e0) % 190.22/30.48 (19) all_162_2 = e1 % 190.22/30.48 (20) ~ (e3 = e1) % 190.22/30.48 (21) ~ (all_244_24 = e1) % 190.22/30.48 (22) op(e0, e3) = e4 % 190.22/30.48 (23) op(e1, e2) = all_4_2 % 190.22/30.48 (24) op(e4, e2) = all_6_2 % 190.22/30.48 (25) ~ (e4 = e1) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | BETA: splitting (13) gives: % 190.22/30.48 | % 190.22/30.48 | Case 1: % 190.22/30.48 | | % 190.22/30.48 | | (26) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 190.22/30.48 | | = e1) % 190.22/30.48 | | % 190.22/30.48 | | REF_CLOSE: (3), (12), (20), (22), (25), (26) are inconsistent by sub-proof % 190.22/30.48 | | #309. % 190.22/30.48 | | % 190.22/30.48 | Case 2: % 190.22/30.48 | | % 190.22/30.48 | | (27) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 190.22/30.48 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.22/30.48 | | % 190.22/30.48 | | BETA: splitting (27) gives: % 190.22/30.48 | | % 190.22/30.48 | | Case 1: % 190.22/30.48 | | | % 190.22/30.48 | | | (28) all_252_22 = e1 & op(e0, e2) = e1 % 190.22/30.48 | | | % 190.22/30.48 | | | ALPHA: (28) implies: % 190.22/30.48 | | | (29) all_252_22 = e1 % 190.22/30.48 | | | % 190.22/30.48 | | | BETA: splitting (4) gives: % 190.22/30.48 | | | % 190.22/30.48 | | | Case 1: % 190.22/30.48 | | | | % 190.22/30.48 | | | | (30) ~ (all_162_2 = e1) % 190.22/30.48 | | | | % 190.22/30.48 | | | | REDUCE: (19), (30) imply: % 190.22/30.48 | | | | (31) $false % 190.22/30.48 | | | | % 190.22/30.48 | | | | CLOSE: (31) is inconsistent. % 190.22/30.48 | | | | % 190.22/30.48 | | | Case 2: % 190.22/30.48 | | | | % 190.22/30.48 | | | | (32) op(e1, e0) = all_162_1 & $i(all_162_1) & ( ~ (all_162_1 = e4) | % 190.22/30.48 | | | | ( ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 190.22/30.48 | | | | $i(all_162_0))) % 190.22/30.48 | | | | % 190.22/30.48 | | | | ALPHA: (32) implies: % 190.22/30.48 | | | | (33) ~ (all_162_1 = e4) | ( ~ (all_162_0 = e3) & op(e0, e4) = % 190.22/30.48 | | | | all_162_0 & $i(all_162_0)) % 190.22/30.48 | | | | % 190.22/30.48 | | | | BETA: splitting (17) gives: % 190.22/30.48 | | | | % 190.22/30.48 | | | | Case 1: % 190.22/30.48 | | | | | % 190.22/30.48 | | | | | (34) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 190.22/30.48 | | | | | e2) = e0) % 190.22/30.48 | | | | | % 190.22/30.48 | | | | | REF_CLOSE: (3), (9), (14), (15), (24), (34) are inconsistent by % 190.22/30.48 | | | | | sub-proof #546. % 190.22/30.48 | | | | | % 190.22/30.48 | | | | Case 2: % 190.22/30.48 | | | | | % 190.22/30.48 | | | | | (35) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, % 190.22/30.48 | | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.48 | | | | | % 190.22/30.48 | | | | | BETA: splitting (35) gives: % 190.22/30.48 | | | | | % 190.22/30.48 | | | | | Case 1: % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | (36) all_252_8 = e0 & op(e2, e2) = e0 % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | ALPHA: (36) implies: % 190.22/30.48 | | | | | | (37) op(e2, e2) = e0 % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | BETA: splitting (33) gives: % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | Case 1: % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | GROUND_INST: instantiating (3) with all_20_2, e2, e1, e0, % 190.22/30.48 | | | | | | | simplifying with (6), (11) gives: % 190.22/30.48 | | | | | | | (38) all_20_2 = e2 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | REF_CLOSE: (2), (3), (8), (10), (16), (37), (38) are inconsistent % 190.22/30.48 | | | | | | | by sub-proof #476. % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | Case 2: % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | (39) ~ (all_162_0 = e3) & op(e0, e4) = all_162_0 & % 190.22/30.48 | | | | | | | $i(all_162_0) % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | ALPHA: (39) implies: % 190.22/30.48 | | | | | | | (40) ~ (all_162_0 = e3) % 190.22/30.48 | | | | | | | (41) op(e0, e4) = all_162_0 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | GROUND_INST: instantiating (3) with e3, all_162_0, e4, e0, % 190.22/30.48 | | | | | | | simplifying with (1), (41) gives: % 190.22/30.48 | | | | | | | (42) all_162_0 = e3 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | REDUCE: (40), (42) imply: % 190.22/30.48 | | | | | | | (43) $false % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | CLOSE: (43) is inconsistent. % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | End of split % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | Case 2: % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | (44) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 190.22/30.48 | | | | | | op(e0, e2) = e0) % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | BETA: splitting (44) gives: % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | | Case 1: % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | (45) all_252_14 = e0 & op(e1, e2) = e0 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | ALPHA: (45) implies: % 190.22/30.48 | | | | | | | (46) op(e1, e2) = e0 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | REF_CLOSE: (3), (7), (23), (46) are inconsistent by sub-proof % 190.22/30.48 | | | | | | | #545. % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | Case 2: % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | (47) all_252_22 = e0 & op(e0, e2) = e0 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | ALPHA: (47) implies: % 190.22/30.48 | | | | | | | (48) all_252_22 = e0 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | COMBINE_EQS: (29), (48) imply: % 190.22/30.48 | | | | | | | (49) e1 = e0 % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | REDUCE: (18), (49) imply: % 190.22/30.48 | | | | | | | (50) $false % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | | CLOSE: (50) is inconsistent. % 190.22/30.48 | | | | | | | % 190.22/30.48 | | | | | | End of split % 190.22/30.48 | | | | | | % 190.22/30.48 | | | | | End of split % 190.22/30.48 | | | | | % 190.22/30.48 | | | | End of split % 190.22/30.48 | | | | % 190.22/30.48 | | | End of split % 190.22/30.48 | | | % 190.22/30.48 | | Case 2: % 190.22/30.48 | | | % 190.22/30.48 | | | (51) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 190.22/30.48 | | | e0) = e1) % 190.22/30.48 | | | % 190.22/30.48 | | | REF_CLOSE: (3), (5), (6), (10), (11), (21), (51) are inconsistent by % 190.22/30.48 | | | sub-proof #473. % 190.22/30.48 | | | % 190.22/30.48 | | End of split % 190.22/30.48 | | % 190.22/30.48 | End of split % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #307 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (2) op(e1, e0) = e4 % 190.22/30.48 (3) op(e1, e0) = e0 % 190.22/30.48 (4) ~ (e4 = e0) % 190.22/30.48 % 190.22/30.48 Begin of proof % 190.22/30.48 | % 190.22/30.48 | GROUND_INST: instantiating (1) with e0, e4, e0, e1, simplifying with (2), (3) % 190.22/30.48 | gives: % 190.22/30.48 | (5) e4 = e0 % 190.22/30.48 | % 190.22/30.48 | REDUCE: (4), (5) imply: % 190.22/30.48 | (6) $false % 190.22/30.48 | % 190.22/30.48 | CLOSE: (6) is inconsistent. % 190.22/30.48 | % 190.22/30.48 End of proof % 190.22/30.48 % 190.22/30.48 Sub-proof #308 shows that the following formulas are inconsistent: % 190.22/30.48 ---------------------------------------------------------------- % 190.22/30.48 (1) ~ (all_28_2 = e1) % 190.22/30.48 (2) op(e2, e2) = all_244_8 % 190.22/30.48 (3) ~ (all_36_2 = e0) | (op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 190.22/30.48 (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 190.22/30.48 $i(all_36_0)))) % 190.22/30.48 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.48 (5) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) | % 190.22/30.48 (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 190.22/30.48 | (all_252_21 = e0 & op(e0, e3) = e0) % 190.22/30.49 (6) ~ (all_174_2 = e3) | (op(e3, e2) = all_174_1 & $i(all_174_1) & ( ~ % 190.22/30.49 (all_174_1 = e1) | ( ~ (all_174_0 = e4) & op(e2, e1) = all_174_0 & % 190.22/30.49 $i(all_174_0)))) % 190.22/30.49 (7) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 190.22/30.49 (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 190.22/30.49 $i(all_102_0)))) % 190.22/30.49 (8) op(e0, e2) = all_28_2 % 190.22/30.49 (9) op(e3, e1) = all_36_2 % 190.22/30.49 (10) ~ (e2 = e1) % 190.22/30.49 (11) all_172_2 = all_10_2 % 190.22/30.49 (12) op(e3, e3) = all_244_3 % 190.22/30.49 (13) ~ (all_172_2 = e0) | (op(e0, e2) = all_172_1 & $i(all_172_1) & ( ~ % 190.22/30.49 (all_172_1 = e1) | ( ~ (all_172_0 = e4) & op(e2, e1) = all_172_0 & % 190.22/30.49 $i(all_172_0)))) % 190.22/30.49 (14) op(e1, e3) = all_62_2 % 190.22/30.49 (15) op(e2, all_38_2) = e1 % 190.22/30.49 (16) ~ (all_26_2 = e0) % 190.22/30.49 (17) op(e1, e1) = all_244_15 % 190.22/30.49 (18) op(e3, e0) = all_12_1 % 190.22/30.49 (19) all_174_2 = all_40_2 % 190.22/30.49 (20) ~ (e4 = e0) % 190.22/30.49 (21) all_76_2 = all_40_2 % 190.22/30.49 (22) op(e2, e3) = all_10_2 % 190.22/30.49 (23) op(all_12_1, e4) = e0 % 190.22/30.49 (24) op(e4, e3) = all_84_2 % 190.22/30.49 (25) ~ (all_4_2 = e0) % 190.22/30.49 (26) ~ (all_30_2 = e3) % 190.22/30.49 (27) op(e4, e0) = all_30_2 % 190.22/30.49 (28) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.22/30.49 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.22/30.49 $i(all_38_0)))) % 190.22/30.49 (29) all_58_2 = all_20_2 % 190.22/30.49 (30) ~ (all_244_15 = all_62_2) % 190.22/30.49 (31) op(e3, e4) = all_100_2 % 190.22/30.49 (32) ~ (all_46_2 = e0) | (op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ % 190.22/30.49 (all_46_1 = e2) | ( ~ (all_46_0 = e4) & op(e3, e2) = all_46_0 & % 190.22/30.49 $i(all_46_0)))) % 190.22/30.49 (33) ~ (all_8_2 = e0) % 190.22/30.49 (34) op(e0, e0) = all_244_24 % 190.22/30.49 (35) op(e0, e1) = all_20_2 % 190.22/30.49 (36) all_252_20 = e3 % 190.22/30.49 (37) op(all_244_24, all_244_24) = e0 % 190.22/30.49 (38) op(e4, all_84_2) = e3 % 190.22/30.49 (39) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 190.22/30.49 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 190.22/30.49 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.22/30.49 (40) op(e0, all_20_2) = e1 % 190.22/30.49 (41) all_98_2 = all_84_2 % 190.22/30.49 (42) ~ (all_76_2 = e3) | (op(e3, e2) = all_76_1 & $i(all_76_1) & ( ~ % 190.22/30.49 (all_76_1 = e4) | ( ~ (all_76_0 = e1) & op(e2, e4) = all_76_0 & % 190.22/30.49 $i(all_76_0)))) % 190.22/30.49 (43) ~ (all_244_3 = all_100_2) % 190.22/30.49 (44) op(e4, e1) = all_26_2 % 190.22/30.49 (45) ~ (all_6_2 = e0) % 190.22/30.49 (46) ~ (all_244_24 = all_40_2) % 190.22/30.49 (47) op(e3, e2) = all_8_2 % 190.22/30.49 (48) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.22/30.49 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.22/30.49 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.49 (49) op(e2, all_40_2) = e0 % 190.22/30.49 (50) ~ (all_244_24 = e4) % 190.22/30.49 (51) op(e1, e4) = all_16_2 % 190.22/30.49 (52) op(e1, all_16_2) = e4 % 190.22/30.49 (53) ~ (all_244_15 = all_20_2) % 190.22/30.49 (54) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.22/30.49 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.22/30.49 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.22/30.49 (55) ~ (e3 = e2) % 190.22/30.49 (56) op(e2, all_10_2) = e3 % 190.22/30.49 (57) op(e3, all_244_3) = e3 % 190.22/30.49 (58) ~ (all_244_8 = all_10_2) % 190.22/30.49 (59) ~ (e4 = e2) % 190.22/30.49 (60) op(e2, e0) = all_40_2 % 190.22/30.49 (61) op(all_28_2, all_40_2) = e2 % 190.22/30.49 (62) ~ (e1 = e0) % 190.22/30.49 (63) all_46_2 = all_36_2 % 190.22/30.49 (64) all_102_2 = all_10_2 % 190.22/30.49 (65) all_70_2 = all_62_2 % 190.22/30.49 (66) ~ (all_70_2 = e0) | (op(e0, e1) = all_70_1 & $i(all_70_1) & ( ~ % 190.22/30.49 (all_70_1 = e2) | ( ~ (all_70_0 = e4) & op(e1, e2) = all_70_0 & % 190.22/30.49 $i(all_70_0)))) % 190.22/30.49 (67) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.22/30.49 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.22/30.49 $i(all_188_0)))) % 190.22/30.49 (68) op(e3, all_12_1) = e0 % 190.22/30.49 (69) op(e3, all_36_2) = e1 % 190.22/30.49 (70) ~ (e3 = e1) % 190.22/30.49 (71) ~ (e2 = e0) % 190.22/30.49 (72) op(e1, e0) = all_34_2 % 190.22/30.49 (73) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.22/30.49 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.22/30.49 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.22/30.49 (74) all_188_2 = all_38_2 % 190.22/30.49 (75) ~ (all_34_2 = e4) % 190.22/30.49 (76) op(e0, e3) = e4 % 190.22/30.49 (77) op(e1, e2) = all_4_2 % 190.22/30.49 (78) op(e4, e2) = all_6_2 % 190.22/30.49 (79) op(e2, e1) = all_38_2 % 190.22/30.49 (80) ~ (all_98_2 = e0) | (op(e0, e4) = all_98_1 & $i(all_98_1) & ( ~ % 190.22/30.49 (all_98_1 = e1) | ( ~ (all_98_0 = e2) & op(e4, e1) = all_98_0 & % 190.22/30.49 $i(all_98_0)))) % 190.22/30.49 (81) ~ (e4 = e1) % 190.22/30.49 (82) ~ (all_244_8 = all_38_2) % 190.22/30.49 (83) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 190.22/30.49 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 190.22/30.49 $i(all_58_0)))) % 190.22/30.49 % 190.22/30.49 Begin of proof % 190.22/30.49 | % 190.22/30.49 | BETA: splitting (3) gives: % 190.22/30.49 | % 190.22/30.49 | Case 1: % 190.22/30.49 | | % 190.22/30.49 | | (84) ~ (all_36_2 = e0) % 190.22/30.49 | | % 190.22/30.49 | | BETA: splitting (28) gives: % 190.22/30.49 | | % 190.22/30.49 | | Case 1: % 190.22/30.49 | | | % 190.22/30.49 | | | (85) ~ (all_38_2 = e0) % 190.22/30.49 | | | % 190.22/30.49 | | | BETA: splitting (83) gives: % 190.22/30.49 | | | % 190.22/30.49 | | | Case 1: % 190.22/30.49 | | | | % 190.22/30.49 | | | | (86) ~ (all_58_2 = e2) % 190.22/30.49 | | | | % 190.22/30.49 | | | | REDUCE: (29), (86) imply: % 190.22/30.49 | | | | (87) ~ (all_20_2 = e2) % 190.22/30.49 | | | | % 190.22/30.49 | | | | BETA: splitting (66) gives: % 190.22/30.49 | | | | % 190.22/30.49 | | | | Case 1: % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | (88) ~ (all_70_2 = e0) % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | REDUCE: (65), (88) imply: % 190.22/30.49 | | | | | (89) ~ (all_62_2 = e0) % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | BETA: splitting (42) gives: % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | Case 1: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | (90) ~ (all_76_2 = e3) % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | REDUCE: (21), (90) imply: % 190.22/30.49 | | | | | | (91) ~ (all_40_2 = e3) % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | BETA: splitting (80) gives: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | Case 1: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | (92) ~ (all_98_2 = e0) % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | REDUCE: (41), (92) imply: % 190.22/30.49 | | | | | | | (93) ~ (all_84_2 = e0) % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | BETA: splitting (7) gives: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | (94) ~ (all_102_2 = e0) % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | REDUCE: (64), (94) imply: % 190.22/30.49 | | | | | | | | (95) ~ (all_10_2 = e0) % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | BETA: splitting (5) gives: % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | (96) (all_252_1 = e0 & op(e4, e3) = e0) | (all_252_3 = e0 & % 190.22/30.49 | | | | | | | | | op(e3, e3) = e0) % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | BETA: splitting (96) gives: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | (97) all_252_1 = e0 & op(e4, e3) = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | ALPHA: (97) implies: % 190.22/30.49 | | | | | | | | | | (98) op(e4, e3) = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | GROUND_INST: instantiating (4) with all_84_2, e0, e3, e4, % 190.22/30.49 | | | | | | | | | | simplifying with (24), (98) gives: % 190.22/30.49 | | | | | | | | | | (99) all_84_2 = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | REDUCE: (93), (99) imply: % 190.22/30.49 | | | | | | | | | | (100) $false % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | CLOSE: (100) is inconsistent. % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | (101) all_252_3 = e0 & op(e3, e3) = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | ALPHA: (101) implies: % 190.22/30.49 | | | | | | | | | | (102) op(e3, e3) = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | GROUND_INST: instantiating (4) with all_244_3, e0, e3, e3, % 190.22/30.49 | | | | | | | | | | simplifying with (12), (102) gives: % 190.22/30.49 | | | | | | | | | | (103) all_244_3 = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | REDUCE: (57), (103) imply: % 190.22/30.49 | | | | | | | | | | (104) op(e3, e0) = e3 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | REF_CLOSE: (4), (12), (18), (23), (31), (43), (68), (104) are % 190.22/30.49 | | | | | | | | | | inconsistent by sub-proof #313. % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | (105) (all_252_7 = e0 & op(e2, e3) = e0) | (all_252_13 = e0 % 190.22/30.49 | | | | | | | | | & op(e1, e3) = e0) | (all_252_21 = e0 & op(e0, e3) % 190.22/30.49 | | | | | | | | | = e0) % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | BETA: splitting (105) gives: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | (106) all_252_7 = e0 & op(e2, e3) = e0 % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | REF_CLOSE: (4), (22), (95), (106) are inconsistent by % 190.22/30.49 | | | | | | | | | | sub-proof #429. % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | (107) (all_252_13 = e0 & op(e1, e3) = e0) | (all_252_21 = % 190.22/30.49 | | | | | | | | | | e0 & op(e0, e3) = e0) % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | BETA: splitting (107) gives: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | (108) all_252_13 = e0 & op(e1, e3) = e0 % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | REF_CLOSE: (4), (14), (89), (108) are inconsistent by % 190.22/30.49 | | | | | | | | | | | sub-proof #319. % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | (109) all_252_21 = e0 & op(e0, e3) = e0 % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | ALPHA: (109) implies: % 190.22/30.49 | | | | | | | | | | | (110) op(e0, e3) = e0 % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | REF_CLOSE: (4), (20), (76), (110) are inconsistent by % 190.22/30.49 | | | | | | | | | | | sub-proof #402. % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | End of split % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | (111) all_102_2 = e0 % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | COMBINE_EQS: (64), (111) imply: % 190.22/30.49 | | | | | | | | (112) all_10_2 = e0 % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | SIMP: (112) implies: % 190.22/30.49 | | | | | | | | (113) all_10_2 = e0 % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | REDUCE: (56), (113) imply: % 190.22/30.49 | | | | | | | | (114) op(e2, e0) = e3 % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | REF_CLOSE: (4), (60), (91), (114) are inconsistent by sub-proof % 190.22/30.49 | | | | | | | | #566. % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | End of split % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | Case 2: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | (115) all_98_2 = e0 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | COMBINE_EQS: (41), (115) imply: % 190.22/30.49 | | | | | | | (116) all_84_2 = e0 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | REDUCE: (38), (116) imply: % 190.22/30.49 | | | | | | | (117) op(e4, e0) = e3 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | REF_CLOSE: (4), (26), (27), (117) are inconsistent by sub-proof % 190.22/30.49 | | | | | | | #539. % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | End of split % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | Case 2: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | (118) all_76_2 = e3 % 190.22/30.49 | | | | | | (119) op(e3, e2) = all_76_1 & $i(all_76_1) & ( ~ (all_76_1 = e4) % 190.22/30.49 | | | | | | | ( ~ (all_76_0 = e1) & op(e2, e4) = all_76_0 & % 190.22/30.49 | | | | | | $i(all_76_0))) % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | ALPHA: (119) implies: % 190.22/30.49 | | | | | | (120) op(e3, e2) = all_76_1 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | COMBINE_EQS: (21), (118) imply: % 190.22/30.49 | | | | | | (121) all_40_2 = e3 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | SIMP: (121) implies: % 190.22/30.49 | | | | | | (122) all_40_2 = e3 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | COMBINE_EQS: (19), (122) imply: % 190.22/30.49 | | | | | | (123) all_174_2 = e3 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | REDUCE: (61), (122) imply: % 190.22/30.49 | | | | | | (124) op(all_28_2, e3) = e2 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | REDUCE: (49), (122) imply: % 190.22/30.49 | | | | | | (125) op(e2, e3) = e0 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | BETA: splitting (6) gives: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | Case 1: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | (126) ~ (all_174_2 = e3) % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | REDUCE: (123), (126) imply: % 190.22/30.49 | | | | | | | (127) $false % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | CLOSE: (127) is inconsistent. % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | Case 2: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | (128) op(e3, e2) = all_174_1 & $i(all_174_1) & ( ~ (all_174_1 = % 190.22/30.49 | | | | | | | e1) | ( ~ (all_174_0 = e4) & op(e2, e1) = all_174_0 & % 190.22/30.49 | | | | | | | $i(all_174_0))) % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | ALPHA: (128) implies: % 190.22/30.49 | | | | | | | (129) op(e3, e2) = all_174_1 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | GROUND_INST: instantiating (4) with all_10_2, e0, e3, e2, % 190.22/30.49 | | | | | | | simplifying with (22), (125) gives: % 190.22/30.49 | | | | | | | (130) all_10_2 = e0 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | GROUND_INST: instantiating (4) with all_8_2, all_174_1, e2, e3, % 190.22/30.49 | | | | | | | simplifying with (47), (129) gives: % 190.22/30.49 | | | | | | | (131) all_174_1 = all_8_2 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | GROUND_INST: instantiating (4) with all_76_1, all_174_1, e2, e3, % 190.22/30.49 | | | | | | | simplifying with (120), (129) gives: % 190.22/30.49 | | | | | | | (132) all_174_1 = all_76_1 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | COMBINE_EQS: (131), (132) imply: % 190.22/30.49 | | | | | | | (133) all_76_1 = all_8_2 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | COMBINE_EQS: (64), (130) imply: % 190.22/30.49 | | | | | | | (134) all_102_2 = e0 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | COMBINE_EQS: (11), (130) imply: % 190.22/30.49 | | | | | | | (135) all_172_2 = e0 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | REDUCE: (58), (130) imply: % 190.22/30.49 | | | | | | | (136) ~ (all_244_8 = e0) % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | BETA: splitting (7) gives: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | (137) ~ (all_102_2 = e0) % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | REDUCE: (134), (137) imply: % 190.22/30.49 | | | | | | | | (138) $false % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | CLOSE: (138) is inconsistent. % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | (139) op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ (all_102_1 % 190.22/30.49 | | | | | | | | = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = % 190.22/30.49 | | | | | | | | all_102_0 & $i(all_102_0))) % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | ALPHA: (139) implies: % 190.22/30.49 | | | | | | | | (140) op(e0, e2) = all_102_1 % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | BETA: splitting (13) gives: % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | (141) ~ (all_172_2 = e0) % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | REDUCE: (135), (141) imply: % 190.22/30.49 | | | | | | | | | (142) $false % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | CLOSE: (142) is inconsistent. % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | (143) op(e0, e2) = all_172_1 & $i(all_172_1) & ( ~ % 190.22/30.49 | | | | | | | | | (all_172_1 = e1) | ( ~ (all_172_0 = e4) & op(e2, % 190.22/30.49 | | | | | | | | | e1) = all_172_0 & $i(all_172_0))) % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | ALPHA: (143) implies: % 190.22/30.49 | | | | | | | | | (144) op(e0, e2) = all_172_1 % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | BETA: splitting (48) gives: % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | (145) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = % 190.22/30.49 | | | | | | | | | | e0 & op(e3, e2) = e0) % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | REF_CLOSE: (4), (33), (45), (47), (78), (145) are % 190.22/30.49 | | | | | | | | | | inconsistent by sub-proof #546. % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | (146) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = % 190.22/30.49 | | | | | | | | | | e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, % 190.22/30.49 | | | | | | | | | | e2) = e0) % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | BETA: splitting (146) gives: % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | (147) all_252_8 = e0 & op(e2, e2) = e0 % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | ALPHA: (147) implies: % 190.22/30.49 | | | | | | | | | | | (148) op(e2, e2) = e0 % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | REF_CLOSE: (2), (4), (136), (148) are inconsistent by % 190.22/30.49 | | | | | | | | | | | sub-proof #448. % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | (149) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 % 190.22/30.49 | | | | | | | | | | | = e0 & op(e0, e2) = e0) % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | BETA: splitting (149) gives: % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | (150) all_252_14 = e0 & op(e1, e2) = e0 % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | ALPHA: (150) implies: % 190.22/30.49 | | | | | | | | | | | | (151) op(e1, e2) = e0 % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | REF_CLOSE: (4), (25), (77), (151) are inconsistent by % 190.22/30.49 | | | | | | | | | | | | sub-proof #545. % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | (152) all_252_22 = e0 & op(e0, e2) = e0 % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | ALPHA: (152) implies: % 190.22/30.49 | | | | | | | | | | | | (153) all_252_22 = e0 % 190.22/30.49 | | | | | | | | | | | | (154) op(e0, e2) = e0 % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | BETA: splitting (73) gives: % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | (155) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 % 190.22/30.49 | | | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | BETA: splitting (155) gives: % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | (156) all_252_20 = e2 & op(e0, e4) = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | ALPHA: (156) implies: % 190.22/30.49 | | | | | | | | | | | | | | (157) all_252_20 = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | COMBINE_EQS: (36), (157) imply: % 190.22/30.49 | | | | | | | | | | | | | | (158) e3 = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | SIMP: (158) implies: % 190.22/30.49 | | | | | | | | | | | | | | (159) e3 = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | REDUCE: (55), (159) imply: % 190.22/30.49 | | | | | | | | | | | | | | (160) $false % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | CLOSE: (160) is inconsistent. % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | (161) all_252_21 = e2 & op(e0, e3) = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | ALPHA: (161) implies: % 190.22/30.49 | | | | | | | | | | | | | | (162) op(e0, e3) = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | REF_CLOSE: (4), (59), (76), (162) are inconsistent by % 190.22/30.49 | | | | | | | | | | | | | | sub-proof #330. % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | (163) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 % 190.22/30.49 | | | | | | | | | | | | | = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 190.22/30.49 | | | | | | | | | | | | | op(e0, e0) = e2) % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | BETA: splitting (163) gives: % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | (164) all_252_22 = e2 & op(e0, e2) = e2 % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | REF_CLOSE: (71), (153), (164) are inconsistent by sub-proof % 190.22/30.49 | | | | | | | | | | | | | | #541. % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | (165) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 % 190.22/30.49 | | | | | | | | | | | | | | = e2 & op(e0, e0) = e2) % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | BETA: splitting (165) gives: % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | Case 1: % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | (166) all_252_23 = e2 & op(e0, e1) = e2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | REF_CLOSE: (4), (35), (87), (166) are inconsistent by % 190.22/30.49 | | | | | | | | | | | | | | | sub-proof #540. % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | Case 2: % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | (167) all_252_24 = e2 & op(e0, e0) = e2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | ALPHA: (167) implies: % 190.22/30.49 | | | | | | | | | | | | | | | (168) op(e0, e0) = e2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_244_24, e2, e0, e0, % 190.22/30.49 | | | | | | | | | | | | | | | simplifying with (34), (168) gives: % 190.22/30.49 | | | | | | | | | | | | | | | (169) all_244_24 = e2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with e0, all_102_1, e2, e0, % 190.22/30.49 | | | | | | | | | | | | | | | simplifying with (140), (154) gives: % 190.22/30.49 | | | | | | | | | | | | | | | (170) all_102_1 = e0 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_28_2, all_172_1, e2, % 190.22/30.49 | | | | | | | | | | | | | | | e0, simplifying with (8), (144) gives: % 190.22/30.49 | | | | | | | | | | | | | | | (171) all_172_1 = all_28_2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_102_1, all_172_1, e2, % 190.22/30.49 | | | | | | | | | | | | | | | e0, simplifying with (140), (144) gives: % 190.22/30.49 | | | | | | | | | | | | | | | (172) all_172_1 = all_102_1 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | COMBINE_EQS: (171), (172) imply: % 190.22/30.49 | | | | | | | | | | | | | | | (173) all_102_1 = all_28_2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | SIMP: (173) implies: % 190.22/30.49 | | | | | | | | | | | | | | | (174) all_102_1 = all_28_2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | COMBINE_EQS: (170), (174) imply: % 190.22/30.49 | | | | | | | | | | | | | | | (175) all_28_2 = e0 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | REDUCE: (50), (169) imply: % 190.22/30.49 | | | | | | | | | | | | | | | (176) ~ (e4 = e2) % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | REDUCE: (124), (175) imply: % 190.22/30.49 | | | | | | | | | | | | | | | (177) op(e0, e3) = e2 % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | | REF_CLOSE: (4), (59), (76), (177) are inconsistent by % 190.22/30.49 | | | | | | | | | | | | | | | sub-proof #330. % 190.22/30.49 | | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | | % 190.22/30.49 | | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | | % 190.22/30.49 | | | | | | | | | End of split % 190.22/30.49 | | | | | | | | | % 190.22/30.49 | | | | | | | | End of split % 190.22/30.49 | | | | | | | | % 190.22/30.49 | | | | | | | End of split % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | End of split % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | End of split % 190.22/30.49 | | | | | % 190.22/30.49 | | | | Case 2: % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | (178) all_70_2 = e0 % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | COMBINE_EQS: (65), (178) imply: % 190.22/30.49 | | | | | (179) all_62_2 = e0 % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | SIMP: (179) implies: % 190.22/30.49 | | | | | (180) all_62_2 = e0 % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | REDUCE: (30), (180) imply: % 190.22/30.49 | | | | | (181) ~ (all_244_15 = e0) % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | REF_CLOSE: (1), (4), (8), (9), (16), (17), (34), (35), (36), (37), % 190.22/30.49 | | | | | (39), (44), (53), (54), (62), (70), (76), (79), (81), (84), % 190.22/30.49 | | | | | (85), (181) are inconsistent by sub-proof #310. % 190.22/30.49 | | | | | % 190.22/30.49 | | | | End of split % 190.22/30.49 | | | | % 190.22/30.49 | | | Case 2: % 190.22/30.49 | | | | % 190.22/30.49 | | | | (182) all_58_2 = e2 % 190.22/30.49 | | | | % 190.22/30.49 | | | | COMBINE_EQS: (29), (182) imply: % 190.22/30.49 | | | | (183) all_20_2 = e2 % 190.22/30.49 | | | | % 190.22/30.49 | | | | REDUCE: (40), (183) imply: % 190.22/30.49 | | | | (184) op(e0, e2) = e1 % 190.22/30.49 | | | | % 190.22/30.49 | | | | REF_CLOSE: (1), (4), (8), (184) are inconsistent by sub-proof #502. % 190.22/30.49 | | | | % 190.22/30.49 | | | End of split % 190.22/30.49 | | | % 190.22/30.49 | | Case 2: % 190.22/30.49 | | | % 190.22/30.49 | | | (185) all_38_2 = e0 % 190.22/30.49 | | | (186) op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e4) | ( ~ % 190.22/30.49 | | | (all_38_0 = e3) & op(e2, e4) = all_38_0 & $i(all_38_0))) % 190.22/30.49 | | | % 190.22/30.49 | | | ALPHA: (186) implies: % 190.22/30.49 | | | (187) op(e0, e2) = all_38_1 % 190.22/30.49 | | | % 190.22/30.49 | | | COMBINE_EQS: (74), (185) imply: % 190.22/30.49 | | | (188) all_188_2 = e0 % 190.22/30.49 | | | % 190.22/30.49 | | | REDUCE: (82), (185) imply: % 190.22/30.49 | | | (189) ~ (all_244_8 = e0) % 190.22/30.49 | | | % 190.22/30.49 | | | REDUCE: (15), (185) imply: % 190.22/30.49 | | | (190) op(e2, e0) = e1 % 190.22/30.49 | | | % 190.22/30.49 | | | BETA: splitting (67) gives: % 190.22/30.49 | | | % 190.22/30.49 | | | Case 1: % 190.22/30.49 | | | | % 190.22/30.49 | | | | (191) ~ (all_188_2 = e0) % 190.22/30.49 | | | | % 190.22/30.49 | | | | REDUCE: (188), (191) imply: % 190.22/30.49 | | | | (192) $false % 190.22/30.49 | | | | % 190.22/30.49 | | | | CLOSE: (192) is inconsistent. % 190.22/30.49 | | | | % 190.22/30.49 | | | Case 2: % 190.22/30.49 | | | | % 190.22/30.49 | | | | (193) op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ (all_188_1 = e3) | % 190.22/30.49 | | | | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.22/30.49 | | | | $i(all_188_0))) % 190.22/30.49 | | | | % 190.22/30.49 | | | | ALPHA: (193) implies: % 190.22/30.49 | | | | (194) op(e0, e2) = all_188_1 % 190.22/30.49 | | | | % 190.22/30.49 | | | | BETA: splitting (48) gives: % 190.22/30.49 | | | | % 190.22/30.49 | | | | Case 1: % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | (195) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 190.22/30.49 | | | | | e2) = e0) % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | REF_CLOSE: (4), (33), (45), (47), (78), (195) are inconsistent by % 190.22/30.49 | | | | | sub-proof #546. % 190.22/30.49 | | | | | % 190.22/30.49 | | | | Case 2: % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | (196) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & % 190.22/30.49 | | | | | op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | BETA: splitting (196) gives: % 190.22/30.49 | | | | | % 190.22/30.49 | | | | | Case 1: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | (197) all_252_8 = e0 & op(e2, e2) = e0 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | ALPHA: (197) implies: % 190.22/30.49 | | | | | | (198) op(e2, e2) = e0 % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | REF_CLOSE: (2), (4), (189), (198) are inconsistent by sub-proof % 190.22/30.49 | | | | | | #448. % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | Case 2: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | (199) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 190.22/30.49 | | | | | | op(e0, e2) = e0) % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | BETA: splitting (199) gives: % 190.22/30.49 | | | | | | % 190.22/30.49 | | | | | | Case 1: % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | (200) all_252_14 = e0 & op(e1, e2) = e0 % 190.22/30.49 | | | | | | | % 190.22/30.49 | | | | | | | ALPHA: (200) implies: % 190.22/30.50 | | | | | | | (201) op(e1, e2) = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | REF_CLOSE: (4), (25), (77), (201) are inconsistent by sub-proof % 190.22/30.50 | | | | | | | #545. % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | Case 2: % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | (202) all_252_22 = e0 & op(e0, e2) = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | ALPHA: (202) implies: % 190.22/30.50 | | | | | | | (203) op(e0, e2) = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | GROUND_INST: instantiating (4) with e0, all_38_1, e2, e0, % 190.22/30.50 | | | | | | | simplifying with (187), (203) gives: % 190.22/30.50 | | | | | | | (204) all_38_1 = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | GROUND_INST: instantiating (4) with all_28_2, all_188_1, e2, e0, % 190.22/30.50 | | | | | | | simplifying with (8), (194) gives: % 190.22/30.50 | | | | | | | (205) all_188_1 = all_28_2 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | GROUND_INST: instantiating (4) with all_38_1, all_188_1, e2, e0, % 190.22/30.50 | | | | | | | simplifying with (187), (194) gives: % 190.22/30.50 | | | | | | | (206) all_188_1 = all_38_1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | GROUND_INST: instantiating (4) with all_40_2, e1, e0, e2, % 190.22/30.50 | | | | | | | simplifying with (60), (190) gives: % 190.22/30.50 | | | | | | | (207) all_40_2 = e1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | COMBINE_EQS: (205), (206) imply: % 190.22/30.50 | | | | | | | (208) all_38_1 = all_28_2 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | SIMP: (208) implies: % 190.22/30.50 | | | | | | | (209) all_38_1 = all_28_2 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | COMBINE_EQS: (204), (209) imply: % 190.22/30.50 | | | | | | | (210) all_28_2 = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | REDUCE: (46), (207) imply: % 190.22/30.50 | | | | | | | (211) ~ (all_244_24 = e1) % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | REDUCE: (61), (207), (210) imply: % 190.22/30.50 | | | | | | | (212) op(e0, e1) = e2 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | BETA: splitting (39) gives: % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | Case 1: % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | | (213) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 % 190.22/30.50 | | | | | | | | & op(e0, e3) = e1) % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | | REF_CLOSE: (4), (36), (70), (76), (81), (213) are inconsistent % 190.22/30.50 | | | | | | | | by sub-proof #309. % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | Case 2: % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | | (214) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 % 190.22/30.50 | | | | | | | | & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = % 190.22/30.50 | | | | | | | | e1) % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | | BETA: splitting (214) gives: % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | | Case 1: % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | | (215) all_252_22 = e1 & op(e0, e2) = e1 % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | | ALPHA: (215) implies: % 190.22/30.50 | | | | | | | | | (216) op(e0, e2) = e1 % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | | REF_CLOSE: (1), (4), (8), (216) are inconsistent by sub-proof % 190.22/30.50 | | | | | | | | | #502. % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | Case 2: % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | | (217) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = % 190.22/30.50 | | | | | | | | | e1 & op(e0, e0) = e1) % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | | REF_CLOSE: (4), (10), (34), (35), (211), (212), (217) are % 190.22/30.50 | | | | | | | | | inconsistent by sub-proof #473. % 190.22/30.50 | | | | | | | | | % 190.22/30.50 | | | | | | | | End of split % 190.22/30.50 | | | | | | | | % 190.22/30.50 | | | | | | | End of split % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | End of split % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | End of split % 190.22/30.50 | | | | | % 190.22/30.50 | | | | End of split % 190.22/30.50 | | | | % 190.22/30.50 | | | End of split % 190.22/30.50 | | | % 190.22/30.50 | | End of split % 190.22/30.50 | | % 190.22/30.50 | Case 2: % 190.22/30.50 | | % 190.22/30.50 | | (218) all_36_2 = e0 % 190.22/30.50 | | (219) op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ (all_36_1 = e4) | ( ~ % 190.22/30.50 | | (all_36_0 = e2) & op(e3, e4) = all_36_0 & $i(all_36_0))) % 190.22/30.50 | | % 190.22/30.50 | | ALPHA: (219) implies: % 190.22/30.50 | | (220) op(e0, e3) = all_36_1 % 190.22/30.50 | | (221) ~ (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 190.22/30.50 | | $i(all_36_0)) % 190.22/30.50 | | % 190.22/30.50 | | COMBINE_EQS: (63), (218) imply: % 190.22/30.50 | | (222) all_46_2 = e0 % 190.22/30.50 | | % 190.22/30.50 | | REDUCE: (69), (218) imply: % 190.22/30.50 | | (223) op(e3, e0) = e1 % 190.22/30.50 | | % 190.22/30.50 | | BETA: splitting (32) gives: % 190.22/30.50 | | % 190.22/30.50 | | Case 1: % 190.22/30.50 | | | % 190.22/30.50 | | | (224) ~ (all_46_2 = e0) % 190.22/30.50 | | | % 190.22/30.50 | | | REDUCE: (222), (224) imply: % 190.22/30.50 | | | (225) $false % 190.22/30.50 | | | % 190.22/30.50 | | | CLOSE: (225) is inconsistent. % 190.22/30.50 | | | % 190.22/30.50 | | Case 2: % 190.22/30.50 | | | % 190.22/30.50 | | | (226) op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ (all_46_1 = e2) | ( ~ % 190.22/30.50 | | | (all_46_0 = e4) & op(e3, e2) = all_46_0 & $i(all_46_0))) % 190.22/30.50 | | | % 190.22/30.50 | | | ALPHA: (226) implies: % 190.22/30.50 | | | (227) op(e0, e3) = all_46_1 % 190.22/30.50 | | | % 190.22/30.50 | | | GROUND_INST: instantiating (4) with e4, all_46_1, e3, e0, simplifying with % 190.22/30.50 | | | (76), (227) gives: % 190.22/30.50 | | | (228) all_46_1 = e4 % 190.22/30.50 | | | % 190.22/30.50 | | | GROUND_INST: instantiating (4) with all_36_1, all_46_1, e3, e0, % 190.22/30.50 | | | simplifying with (220), (227) gives: % 190.22/30.50 | | | (229) all_46_1 = all_36_1 % 190.22/30.50 | | | % 190.22/30.50 | | | GROUND_INST: instantiating (4) with all_12_1, e1, e0, e3, simplifying with % 190.22/30.50 | | | (18), (223) gives: % 190.22/30.50 | | | (230) all_12_1 = e1 % 190.22/30.50 | | | % 190.22/30.50 | | | COMBINE_EQS: (228), (229) imply: % 190.22/30.50 | | | (231) all_36_1 = e4 % 190.22/30.50 | | | % 190.22/30.50 | | | SIMP: (231) implies: % 190.22/30.50 | | | (232) all_36_1 = e4 % 190.22/30.50 | | | % 190.22/30.50 | | | REDUCE: (23), (230) imply: % 190.22/30.50 | | | (233) op(e1, e4) = e0 % 190.22/30.50 | | | % 190.22/30.50 | | | BETA: splitting (221) gives: % 190.22/30.50 | | | % 190.22/30.50 | | | Case 1: % 190.22/30.50 | | | | % 190.22/30.50 | | | | (234) ~ (all_36_1 = e4) % 190.22/30.50 | | | | % 190.22/30.50 | | | | REDUCE: (232), (234) imply: % 190.22/30.50 | | | | (235) $false % 190.22/30.50 | | | | % 190.22/30.50 | | | | CLOSE: (235) is inconsistent. % 190.22/30.50 | | | | % 190.22/30.50 | | | Case 2: % 190.22/30.50 | | | | % 190.22/30.50 | | | | % 190.22/30.50 | | | | GROUND_INST: instantiating (4) with all_16_2, e0, e4, e1, simplifying % 190.22/30.50 | | | | with (51), (233) gives: % 190.22/30.50 | | | | (236) all_16_2 = e0 % 190.22/30.50 | | | | % 190.22/30.50 | | | | REDUCE: (52), (236) imply: % 190.22/30.50 | | | | (237) op(e1, e0) = e4 % 190.22/30.50 | | | | % 190.22/30.50 | | | | REF_CLOSE: (4), (72), (75), (237) are inconsistent by sub-proof #571. % 190.22/30.50 | | | | % 190.22/30.50 | | | End of split % 190.22/30.50 | | | % 190.22/30.50 | | End of split % 190.22/30.50 | | % 190.22/30.50 | End of split % 190.22/30.50 | % 190.22/30.50 End of proof % 190.22/30.50 % 190.22/30.50 Sub-proof #309 shows that the following formulas are inconsistent: % 190.22/30.50 ---------------------------------------------------------------- % 190.22/30.50 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.50 (2) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 190.22/30.50 (3) all_252_20 = e3 % 190.22/30.50 (4) ~ (e3 = e1) % 190.22/30.50 (5) op(e0, e3) = e4 % 190.22/30.50 (6) ~ (e4 = e1) % 190.22/30.50 % 190.22/30.50 Begin of proof % 190.22/30.50 | % 190.22/30.50 | BETA: splitting (2) gives: % 190.22/30.50 | % 190.22/30.50 | Case 1: % 190.22/30.50 | | % 190.22/30.50 | | (7) all_252_20 = e1 & op(e0, e4) = e1 % 190.22/30.50 | | % 190.22/30.50 | | ALPHA: (7) implies: % 190.22/30.50 | | (8) all_252_20 = e1 % 190.22/30.50 | | % 190.22/30.50 | | COMBINE_EQS: (3), (8) imply: % 190.22/30.50 | | (9) e3 = e1 % 190.22/30.50 | | % 190.22/30.50 | | REDUCE: (4), (9) imply: % 190.22/30.50 | | (10) $false % 190.22/30.50 | | % 190.22/30.50 | | CLOSE: (10) is inconsistent. % 190.22/30.50 | | % 190.22/30.50 | Case 2: % 190.22/30.50 | | % 190.22/30.50 | | (11) all_252_21 = e1 & op(e0, e3) = e1 % 190.22/30.50 | | % 190.22/30.50 | | REF_CLOSE: (1), (5), (6), (11) are inconsistent by sub-proof #311. % 190.22/30.50 | | % 190.22/30.50 | End of split % 190.22/30.50 | % 190.22/30.50 End of proof % 190.22/30.50 % 190.22/30.50 Sub-proof #310 shows that the following formulas are inconsistent: % 190.22/30.50 ---------------------------------------------------------------- % 190.22/30.50 (1) ~ (all_28_2 = e1) % 190.22/30.50 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.50 (3) ~ (all_36_2 = e0) % 190.22/30.50 (4) op(e0, e2) = all_28_2 % 190.22/30.50 (5) op(e3, e1) = all_36_2 % 190.22/30.50 (6) ~ (all_26_2 = e0) % 190.22/30.50 (7) op(e1, e1) = all_244_15 % 190.22/30.50 (8) op(e0, e0) = all_244_24 % 190.22/30.50 (9) op(e0, e1) = all_20_2 % 190.22/30.50 (10) all_252_20 = e3 % 190.22/30.50 (11) op(all_244_24, all_244_24) = e0 % 190.22/30.50 (12) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 190.22/30.50 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 190.22/30.50 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.22/30.50 (13) ~ (all_38_2 = e0) % 190.22/30.50 (14) op(e4, e1) = all_26_2 % 190.22/30.50 (15) ~ (all_244_15 = e0) % 190.22/30.50 (16) ~ (all_244_15 = all_20_2) % 190.22/30.50 (17) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.22/30.50 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.22/30.50 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.22/30.50 (18) ~ (e1 = e0) % 190.22/30.50 (19) ~ (e3 = e1) % 190.22/30.50 (20) op(e0, e3) = e4 % 190.22/30.50 (21) op(e2, e1) = all_38_2 % 190.22/30.50 (22) ~ (e4 = e1) % 190.22/30.50 % 190.22/30.50 Begin of proof % 190.22/30.50 | % 190.22/30.50 | BETA: splitting (17) gives: % 190.22/30.50 | % 190.22/30.50 | Case 1: % 190.22/30.50 | | % 190.22/30.50 | | (23) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = % 190.22/30.50 | | e0) % 190.22/30.50 | | % 190.22/30.50 | | REF_CLOSE: (2), (3), (5), (6), (14), (23) are inconsistent by sub-proof % 190.22/30.50 | | #451. % 190.22/30.50 | | % 190.22/30.50 | Case 2: % 190.22/30.50 | | % 190.22/30.50 | | (24) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) % 190.22/30.50 | | = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.22/30.50 | | % 190.22/30.50 | | BETA: splitting (24) gives: % 190.22/30.50 | | % 190.22/30.50 | | Case 1: % 190.22/30.50 | | | % 190.22/30.50 | | | (25) all_252_11 = e0 & op(e2, e1) = e0 % 190.22/30.50 | | | % 190.22/30.50 | | | ALPHA: (25) implies: % 190.22/30.50 | | | (26) op(e2, e1) = e0 % 190.22/30.50 | | | % 190.22/30.50 | | | REF_CLOSE: (2), (13), (21), (26) are inconsistent by sub-proof #549. % 190.22/30.50 | | | % 190.22/30.50 | | Case 2: % 190.22/30.50 | | | % 190.22/30.50 | | | (27) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, % 190.22/30.50 | | | e1) = e0) % 190.22/30.50 | | | % 190.22/30.50 | | | BETA: splitting (27) gives: % 190.22/30.50 | | | % 190.22/30.50 | | | Case 1: % 190.22/30.50 | | | | % 190.22/30.50 | | | | (28) all_252_15 = e0 & op(e1, e1) = e0 % 190.22/30.50 | | | | % 190.22/30.50 | | | | ALPHA: (28) implies: % 190.22/30.50 | | | | (29) op(e1, e1) = e0 % 190.22/30.50 | | | | % 190.22/30.50 | | | | REF_CLOSE: (2), (7), (15), (29) are inconsistent by sub-proof #440. % 190.22/30.50 | | | | % 190.22/30.50 | | | Case 2: % 190.22/30.50 | | | | % 190.22/30.50 | | | | (30) all_252_23 = e0 & op(e0, e1) = e0 % 190.22/30.50 | | | | % 190.22/30.50 | | | | ALPHA: (30) implies: % 190.22/30.50 | | | | (31) all_252_23 = e0 % 190.22/30.50 | | | | (32) op(e0, e1) = e0 % 190.22/30.50 | | | | % 190.22/30.50 | | | | BETA: splitting (12) gives: % 190.22/30.50 | | | | % 190.22/30.50 | | | | Case 1: % 190.22/30.50 | | | | | % 190.22/30.50 | | | | | (33) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & % 190.22/30.50 | | | | | op(e0, e3) = e1) % 190.22/30.50 | | | | | % 190.22/30.50 | | | | | BETA: splitting (33) gives: % 190.22/30.50 | | | | | % 190.22/30.50 | | | | | Case 1: % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | (34) all_252_20 = e1 & op(e0, e4) = e1 % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | ALPHA: (34) implies: % 190.22/30.50 | | | | | | (35) all_252_20 = e1 % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | REF_CLOSE: (10), (19), (35) are inconsistent by sub-proof #312. % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | Case 2: % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | (36) all_252_21 = e1 & op(e0, e3) = e1 % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | REF_CLOSE: (2), (20), (22), (36) are inconsistent by sub-proof #311. % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | End of split % 190.22/30.50 | | | | | % 190.22/30.50 | | | | Case 2: % 190.22/30.50 | | | | | % 190.22/30.50 | | | | | (37) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & % 190.22/30.50 | | | | | op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.22/30.50 | | | | | % 190.22/30.50 | | | | | BETA: splitting (37) gives: % 190.22/30.50 | | | | | % 190.22/30.50 | | | | | Case 1: % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | (38) all_252_22 = e1 & op(e0, e2) = e1 % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | ALPHA: (38) implies: % 190.22/30.50 | | | | | | (39) op(e0, e2) = e1 % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | REF_CLOSE: (1), (2), (4), (39) are inconsistent by sub-proof #502. % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | Case 2: % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | (40) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & % 190.22/30.50 | | | | | | op(e0, e0) = e1) % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | BETA: splitting (40) gives: % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | | Case 1: % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | (41) all_252_23 = e1 & op(e0, e1) = e1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | ALPHA: (41) implies: % 190.22/30.50 | | | | | | | (42) all_252_23 = e1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | REF_CLOSE: (18), (31), (42) are inconsistent by sub-proof #351. % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | Case 2: % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | (43) all_252_24 = e1 & op(e0, e0) = e1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | ALPHA: (43) implies: % 190.22/30.50 | | | | | | | (44) op(e0, e0) = e1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | GROUND_INST: instantiating (2) with all_244_24, e1, e0, e0, % 190.22/30.50 | | | | | | | simplifying with (8), (44) gives: % 190.22/30.50 | | | | | | | (45) all_244_24 = e1 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | GROUND_INST: instantiating (2) with all_20_2, e0, e1, e0, % 190.22/30.50 | | | | | | | simplifying with (9), (32) gives: % 190.22/30.50 | | | | | | | (46) all_20_2 = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | REDUCE: (11), (45) imply: % 190.22/30.50 | | | | | | | (47) op(e1, e1) = e0 % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | | REF_CLOSE: (2), (7), (15), (47) are inconsistent by sub-proof % 190.22/30.50 | | | | | | | #440. % 190.22/30.50 | | | | | | | % 190.22/30.50 | | | | | | End of split % 190.22/30.50 | | | | | | % 190.22/30.50 | | | | | End of split % 190.22/30.50 | | | | | % 190.22/30.50 | | | | End of split % 190.22/30.50 | | | | % 190.22/30.50 | | | End of split % 190.22/30.50 | | | % 190.22/30.50 | | End of split % 190.22/30.50 | | % 190.22/30.50 | End of split % 190.22/30.50 | % 190.22/30.50 End of proof % 190.22/30.50 % 190.22/30.50 Sub-proof #311 shows that the following formulas are inconsistent: % 190.22/30.50 ---------------------------------------------------------------- % 190.22/30.50 (1) all_252_21 = e1 & op(e0, e3) = e1 % 190.22/30.50 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.50 (3) op(e0, e3) = e4 % 190.22/30.50 (4) ~ (e4 = e1) % 190.22/30.50 % 190.22/30.50 Begin of proof % 190.22/30.50 | % 190.22/30.50 | ALPHA: (1) implies: % 190.22/30.50 | (5) op(e0, e3) = e1 % 190.22/30.50 | % 190.22/30.50 | GROUND_INST: instantiating (2) with e4, e1, e3, e0, simplifying with (3), (5) % 190.22/30.50 | gives: % 190.22/30.50 | (6) e4 = e1 % 190.22/30.50 | % 190.22/30.50 | REDUCE: (4), (6) imply: % 190.22/30.50 | (7) $false % 190.22/30.50 | % 190.22/30.50 | CLOSE: (7) is inconsistent. % 190.22/30.50 | % 190.22/30.50 End of proof % 190.22/30.50 % 190.22/30.50 Sub-proof #312 shows that the following formulas are inconsistent: % 190.22/30.50 ---------------------------------------------------------------- % 190.22/30.50 (1) all_252_20 = e3 % 190.22/30.50 (2) all_252_20 = e1 % 190.22/30.50 (3) ~ (e3 = e1) % 190.22/30.50 % 190.22/30.50 Begin of proof % 190.22/30.50 | % 190.22/30.50 | COMBINE_EQS: (1), (2) imply: % 190.22/30.50 | (4) e3 = e1 % 190.22/30.50 | % 190.22/30.50 | SIMP: (4) implies: % 190.22/30.50 | (5) e3 = e1 % 190.22/30.50 | % 190.22/30.50 | REDUCE: (3), (5) imply: % 190.22/30.50 | (6) $false % 190.22/30.50 | % 190.22/30.50 | CLOSE: (6) is inconsistent. % 190.22/30.50 | % 190.22/30.50 End of proof % 190.22/30.50 % 190.22/30.50 Sub-proof #313 shows that the following formulas are inconsistent: % 190.22/30.50 ---------------------------------------------------------------- % 190.22/30.50 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.50 (2) op(e3, e3) = all_244_3 % 190.22/30.50 (3) op(e3, e0) = all_12_1 % 190.22/30.50 (4) op(all_12_1, e4) = e0 % 190.22/30.50 (5) op(e3, e4) = all_100_2 % 190.22/30.50 (6) ~ (all_244_3 = all_100_2) % 190.22/30.50 (7) op(e3, all_12_1) = e0 % 190.22/30.50 (8) op(e3, e0) = e3 % 190.22/30.50 % 190.22/30.50 Begin of proof % 190.22/30.50 | % 190.22/30.50 | GROUND_INST: instantiating (1) with all_12_1, e3, e0, e3, simplifying with % 190.22/30.50 | (3), (8) gives: % 190.22/30.50 | (9) all_12_1 = e3 % 190.22/30.50 | % 190.22/30.50 | REDUCE: (4), (9) imply: % 190.22/30.50 | (10) op(e3, e4) = e0 % 190.22/30.50 | % 190.22/30.50 | REDUCE: (7), (9) imply: % 190.22/30.50 | (11) op(e3, e3) = e0 % 190.22/30.50 | % 190.22/30.50 | GROUND_INST: instantiating (1) with all_244_3, e0, e3, e3, simplifying with % 190.22/30.50 | (2), (11) gives: % 190.22/30.50 | (12) all_244_3 = e0 % 190.22/30.50 | % 190.22/30.50 | GROUND_INST: instantiating (1) with all_100_2, e0, e4, e3, simplifying with % 190.22/30.50 | (5), (10) gives: % 190.22/30.50 | (13) all_100_2 = e0 % 190.22/30.50 | % 190.22/30.50 | REDUCE: (6), (12), (13) imply: % 190.22/30.50 | (14) $false % 190.22/30.50 | % 190.22/30.50 | CLOSE: (14) is inconsistent. % 190.22/30.50 | % 190.22/30.50 End of proof % 190.22/30.50 % 190.22/30.50 Sub-proof #314 shows that the following formulas are inconsistent: % 190.22/30.50 ---------------------------------------------------------------- % 190.22/30.50 (1) ~ (all_26_2 = e0) | (op(e0, e4) = all_26_1 & $i(all_26_1) & ( ~ % 190.22/30.50 (all_26_1 = e3) | ( ~ (all_26_0 = e2) & op(e4, e3) = all_26_0 & % 190.22/30.50 $i(all_26_0)))) % 190.22/30.50 (2) ~ (all_48_2 = all_36_2) % 190.22/30.50 (3) ~ (all_144_2 = e3) | (op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ % 190.22/30.50 (all_144_1 = e0) | ( ~ (all_144_0 = e2) & op(e1, e0) = all_144_0 & % 190.22/30.50 $i(all_144_0)))) % 190.22/30.50 (4) ~ (all_28_2 = e1) % 190.22/30.50 (5) op(e2, e2) = all_244_8 % 190.22/30.50 (6) ~ (all_84_2 = all_22_2) % 190.22/30.50 (7) ~ (all_36_2 = e0) | (op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 190.22/30.50 (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 190.22/30.50 $i(all_36_0)))) % 190.22/30.50 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.50 (9) ~ (all_180_2 = e4) | (op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 190.22/30.50 (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 190.22/30.50 $i(all_180_0)))) % 190.22/30.50 (10) ~ (all_16_2 = e3) | (op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ % 190.22/30.50 (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 & % 190.22/30.50 $i(all_16_0)))) % 190.22/30.50 (11) op(e0, e2) = all_28_2 % 190.22/30.50 (12) op(all_26_2, all_16_2) = e1 % 190.22/30.50 (13) op(e3, e1) = all_36_2 % 190.22/30.50 (14) ~ (all_166_2 = e0) | (op(e0, e1) = all_166_1 & $i(all_166_1) & ( ~ % 190.22/30.50 (all_166_1 = e4) | ( ~ (all_166_0 = e2) & op(e1, e4) = all_166_0 & % 190.22/30.50 $i(all_166_0)))) % 190.22/30.50 (15) ~ (e2 = e1) % 190.22/30.50 (16) all_250_21 = all_22_2 % 190.22/30.50 (17) all_130_2 = all_62_2 % 190.22/30.50 (18) op(e3, e3) = all_244_3 % 190.22/30.50 (19) all_166_2 = all_62_2 % 190.22/30.50 (20) ~ (all_244_24 = all_22_2) % 190.22/30.50 (21) op(e1, e3) = all_62_2 % 190.22/30.50 (22) ~ (all_30_2 = e3) | (op(e3, e4) = all_30_1 & $i(all_30_1) & ( ~ % 190.22/30.50 (all_30_1 = e2) | ( ~ (all_30_0 = e1) & op(e4, e2) = all_30_0 & % 190.22/30.50 $i(all_30_0)))) % 190.22/30.50 (23) ~ (all_24_2 = e2) | (op(e2, e1) = all_24_1 & $i(all_24_1) & ( ~ % 190.22/30.50 (all_24_1 = e3) | ( ~ (all_24_0 = e0) & op(e1, e3) = all_24_0 & % 190.22/30.50 $i(all_24_0)))) % 190.22/30.50 (24) op(e2, all_38_2) = e1 % 190.22/30.50 (25) op(e1, e1) = all_244_15 % 190.22/30.50 (26) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 190.22/30.50 (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 190.22/30.50 $i(all_158_0)))) % 190.22/30.50 (27) op(all_62_2, all_36_2) = e3 % 190.22/30.50 (28) all_24_2 = all_16_2 % 190.22/30.50 (29) ~ (e4 = e0) % 190.22/30.50 (30) op(e2, e3) = all_10_2 % 190.22/30.50 (31) ~ (all_244_15 = all_36_2) % 190.22/30.50 (32) all_158_2 = all_28_2 % 190.22/30.50 (33) op(e4, e3) = all_84_2 % 190.22/30.50 (34) ~ (all_4_2 = e0) % 190.22/30.50 (35) ~ (all_42_2 = e1) | (op(e1, e0) = all_42_1 & $i(all_42_1) & ( ~ % 190.22/30.50 (all_42_1 = e3) | ( ~ (all_42_0 = e2) & op(e0, e3) = all_42_0 & % 190.22/30.50 $i(all_42_0)))) % 190.22/30.50 (36) op(e0, e1) = e4 % 190.22/30.50 (37) all_92_2 = all_20_2 % 190.22/30.50 (38) ~ (all_192_2 = e4) | (op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 190.22/30.50 (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, e3) = all_192_0 & % 190.22/30.50 $i(all_192_0)))) % 190.22/30.50 (39) ~ (all_64_2 = all_16_2) % 190.22/30.50 (40) ~ (all_22_2 = e2) | (op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ % 190.22/30.50 (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & % 190.22/30.50 $i(all_22_0)))) % 190.22/30.50 (41) op(e4, e0) = all_30_2 % 190.22/30.50 (42) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = % 190.22/30.50 e0) | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, % 190.22/30.50 e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 190.22/30.50 (43) ~ (all_244_24 = all_20_2) % 190.22/30.50 (44) ~ (all_114_2 = e4) | (op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ % 190.22/30.50 (all_114_1 = e0) | ( ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 & % 190.22/30.50 $i(all_114_0)))) % 190.22/30.50 (45) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.22/30.50 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.22/30.50 $i(all_38_0)))) % 190.22/30.50 (46) ~ (all_66_2 = e0) | (op(e0, e1) = all_66_1 & $i(all_66_1) & ( ~ % 190.22/30.50 (all_66_1 = e3) | ( ~ (all_66_0 = e2) & op(e1, e3) = all_66_0 & % 190.22/30.50 $i(all_66_0)))) % 190.22/30.50 (47) ~ (all_28_2 = all_20_2) % 190.22/30.50 (48) op(e3, e4) = all_100_2 % 190.22/30.50 (49) ~ (all_8_2 = e0) % 190.22/30.50 (50) op(e0, e0) = all_244_24 % 190.22/30.50 (51) all_66_2 = all_16_2 % 190.22/30.50 (52) ~ (all_92_2 = e4) | (op(e4, e0) = all_92_1 & $i(all_92_1) & ( ~ % 190.22/30.50 (all_92_1 = e3) | ( ~ (all_92_0 = e2) & op(e0, e3) = all_92_0 & % 190.22/30.50 $i(all_92_0)))) % 190.22/30.50 (53) op(e0, e1) = all_20_2 % 190.22/30.50 (54) op(e0, all_20_2) = e1 % 190.22/30.50 (55) all_250_15 = all_16_2 % 190.22/30.50 (56) ~ (all_32_2 = e4) | (op(e4, e0) = all_32_1 & $i(all_32_1) & ( ~ % 190.22/30.50 (all_32_1 = e2) | ( ~ (all_32_0 = e3) & op(e0, e2) = all_32_0 & % 190.22/30.50 $i(all_32_0)))) % 190.22/30.50 (57) ~ (all_16_2 = e1) % 190.22/30.50 (58) op(e4, e1) = all_26_2 % 190.22/30.50 (59) ~ (all_6_2 = e0) % 190.22/30.50 (60) op(e0, e3) = all_22_2 % 190.22/30.50 (61) op(e0, all_22_2) = e3 % 190.22/30.50 (62) op(e4, e4) = all_244_0 % 190.22/30.50 (63) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 | % 190.22/30.50 all_250_15 = e0 % 190.22/30.50 (64) all_192_2 = all_4_2 % 190.22/30.50 (65) ~ (all_244_0 = e1) % 190.22/30.50 (66) ~ (e3 = e0) % 190.22/30.51 (67) op(e3, e2) = all_8_2 % 190.22/30.51 (68) op(all_244_8, all_244_8) = e2 % 190.22/30.51 (69) op(all_244_15, all_244_15) = e1 % 190.22/30.51 (70) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.22/30.51 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.22/30.51 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.51 (71) op(e3, all_48_2) = e0 % 190.22/30.51 (72) ~ (all_244_3 = all_22_2) % 190.22/30.51 (73) all_42_2 = e1 % 190.22/30.51 (74) op(e1, all_16_2) = e4 % 190.22/30.51 (75) all_114_2 = all_62_2 % 190.22/30.51 (76) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 190.22/30.51 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 190.22/30.51 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.22/30.51 (77) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.22/30.51 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.22/30.51 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.22/30.51 (78) op(e4, all_30_2) = e0 % 190.22/30.51 (79) ~ (all_130_2 = e4) | (op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ % 190.22/30.51 (all_130_1 = e2) | ( ~ (all_130_0 = e0) & op(e1, e2) = all_130_0 & % 190.22/30.51 $i(all_130_0)))) % 190.22/30.51 (80) ~ (all_244_24 = all_28_2) % 190.22/30.51 (81) ~ (all_100_2 = all_16_2) % 190.22/30.51 (82) op(all_34_2, all_20_2) = e0 % 190.22/30.51 (83) op(e2, e4) = all_64_2 % 190.22/30.51 (84) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 190.22/30.51 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 190.22/30.51 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 190.22/30.51 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 190.22/30.51 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 190.22/30.51 op(e0, e1) = e0))) % 190.22/30.51 (85) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2) % 190.22/30.51 | (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 & op(e1, e4) = % 190.22/30.51 e2) | (all_252_20 = e2 & op(e0, e4) = e2) % 190.22/30.51 (86) ~ (e4 = e2) % 190.22/30.51 (87) op(e2, e0) = all_40_2 % 190.22/30.51 (88) op(all_28_2, all_40_2) = e2 % 190.22/30.51 (89) op(all_22_2, all_48_2) = e3 % 190.22/30.51 (90) op(e4, all_26_2) = e1 % 190.22/30.51 (91) op(all_20_2, all_34_2) = e1 % 190.22/30.51 (92) op(e3, e0) = all_48_2 % 190.22/30.51 (93) all_144_2 = all_16_2 % 190.22/30.51 (94) all_32_2 = all_20_2 % 190.22/30.51 (95) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.22/30.51 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.22/30.51 $i(all_188_0)))) % 190.22/30.51 (96) ~ (all_22_2 = e1) % 190.22/30.51 (97) op(e0, e4) = all_12_2 % 190.22/30.51 (98) op(e3, all_36_2) = e1 % 190.22/30.51 (99) ~ (all_244_0 = all_16_2) % 190.22/30.51 (100) ~ (e2 = e0) % 190.22/30.51 (101) op(e1, e0) = all_34_2 % 190.22/30.51 (102) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.22/30.51 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.22/30.51 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.22/30.51 (103) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | % 190.22/30.51 all_250_21 = e0 % 190.22/30.51 (104) all_188_2 = all_38_2 % 190.22/30.51 (105) ~ (all_244_24 = e1) % 190.22/30.51 (106) ~ (all_28_2 = all_22_2) % 190.22/30.51 (107) op(e1, e0) = all_14_1 % 190.22/30.51 (108) ~ (all_12_2 = e3) % 190.22/30.51 (109) all_180_2 = all_4_2 % 190.22/30.51 (110) ~ (all_34_2 = e4) | (op(e4, e1) = all_34_1 & $i(all_34_1) & ( ~ % 190.22/30.51 (all_34_1 = e2) | ( ~ (all_34_0 = e3) & op(e1, e2) = all_34_0 & % 190.22/30.51 $i(all_34_0)))) % 190.22/30.51 (111) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 190.22/30.51 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.22/30.51 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.22/30.51 (112) op(e1, e2) = all_4_2 % 190.22/30.51 (113) ~ (all_22_2 = all_20_2) % 190.22/30.51 (114) op(e4, e2) = all_6_2 % 190.22/30.51 (115) ~ (all_62_2 = all_22_2) % 190.22/30.51 (116) op(e2, e1) = all_38_2 % 190.22/30.51 (117) op(all_16_2, all_26_2) = e4 % 190.22/30.51 (118) ~ (all_244_8 = all_38_2) % 190.22/30.51 (119) ~ (all_22_2 = all_10_2) % 190.22/30.51 % 190.22/30.51 Begin of proof % 190.22/30.51 | % 190.22/30.51 | BETA: splitting (35) gives: % 190.22/30.51 | % 190.22/30.51 | Case 1: % 190.22/30.51 | | % 190.22/30.51 | | (120) ~ (all_42_2 = e1) % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (73), (120) imply: % 190.22/30.51 | | (121) $false % 190.22/30.51 | | % 190.22/30.51 | | CLOSE: (121) is inconsistent. % 190.22/30.51 | | % 190.22/30.51 | Case 2: % 190.22/30.51 | | % 190.22/30.51 | | (122) op(e1, e0) = all_42_1 & $i(all_42_1) & ( ~ (all_42_1 = e3) | ( ~ % 190.22/30.51 | | (all_42_0 = e2) & op(e0, e3) = all_42_0 & $i(all_42_0))) % 190.22/30.51 | | % 190.22/30.51 | | ALPHA: (122) implies: % 190.22/30.51 | | (123) op(e1, e0) = all_42_1 % 190.22/30.51 | | % 190.22/30.51 | | GROUND_INST: instantiating (8) with all_20_2, e4, e1, e0, simplifying with % 190.22/30.51 | | (36), (53) gives: % 190.22/30.51 | | (124) all_20_2 = e4 % 190.22/30.51 | | % 190.22/30.51 | | GROUND_INST: instantiating (8) with all_34_2, all_42_1, e0, e1, simplifying % 190.22/30.51 | | with (101), (123) gives: % 190.22/30.51 | | (125) all_42_1 = all_34_2 % 190.22/30.51 | | % 190.22/30.51 | | GROUND_INST: instantiating (8) with all_14_1, all_42_1, e0, e1, simplifying % 190.22/30.51 | | with (107), (123) gives: % 190.22/30.51 | | (126) all_42_1 = all_14_1 % 190.22/30.51 | | % 190.22/30.51 | | COMBINE_EQS: (125), (126) imply: % 190.22/30.51 | | (127) all_34_2 = all_14_1 % 190.22/30.51 | | % 190.22/30.51 | | SIMP: (127) implies: % 190.22/30.51 | | (128) all_34_2 = all_14_1 % 190.22/30.51 | | % 190.22/30.51 | | COMBINE_EQS: (94), (124) imply: % 190.22/30.51 | | (129) all_32_2 = e4 % 190.22/30.51 | | % 190.22/30.51 | | COMBINE_EQS: (37), (124) imply: % 190.22/30.51 | | (130) all_92_2 = e4 % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (43), (124) imply: % 190.22/30.51 | | (131) ~ (all_244_24 = e4) % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (47), (124) imply: % 190.22/30.51 | | (132) ~ (all_28_2 = e4) % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (113), (124) imply: % 190.22/30.51 | | (133) ~ (all_22_2 = e4) % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (82), (124), (128) imply: % 190.22/30.51 | | (134) op(all_14_1, e4) = e0 % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (91), (124), (128) imply: % 190.22/30.51 | | (135) op(e4, all_14_1) = e1 % 190.22/30.51 | | % 190.22/30.51 | | REDUCE: (54), (124) imply: % 190.22/30.51 | | (136) op(e0, e4) = e1 % 190.22/30.51 | | % 190.22/30.51 | | BETA: splitting (56) gives: % 190.22/30.51 | | % 190.22/30.51 | | Case 1: % 190.22/30.51 | | | % 190.22/30.51 | | | (137) ~ (all_32_2 = e4) % 190.22/30.51 | | | % 190.22/30.51 | | | REDUCE: (129), (137) imply: % 190.22/30.51 | | | (138) $false % 190.22/30.51 | | | % 190.22/30.51 | | | CLOSE: (138) is inconsistent. % 190.22/30.51 | | | % 190.22/30.51 | | Case 2: % 190.22/30.51 | | | % 190.22/30.51 | | | (139) op(e4, e0) = all_32_1 & $i(all_32_1) & ( ~ (all_32_1 = e2) | ( ~ % 190.22/30.51 | | | (all_32_0 = e3) & op(e0, e2) = all_32_0 & $i(all_32_0))) % 190.22/30.51 | | | % 190.22/30.51 | | | ALPHA: (139) implies: % 190.22/30.51 | | | (140) op(e4, e0) = all_32_1 % 190.22/30.51 | | | % 190.22/30.51 | | | BETA: splitting (52) gives: % 190.22/30.51 | | | % 190.22/30.51 | | | Case 1: % 190.22/30.51 | | | | % 190.22/30.51 | | | | (141) ~ (all_92_2 = e4) % 190.22/30.51 | | | | % 190.22/30.51 | | | | REDUCE: (130), (141) imply: % 190.22/30.51 | | | | (142) $false % 190.22/30.51 | | | | % 190.22/30.51 | | | | CLOSE: (142) is inconsistent. % 190.22/30.51 | | | | % 190.22/30.51 | | | Case 2: % 190.22/30.51 | | | | % 190.22/30.51 | | | | (143) op(e4, e0) = all_92_1 & $i(all_92_1) & ( ~ (all_92_1 = e3) | ( % 190.22/30.51 | | | | ~ (all_92_0 = e2) & op(e0, e3) = all_92_0 & $i(all_92_0))) % 190.22/30.51 | | | | % 190.22/30.51 | | | | ALPHA: (143) implies: % 190.22/30.51 | | | | (144) op(e4, e0) = all_92_1 % 190.22/30.51 | | | | (145) ~ (all_92_1 = e3) | ( ~ (all_92_0 = e2) & op(e0, e3) = % 190.22/30.51 | | | | all_92_0 & $i(all_92_0)) % 190.22/30.51 | | | | % 190.22/30.51 | | | | GROUND_INST: instantiating (8) with all_30_2, all_92_1, e0, e4, % 190.22/30.51 | | | | simplifying with (41), (144) gives: % 190.22/30.51 | | | | (146) all_92_1 = all_30_2 % 190.22/30.51 | | | | % 190.22/30.51 | | | | GROUND_INST: instantiating (8) with all_32_1, all_92_1, e0, e4, % 190.22/30.51 | | | | simplifying with (140), (144) gives: % 190.22/30.51 | | | | (147) all_92_1 = all_32_1 % 190.22/30.51 | | | | % 190.22/30.51 | | | | COMBINE_EQS: (146), (147) imply: % 190.22/30.51 | | | | (148) all_32_1 = all_30_2 % 190.22/30.51 | | | | % 190.22/30.51 | | | | SIMP: (148) implies: % 190.22/30.51 | | | | (149) all_32_1 = all_30_2 % 190.22/30.51 | | | | % 190.22/30.51 | | | | BETA: splitting (10) gives: % 190.22/30.51 | | | | % 190.22/30.51 | | | | Case 1: % 190.22/30.51 | | | | | % 190.22/30.51 | | | | | (150) ~ (all_16_2 = e3) % 190.22/30.51 | | | | | % 190.22/30.51 | | | | | BETA: splitting (40) gives: % 190.22/30.51 | | | | | % 190.22/30.51 | | | | | Case 1: % 190.22/30.51 | | | | | | % 190.22/30.51 | | | | | | (151) ~ (all_22_2 = e2) % 190.22/30.51 | | | | | | % 190.22/30.51 | | | | | | BETA: splitting (23) gives: % 190.22/30.51 | | | | | | % 190.22/30.51 | | | | | | Case 1: % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | (152) ~ (all_24_2 = e2) % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | REDUCE: (28), (152) imply: % 190.22/30.51 | | | | | | | (153) ~ (all_16_2 = e2) % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | BETA: splitting (110) gives: % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | (154) ~ (all_34_2 = e4) % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | BETA: splitting (46) gives: % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | (155) ~ (all_66_2 = e0) % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | REDUCE: (51), (155) imply: % 190.22/30.51 | | | | | | | | | (156) ~ (all_16_2 = e0) % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | BETA: splitting (63) gives: % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | (157) all_250_15 = e4 % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | COMBINE_EQS: (55), (157) imply: % 190.22/30.51 | | | | | | | | | | (158) all_16_2 = e4 % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | SIMP: (158) implies: % 190.22/30.51 | | | | | | | | | | (159) all_16_2 = e4 % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | REDUCE: (57), (159) imply: % 190.22/30.51 | | | | | | | | | | (160) ~ (e4 = e1) % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | REDUCE: (117), (159) imply: % 190.22/30.51 | | | | | | | | | | (161) op(e4, all_26_2) = e4 % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | REF_CLOSE: (8), (90), (160), (161) are inconsistent by % 190.22/30.51 | | | | | | | | | | sub-proof #579. % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | (162) all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 % 190.22/30.51 | | | | | | | | | | | all_250_15 = e0 % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | BETA: splitting (162) gives: % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | (163) all_250_15 = e3 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | REF_CLOSE: (55), (150), (163) are inconsistent by sub-proof % 190.22/30.51 | | | | | | | | | | | #578. % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | (164) all_250_15 = e2 | all_250_15 = e1 | all_250_15 = % 190.22/30.51 | | | | | | | | | | | e0 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | REF_CLOSE: (55), (57), (153), (156), (164) are inconsistent % 190.22/30.51 | | | | | | | | | | | by sub-proof #326. % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | (165) all_66_2 = e0 % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | REF_CLOSE: (8), (51), (74), (101), (154), (165) are % 190.22/30.51 | | | | | | | | | inconsistent by sub-proof #570. % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | End of split % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | (166) all_34_2 = e4 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | COMBINE_EQS: (128), (166) imply: % 190.22/30.51 | | | | | | | | (167) all_14_1 = e4 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | SIMP: (167) implies: % 190.22/30.51 | | | | | | | | (168) all_14_1 = e4 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | REDUCE: (135), (168) imply: % 190.22/30.51 | | | | | | | | (169) op(e4, e4) = e1 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | GROUND_INST: instantiating (8) with all_244_0, e1, e4, e4, % 190.22/30.51 | | | | | | | | simplifying with (62), (169) gives: % 190.22/30.51 | | | | | | | | (170) all_244_0 = e1 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | REDUCE: (65), (170) imply: % 190.22/30.51 | | | | | | | | (171) $false % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | CLOSE: (171) is inconsistent. % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | End of split % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | Case 2: % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | (172) all_24_2 = e2 % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | COMBINE_EQS: (28), (172) imply: % 190.22/30.51 | | | | | | | (173) all_16_2 = e2 % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | SIMP: (173) implies: % 190.22/30.51 | | | | | | | (174) all_16_2 = e2 % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | REDUCE: (99), (174) imply: % 190.22/30.51 | | | | | | | (175) ~ (all_244_0 = e2) % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | REDUCE: (81), (174) imply: % 190.22/30.51 | | | | | | | (176) ~ (all_100_2 = e2) % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | REDUCE: (39), (174) imply: % 190.22/30.51 | | | | | | | (177) ~ (all_64_2 = e2) % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | REDUCE: (12), (174) imply: % 190.22/30.51 | | | | | | | (178) op(all_26_2, e2) = e1 % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | REDUCE: (74), (174) imply: % 190.22/30.51 | | | | | | | (179) op(e1, e2) = e4 % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | BETA: splitting (14) gives: % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | (180) ~ (all_166_2 = e0) % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | REDUCE: (19), (180) imply: % 190.22/30.51 | | | | | | | | (181) ~ (all_62_2 = e0) % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | BETA: splitting (85) gives: % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | (182) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 % 190.22/30.51 | | | | | | | | | & op(e3, e4) = e2) % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | REF_CLOSE: (8), (48), (62), (175), (176), (182) are % 190.22/30.51 | | | | | | | | | inconsistent by sub-proof #325. % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | (183) (all_252_6 = e2 & op(e2, e4) = e2) | (all_252_12 = e2 % 190.22/30.51 | | | | | | | | | & op(e1, e4) = e2) | (all_252_20 = e2 & op(e0, e4) % 190.22/30.51 | | | | | | | | | = e2) % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | BETA: splitting (183) gives: % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | (184) all_252_6 = e2 & op(e2, e4) = e2 % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | REF_CLOSE: (8), (83), (177), (184) are inconsistent by % 190.22/30.51 | | | | | | | | | | sub-proof #467. % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | (185) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_20 = % 190.22/30.51 | | | | | | | | | | e2 & op(e0, e4) = e2) % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | BETA: splitting (185) gives: % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | (186) all_252_12 = e2 & op(e1, e4) = e2 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | ALPHA: (186) implies: % 190.22/30.51 | | | | | | | | | | | (187) all_252_12 = e2 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_4_2, e4, e2, e1, % 190.22/30.51 | | | | | | | | | | | simplifying with (112), (179) gives: % 190.22/30.51 | | | | | | | | | | | (188) all_4_2 = e4 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | COMBINE_EQS: (109), (188) imply: % 190.22/30.51 | | | | | | | | | | | (189) all_180_2 = e4 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | COMBINE_EQS: (64), (188) imply: % 190.22/30.51 | | | | | | | | | | | (190) all_192_2 = e4 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | BETA: splitting (9) gives: % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | (191) ~ (all_180_2 = e4) % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | REDUCE: (189), (191) imply: % 190.22/30.51 | | | | | | | | | | | | (192) $false % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | CLOSE: (192) is inconsistent. % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | (193) op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 190.22/30.51 | | | | | | | | | | | | (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, % 190.22/30.51 | | | | | | | | | | | | e0) = all_180_0 & $i(all_180_0))) % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | ALPHA: (193) implies: % 190.22/30.51 | | | | | | | | | | | | (194) op(e4, e1) = all_180_1 % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | BETA: splitting (38) gives: % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | (195) ~ (all_192_2 = e4) % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | REDUCE: (190), (195) imply: % 190.22/30.51 | | | | | | | | | | | | | (196) $false % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | CLOSE: (196) is inconsistent. % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | (197) op(e4, e1) = all_192_1 & $i(all_192_1) & ( ~ % 190.22/30.51 | | | | | | | | | | | | | (all_192_1 = e3) | ( ~ (all_192_0 = e0) & op(e1, % 190.22/30.51 | | | | | | | | | | | | | e3) = all_192_0 & $i(all_192_0))) % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | ALPHA: (197) implies: % 190.22/30.51 | | | | | | | | | | | | | (198) op(e4, e1) = all_192_1 % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_26_2, all_192_1, e1, % 190.22/30.51 | | | | | | | | | | | | | e4, simplifying with (58), (198) gives: % 190.22/30.51 | | | | | | | | | | | | | (199) all_192_1 = all_26_2 % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_180_1, all_192_1, e1, % 190.22/30.51 | | | | | | | | | | | | | e4, simplifying with (194), (198) gives: % 190.22/30.51 | | | | | | | | | | | | | (200) all_192_1 = all_180_1 % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | COMBINE_EQS: (199), (200) imply: % 190.22/30.51 | | | | | | | | | | | | | (201) all_180_1 = all_26_2 % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | SIMP: (201) implies: % 190.22/30.51 | | | | | | | | | | | | | (202) all_180_1 = all_26_2 % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | BETA: splitting (1) gives: % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | (203) ~ (all_26_2 = e0) % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | BETA: splitting (7) gives: % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | (204) ~ (all_36_2 = e0) % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (13), (15), (24), (25), (29), % 190.22/30.51 | | | | | | | | | | | | | | | (34), (36), (45), (49), (50), (58), (59), (60), % 190.22/30.51 | | | | | | | | | | | | | | | (67), (69), (70), (77), (84), (86), (87), (88), % 190.22/30.51 | | | | | | | | | | | | | | | (95), (100), (102), (104), (105), (112), (114), % 190.22/30.51 | | | | | | | | | | | | | | | (116), (118), (131), (136), (151), (203), (204) % 190.22/30.51 | | | | | | | | | | | | | | | are inconsistent by sub-proof #321. % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | (205) all_36_2 = e0 % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | REDUCE: (31), (205) imply: % 190.22/30.51 | | | | | | | | | | | | | | | (206) ~ (all_244_15 = e0) % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | REDUCE: (2), (205) imply: % 190.22/30.51 | | | | | | | | | | | | | | | (207) ~ (all_48_2 = e0) % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | REDUCE: (98), (205) imply: % 190.22/30.51 | | | | | | | | | | | | | | | (208) op(e3, e0) = e1 % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | BETA: splitting (42) gives: % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | (209) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 % 190.22/30.51 | | | | | | | | | | | | | | | | = e0 & op(e1, e3) = e0) % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | BETA: splitting (209) gives: % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | (210) all_252_12 = e0 & op(e1, e4) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (187), (210) are inconsistent by sub-proof % 190.22/30.51 | | | | | | | | | | | | | | | | | #320. % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | (211) all_252_13 = e0 & op(e1, e3) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21), (181), (211) are inconsistent by % 190.22/30.51 | | | | | | | | | | | | | | | | | sub-proof #319. % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | (212) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 % 190.22/30.51 | | | | | | | | | | | | | | | | = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 190.22/30.51 | | | | | | | | | | | | | | | | op(e1, e0) = e0) % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | BETA: splitting (212) gives: % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | (213) all_252_14 = e0 & op(e1, e2) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | ALPHA: (213) implies: % 190.22/30.51 | | | | | | | | | | | | | | | | | (214) op(e1, e2) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (34), (112), (214) are inconsistent by % 190.22/30.51 | | | | | | | | | | | | | | | | | sub-proof #545. % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | (215) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 % 190.22/30.51 | | | | | | | | | | | | | | | | | = e0 & op(e1, e0) = e0) % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | BETA: splitting (215) gives: % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | Case 1: % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | (216) all_252_15 = e0 & op(e1, e1) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | ALPHA: (216) implies: % 190.22/30.51 | | | | | | | | | | | | | | | | | | (217) op(e1, e1) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (25), (206), (217) are inconsistent by % 190.22/30.51 | | | | | | | | | | | | | | | | | | sub-proof #440. % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | (218) all_252_19 = e0 & op(e1, e0) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | ALPHA: (218) implies: % 190.22/30.51 | | | | | | | | | | | | | | | | | | (219) op(e1, e0) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_14_1, e0, e0, e1, % 190.22/30.51 | | | | | | | | | | | | | | | | | | simplifying with (107), (219) gives: % 190.22/30.51 | | | | | | | | | | | | | | | | | | (220) all_14_1 = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_48_2, e1, e0, e3, % 190.22/30.51 | | | | | | | | | | | | | | | | | | simplifying with (92), (208) gives: % 190.22/30.51 | | | | | | | | | | | | | | | | | | (221) all_48_2 = e1 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | REDUCE: (207), (221) imply: % 190.22/30.51 | | | | | | | | | | | | | | | | | | (222) ~ (e1 = e0) % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | REDUCE: (134), (220) imply: % 190.22/30.51 | | | | | | | | | | | | | | | | | | (223) op(e0, e4) = e0 % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (136), (222), (223) are inconsistent by % 190.22/30.51 | | | | | | | | | | | | | | | | | | sub-proof #318. % 190.22/30.51 | | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | (224) all_26_2 = e0 % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | REDUCE: (178), (224) imply: % 190.22/30.51 | | | | | | | | | | | | | | (225) op(e0, e2) = e1 % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (11), (225) are inconsistent by % 190.22/30.51 | | | | | | | | | | | | | | sub-proof #502. % 190.22/30.51 | | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | (226) all_252_20 = e2 & op(e0, e4) = e2 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | ALPHA: (226) implies: % 190.22/30.51 | | | | | | | | | | | (227) op(e0, e4) = e2 % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | | REF_CLOSE: (8), (15), (136), (227) are inconsistent by % 190.22/30.51 | | | | | | | | | | | sub-proof #323. % 190.22/30.51 | | | | | | | | | | | % 190.22/30.51 | | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | | % 190.22/30.51 | | | | | | | | | End of split % 190.22/30.51 | | | | | | | | | % 190.22/30.51 | | | | | | | | End of split % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | Case 2: % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | (228) all_166_2 = e0 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | COMBINE_EQS: (19), (228) imply: % 190.22/30.51 | | | | | | | | (229) all_62_2 = e0 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | SIMP: (229) implies: % 190.22/30.51 | | | | | | | | (230) all_62_2 = e0 % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | REDUCE: (115), (230) imply: % 190.22/30.51 | | | | | | | | (231) ~ (all_22_2 = e0) % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | | REF_CLOSE: (8), (16), (71), (89), (96), (103), (133), (151), % 190.22/30.51 | | | | | | | | (231) are inconsistent by sub-proof #317. % 190.22/30.51 | | | | | | | | % 190.22/30.51 | | | | | | | End of split % 190.22/30.51 | | | | | | | % 190.22/30.51 | | | | | | End of split % 190.22/30.51 | | | | | | % 190.22/30.51 | | | | | Case 2: % 190.22/30.51 | | | | | | % 190.22/30.51 | | | | | | (232) all_22_2 = e2 % 190.22/30.51 | | | | | | (233) op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 = e1) % 190.22/30.51 | | | | | | | ( ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & % 190.22/30.51 | | | | | | $i(all_22_0))) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | ALPHA: (233) implies: % 190.22/30.52 | | | | | | (234) ~ (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = % 190.22/30.52 | | | | | | all_22_0 & $i(all_22_0)) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (72), (232) imply: % 190.22/30.52 | | | | | | (235) ~ (all_244_3 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (20), (232) imply: % 190.22/30.52 | | | | | | (236) ~ (all_244_24 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (6), (232) imply: % 190.22/30.52 | | | | | | (237) ~ (all_84_2 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (115), (232) imply: % 190.22/30.52 | | | | | | (238) ~ (all_62_2 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (106), (232) imply: % 190.22/30.52 | | | | | | (239) ~ (all_28_2 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (119), (232) imply: % 190.22/30.52 | | | | | | (240) ~ (all_10_2 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | SIMP: (240) implies: % 190.22/30.52 | | | | | | (241) ~ (all_10_2 = e2) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (61), (232) imply: % 190.22/30.52 | | | | | | (242) op(e0, e2) = e3 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | BETA: splitting (76) gives: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | Case 1: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | (243) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & % 190.22/30.52 | | | | | | | op(e3, e3) = e2) % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | BETA: splitting (243) gives: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (244) all_252_1 = e2 & op(e4, e3) = e2 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | REF_CLOSE: (8), (33), (237), (244) are inconsistent by sub-proof % 190.22/30.52 | | | | | | | | #523. % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (245) all_252_3 = e2 & op(e3, e3) = e2 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | REF_CLOSE: (8), (18), (235), (245) are inconsistent by sub-proof % 190.22/30.52 | | | | | | | | #496. % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | End of split % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | Case 2: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | (246) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & % 190.22/30.52 | | | | | | | op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | BETA: splitting (246) gives: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (247) all_252_7 = e2 & op(e2, e3) = e2 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | REF_CLOSE: (8), (30), (241), (247) are inconsistent by sub-proof % 190.22/30.52 | | | | | | | | #458. % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (248) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 % 190.22/30.52 | | | | | | | | & op(e0, e3) = e2) % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | BETA: splitting (248) gives: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | (249) all_252_13 = e2 & op(e1, e3) = e2 % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | ALPHA: (249) implies: % 190.22/30.52 | | | | | | | | | (250) op(e1, e3) = e2 % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REF_CLOSE: (8), (21), (238), (250) are inconsistent by % 190.22/30.52 | | | | | | | | | sub-proof #572. % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | (251) all_252_21 = e2 & op(e0, e3) = e2 % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REF_CLOSE: (5), (8), (11), (26), (32), (34), (36), (49), (50), % 190.22/30.52 | | | | | | | | | (59), (66), (67), (68), (70), (80), (97), (108), % 190.22/30.52 | | | | | | | | | (111), (112), (114), (132), (234), (236), (239), % 190.22/30.52 | | | | | | | | | (242), (251) are inconsistent by sub-proof #315. % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | End of split % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | End of split % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | End of split % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | End of split % 190.22/30.52 | | | | | % 190.22/30.52 | | | | Case 2: % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | (252) all_16_2 = e3 % 190.22/30.52 | | | | | (253) op(e3, e1) = all_16_1 & $i(all_16_1) & ( ~ (all_16_1 = e2) | % 190.22/30.52 | | | | | ( ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 & % 190.22/30.52 | | | | | $i(all_16_0))) % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | ALPHA: (253) implies: % 190.22/30.52 | | | | | (254) op(e3, e1) = all_16_1 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | COMBINE_EQS: (93), (252) imply: % 190.22/30.52 | | | | | (255) all_144_2 = e3 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | REDUCE: (12), (252) imply: % 190.22/30.52 | | | | | (256) op(all_26_2, e3) = e1 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | REDUCE: (74), (252) imply: % 190.22/30.52 | | | | | (257) op(e1, e3) = e4 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | BETA: splitting (3) gives: % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | Case 1: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | (258) ~ (all_144_2 = e3) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (255), (258) imply: % 190.22/30.52 | | | | | | (259) $false % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | CLOSE: (259) is inconsistent. % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | Case 2: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | (260) op(e3, e1) = all_144_1 & $i(all_144_1) & ( ~ (all_144_1 = % 190.22/30.52 | | | | | | e0) | ( ~ (all_144_0 = e2) & op(e1, e0) = all_144_0 & % 190.22/30.52 | | | | | | $i(all_144_0))) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | ALPHA: (260) implies: % 190.22/30.52 | | | | | | (261) op(e3, e1) = all_144_1 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | GROUND_INST: instantiating (8) with all_62_2, e4, e3, e1, % 190.22/30.52 | | | | | | simplifying with (21), (257) gives: % 190.22/30.52 | | | | | | (262) all_62_2 = e4 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | GROUND_INST: instantiating (8) with all_36_2, all_144_1, e1, e3, % 190.22/30.52 | | | | | | simplifying with (13), (261) gives: % 190.22/30.52 | | | | | | (263) all_144_1 = all_36_2 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | GROUND_INST: instantiating (8) with all_16_1, all_144_1, e1, e3, % 190.22/30.52 | | | | | | simplifying with (254), (261) gives: % 190.22/30.52 | | | | | | (264) all_144_1 = all_16_1 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | COMBINE_EQS: (263), (264) imply: % 190.22/30.52 | | | | | | (265) all_36_2 = all_16_1 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | SIMP: (265) implies: % 190.22/30.52 | | | | | | (266) all_36_2 = all_16_1 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | COMBINE_EQS: (75), (262) imply: % 190.22/30.52 | | | | | | (267) all_114_2 = e4 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | COMBINE_EQS: (17), (262) imply: % 190.22/30.52 | | | | | | (268) all_130_2 = e4 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (115), (262) imply: % 190.22/30.52 | | | | | | (269) ~ (all_22_2 = e4) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REDUCE: (27), (262), (266) imply: % 190.22/30.52 | | | | | | (270) op(e4, all_16_1) = e3 % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | BETA: splitting (79) gives: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | Case 1: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | (271) ~ (all_130_2 = e4) % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | REDUCE: (268), (271) imply: % 190.22/30.52 | | | | | | | (272) $false % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | CLOSE: (272) is inconsistent. % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | Case 2: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | (273) op(e4, e1) = all_130_1 & $i(all_130_1) & ( ~ (all_130_1 = % 190.22/30.52 | | | | | | | e2) | ( ~ (all_130_0 = e0) & op(e1, e2) = all_130_0 & % 190.22/30.52 | | | | | | | $i(all_130_0))) % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | ALPHA: (273) implies: % 190.22/30.52 | | | | | | | (274) op(e4, e1) = all_130_1 % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | BETA: splitting (44) gives: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (275) ~ (all_114_2 = e4) % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | REDUCE: (267), (275) imply: % 190.22/30.52 | | | | | | | | (276) $false % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | CLOSE: (276) is inconsistent. % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (277) op(e4, e1) = all_114_1 & $i(all_114_1) & ( ~ (all_114_1 % 190.22/30.52 | | | | | | | | = e0) | ( ~ (all_114_0 = e2) & op(e1, e0) = % 190.22/30.52 | | | | | | | | all_114_0 & $i(all_114_0))) % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | ALPHA: (277) implies: % 190.22/30.52 | | | | | | | | (278) op(e4, e1) = all_114_1 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | GROUND_INST: instantiating (8) with all_26_2, all_130_1, e1, e4, % 190.22/30.52 | | | | | | | | simplifying with (58), (274) gives: % 190.22/30.52 | | | | | | | | (279) all_130_1 = all_26_2 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | GROUND_INST: instantiating (8) with all_114_1, all_130_1, e1, % 190.22/30.52 | | | | | | | | e4, simplifying with (274), (278) gives: % 190.22/30.52 | | | | | | | | (280) all_130_1 = all_114_1 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | COMBINE_EQS: (279), (280) imply: % 190.22/30.52 | | | | | | | | (281) all_114_1 = all_26_2 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | BETA: splitting (40) gives: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | (282) ~ (all_22_2 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | BETA: splitting (1) gives: % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | (283) ~ (all_26_2 = e0) % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | BETA: splitting (22) gives: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | (284) ~ (all_30_2 = e3) % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | BETA: splitting (7) gives: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | (285) ~ (all_36_2 = e0) % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (13), (15), (24), (25), (29), % 190.22/30.52 | | | | | | | | | | | | (34), (36), (45), (49), (50), (58), (59), (60), % 190.22/30.52 | | | | | | | | | | | | (67), (69), (70), (77), (84), (86), (87), (88), % 190.22/30.52 | | | | | | | | | | | | (95), (100), (102), (104), (105), (112), (114), % 190.22/30.52 | | | | | | | | | | | | (116), (118), (131), (136), (282), (283), (285) % 190.22/30.52 | | | | | | | | | | | | are inconsistent by sub-proof #321. % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | (286) all_36_2 = e0 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REF_CLOSE: (8), (41), (266), (270), (284), (286) are % 190.22/30.52 | | | | | | | | | | | | inconsistent by sub-proof #344. % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | (287) all_30_2 = e3 % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | COMBINE_EQS: (146), (287) imply: % 190.22/30.52 | | | | | | | | | | | (288) all_92_1 = e3 % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | REDUCE: (78), (287) imply: % 190.22/30.52 | | | | | | | | | | | (289) op(e4, e3) = e0 % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | BETA: splitting (145) gives: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | (290) ~ (all_92_1 = e3) % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REDUCE: (288), (290) imply: % 190.22/30.52 | | | | | | | | | | | | (291) $false % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | CLOSE: (291) is inconsistent. % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | (292) ~ (all_92_0 = e2) & op(e0, e3) = all_92_0 & % 190.22/30.52 | | | | | | | | | | | | $i(all_92_0) % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | ALPHA: (292) implies: % 190.22/30.52 | | | | | | | | | | | | (293) ~ (all_92_0 = e2) % 190.22/30.52 | | | | | | | | | | | | (294) op(e0, e3) = all_92_0 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_22_2, all_92_0, e3, e0, % 190.22/30.52 | | | | | | | | | | | | simplifying with (60), (294) gives: % 190.22/30.52 | | | | | | | | | | | | (295) all_92_0 = all_22_2 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_84_2, e0, e3, e4, % 190.22/30.52 | | | | | | | | | | | | simplifying with (33), (289) gives: % 190.22/30.52 | | | | | | | | | | | | (296) all_84_2 = e0 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REDUCE: (6), (296) imply: % 190.22/30.52 | | | | | | | | | | | | (297) ~ (all_22_2 = e0) % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REF_CLOSE: (8), (16), (71), (89), (96), (103), (133), (282), % 190.22/30.52 | | | | | | | | | | | | (297) are inconsistent by sub-proof #317. % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | (298) all_26_2 = e0 % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | REDUCE: (256), (298) imply: % 190.22/30.52 | | | | | | | | | | (299) op(e0, e3) = e1 % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | REF_CLOSE: (8), (60), (96), (299) are inconsistent by % 190.22/30.52 | | | | | | | | | | sub-proof #479. % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | (300) all_22_2 = e2 % 190.22/30.52 | | | | | | | | | (301) op(e2, e0) = all_22_1 & $i(all_22_1) & ( ~ (all_22_1 % 190.22/30.52 | | | | | | | | | = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = % 190.22/30.52 | | | | | | | | | all_22_0 & $i(all_22_0))) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | ALPHA: (301) implies: % 190.22/30.52 | | | | | | | | | (302) ~ (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) % 190.22/30.52 | | | | | | | | | = all_22_0 & $i(all_22_0)) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (72), (300) imply: % 190.22/30.52 | | | | | | | | | (303) ~ (all_244_3 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (20), (300) imply: % 190.22/30.52 | | | | | | | | | (304) ~ (all_244_24 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (6), (300) imply: % 190.22/30.52 | | | | | | | | | (305) ~ (all_84_2 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (106), (300) imply: % 190.22/30.52 | | | | | | | | | (306) ~ (all_28_2 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (119), (300) imply: % 190.22/30.52 | | | | | | | | | (307) ~ (all_10_2 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | SIMP: (307) implies: % 190.22/30.52 | | | | | | | | | (308) ~ (all_10_2 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (133), (300) imply: % 190.22/30.52 | | | | | | | | | (309) ~ (e4 = e2) % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | REDUCE: (61), (300) imply: % 190.22/30.52 | | | | | | | | | (310) op(e0, e2) = e3 % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | BETA: splitting (76) gives: % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | (311) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = % 190.22/30.52 | | | | | | | | | | e2 & op(e3, e3) = e2) % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | BETA: splitting (311) gives: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | (312) all_252_1 = e2 & op(e4, e3) = e2 % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | REF_CLOSE: (8), (33), (305), (312) are inconsistent by % 190.22/30.52 | | | | | | | | | | | sub-proof #523. % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | (313) all_252_3 = e2 & op(e3, e3) = e2 % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | REF_CLOSE: (8), (18), (303), (313) are inconsistent by % 190.22/30.52 | | | | | | | | | | | sub-proof #496. % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | (314) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = % 190.22/30.52 | | | | | | | | | | e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, % 190.22/30.52 | | | | | | | | | | e3) = e2) % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | BETA: splitting (314) gives: % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | (315) all_252_7 = e2 & op(e2, e3) = e2 % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | REF_CLOSE: (8), (30), (308), (315) are inconsistent by % 190.22/30.52 | | | | | | | | | | | sub-proof #458. % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | (316) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 % 190.22/30.52 | | | | | | | | | | | = e2 & op(e0, e3) = e2) % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | BETA: splitting (316) gives: % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | (317) all_252_13 = e2 & op(e1, e3) = e2 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | ALPHA: (317) implies: % 190.22/30.52 | | | | | | | | | | | | (318) op(e1, e3) = e2 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REF_CLOSE: (8), (86), (257), (318) are inconsistent by % 190.22/30.52 | | | | | | | | | | | | sub-proof #529. % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | (319) all_252_21 = e2 & op(e0, e3) = e2 % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | | REF_CLOSE: (5), (8), (11), (26), (32), (34), (36), (49), % 190.22/30.52 | | | | | | | | | | | | (50), (59), (66), (67), (68), (70), (80), (97), % 190.22/30.52 | | | | | | | | | | | | (108), (111), (112), (114), (132), (302), (304), % 190.22/30.52 | | | | | | | | | | | | (306), (310), (319) are inconsistent by sub-proof % 190.22/30.52 | | | | | | | | | | | | #315. % 190.22/30.52 | | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | | | % 190.22/30.52 | | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | | % 190.22/30.52 | | | | | | | | | End of split % 190.22/30.52 | | | | | | | | | % 190.22/30.52 | | | | | | | | End of split % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | End of split % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | End of split % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | End of split % 190.22/30.52 | | | | | % 190.22/30.52 | | | | End of split % 190.22/30.52 | | | | % 190.22/30.52 | | | End of split % 190.22/30.52 | | | % 190.22/30.52 | | End of split % 190.22/30.52 | | % 190.22/30.52 | End of split % 190.22/30.52 | % 190.22/30.52 End of proof % 190.22/30.52 % 190.22/30.52 Sub-proof #315 shows that the following formulas are inconsistent: % 190.22/30.52 ---------------------------------------------------------------- % 190.22/30.52 (1) op(e2, e2) = all_244_8 % 190.22/30.52 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.52 (3) op(e0, e2) = all_28_2 % 190.22/30.52 (4) ~ (all_244_24 = e2) % 190.22/30.52 (5) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 190.22/30.52 (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 190.22/30.52 $i(all_158_0)))) % 190.22/30.52 (6) all_158_2 = all_28_2 % 190.22/30.52 (7) ~ (all_4_2 = e0) % 190.22/30.52 (8) op(e0, e1) = e4 % 190.22/30.52 (9) ~ (all_22_1 = e1) | ( ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & % 190.22/30.52 $i(all_22_0)) % 190.22/30.52 (10) all_252_21 = e2 & op(e0, e3) = e2 % 190.22/30.52 (11) ~ (all_8_2 = e0) % 190.22/30.52 (12) op(e0, e0) = all_244_24 % 190.22/30.52 (13) ~ (all_6_2 = e0) % 190.22/30.52 (14) ~ (e3 = e0) % 190.22/30.52 (15) op(e3, e2) = all_8_2 % 190.22/30.52 (16) op(all_244_8, all_244_8) = e2 % 190.22/30.52 (17) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.22/30.52 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.22/30.52 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.52 (18) ~ (all_244_24 = all_28_2) % 190.22/30.52 (19) ~ (all_28_2 = e4) % 190.22/30.52 (20) op(e0, e2) = e3 % 190.22/30.52 (21) op(e0, e4) = all_12_2 % 190.22/30.52 (22) ~ (all_28_2 = e2) % 190.22/30.52 (23) ~ (all_12_2 = e3) % 190.22/30.52 (24) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 190.22/30.52 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.22/30.52 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.22/30.52 (25) op(e1, e2) = all_4_2 % 190.22/30.52 (26) op(e4, e2) = all_6_2 % 190.22/30.52 % 190.22/30.52 Begin of proof % 190.22/30.52 | % 190.22/30.52 | ALPHA: (10) implies: % 190.22/30.52 | (27) all_252_21 = e2 % 190.22/30.52 | % 190.22/30.52 | BETA: splitting (9) gives: % 190.22/30.52 | % 190.22/30.52 | Case 1: % 190.22/30.52 | | % 190.22/30.52 | | % 190.22/30.52 | | GROUND_INST: instantiating (2) with all_28_2, e3, e2, e0, simplifying with % 190.22/30.52 | | (3), (20) gives: % 190.22/30.52 | | (28) all_28_2 = e3 % 190.22/30.52 | | % 190.22/30.52 | | COMBINE_EQS: (6), (28) imply: % 190.22/30.52 | | (29) all_158_2 = e3 % 190.22/30.52 | | % 190.22/30.52 | | REDUCE: (18), (28) imply: % 190.22/30.52 | | (30) ~ (all_244_24 = e3) % 190.22/30.52 | | % 190.22/30.52 | | REDUCE: (19), (28) imply: % 190.22/30.52 | | (31) ~ (e4 = e3) % 190.22/30.52 | | % 190.22/30.52 | | SIMP: (31) implies: % 190.22/30.52 | | (32) ~ (e4 = e3) % 190.22/30.52 | | % 190.22/30.52 | | REDUCE: (22), (28) imply: % 190.22/30.52 | | (33) ~ (e3 = e2) % 190.22/30.52 | | % 190.22/30.52 | | BETA: splitting (17) gives: % 190.22/30.52 | | % 190.22/30.52 | | Case 1: % 190.22/30.52 | | | % 190.22/30.52 | | | (34) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) % 190.22/30.52 | | | = e0) % 190.22/30.52 | | | % 190.22/30.52 | | | REF_CLOSE: (2), (11), (13), (15), (26), (34) are inconsistent by sub-proof % 190.22/30.52 | | | #546. % 190.22/30.52 | | | % 190.22/30.52 | | Case 2: % 190.22/30.52 | | | % 190.22/30.52 | | | (35) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) % 190.22/30.52 | | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.52 | | | % 190.22/30.52 | | | BETA: splitting (35) gives: % 190.22/30.52 | | | % 190.22/30.52 | | | Case 1: % 190.22/30.52 | | | | % 190.22/30.52 | | | | (36) all_252_8 = e0 & op(e2, e2) = e0 % 190.22/30.52 | | | | % 190.22/30.52 | | | | REF_CLOSE: (1), (2), (4), (5), (12), (16), (29), (36) are inconsistent % 190.22/30.52 | | | | by sub-proof #456. % 190.22/30.52 | | | | % 190.22/30.52 | | | Case 2: % 190.22/30.52 | | | | % 190.22/30.52 | | | | (37) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, % 190.22/30.52 | | | | e2) = e0) % 190.22/30.52 | | | | % 190.22/30.52 | | | | BETA: splitting (37) gives: % 190.22/30.52 | | | | % 190.22/30.52 | | | | Case 1: % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | (38) all_252_14 = e0 & op(e1, e2) = e0 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | ALPHA: (38) implies: % 190.22/30.52 | | | | | (39) op(e1, e2) = e0 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | REF_CLOSE: (2), (7), (25), (39) are inconsistent by sub-proof #545. % 190.22/30.52 | | | | | % 190.22/30.52 | | | | Case 2: % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | (40) all_252_22 = e0 & op(e0, e2) = e0 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | ALPHA: (40) implies: % 190.22/30.52 | | | | | (41) all_252_22 = e0 % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | BETA: splitting (24) gives: % 190.22/30.52 | | | | | % 190.22/30.52 | | | | | Case 1: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | (42) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & % 190.22/30.52 | | | | | | op(e0, e3) = e3) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | REF_CLOSE: (2), (21), (23), (27), (33), (42) are inconsistent by % 190.22/30.52 | | | | | | sub-proof #457. % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | Case 2: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | (43) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & % 190.22/30.52 | | | | | | op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | BETA: splitting (43) gives: % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | | Case 1: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | (44) all_252_22 = e3 & op(e0, e2) = e3 % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | ALPHA: (44) implies: % 190.22/30.52 | | | | | | | (45) all_252_22 = e3 % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | REF_CLOSE: (14), (41), (45) are inconsistent by sub-proof #389. % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | Case 2: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | (46) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & % 190.22/30.52 | | | | | | | op(e0, e0) = e3) % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | BETA: splitting (46) gives: % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | | Case 1: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (47) all_252_23 = e3 & op(e0, e1) = e3 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | REF_CLOSE: (2), (8), (32), (47) are inconsistent by sub-proof % 190.22/30.52 | | | | | | | | #316. % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | Case 2: % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | (48) all_252_24 = e3 & op(e0, e0) = e3 % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | | REF_CLOSE: (2), (12), (30), (48) are inconsistent by sub-proof % 190.22/30.52 | | | | | | | | #507. % 190.22/30.52 | | | | | | | | % 190.22/30.52 | | | | | | | End of split % 190.22/30.52 | | | | | | | % 190.22/30.52 | | | | | | End of split % 190.22/30.52 | | | | | | % 190.22/30.52 | | | | | End of split % 190.22/30.52 | | | | | % 190.22/30.52 | | | | End of split % 190.22/30.52 | | | | % 190.22/30.52 | | | End of split % 190.22/30.52 | | | % 190.22/30.52 | | End of split % 190.22/30.52 | | % 190.22/30.52 | Case 2: % 190.22/30.52 | | % 190.22/30.52 | | (49) ~ (all_22_0 = e4) & op(e0, e1) = all_22_0 & $i(all_22_0) % 190.22/30.52 | | % 190.22/30.52 | | ALPHA: (49) implies: % 190.22/30.52 | | (50) ~ (all_22_0 = e4) % 190.22/30.52 | | (51) op(e0, e1) = all_22_0 % 190.22/30.52 | | % 190.22/30.52 | | GROUND_INST: instantiating (2) with e4, all_22_0, e1, e0, simplifying with % 190.22/30.52 | | (8), (51) gives: % 190.22/30.52 | | (52) all_22_0 = e4 % 190.22/30.52 | | % 190.22/30.52 | | REDUCE: (50), (52) imply: % 190.22/30.52 | | (53) $false % 190.22/30.52 | | % 190.22/30.52 | | CLOSE: (53) is inconsistent. % 190.22/30.52 | | % 190.22/30.52 | End of split % 190.22/30.52 | % 190.22/30.52 End of proof % 190.22/30.52 % 190.22/30.52 Sub-proof #316 shows that the following formulas are inconsistent: % 190.22/30.52 ---------------------------------------------------------------- % 190.22/30.52 (1) all_252_23 = e3 & op(e0, e1) = e3 % 190.22/30.52 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.52 (3) op(e0, e1) = e4 % 190.22/30.52 (4) ~ (e4 = e3) % 190.22/30.52 % 190.22/30.52 Begin of proof % 190.22/30.52 | % 190.22/30.52 | ALPHA: (1) implies: % 190.22/30.52 | (5) op(e0, e1) = e3 % 190.22/30.52 | % 190.22/30.52 | GROUND_INST: instantiating (2) with e4, e3, e1, e0, simplifying with (3), (5) % 190.22/30.52 | gives: % 190.22/30.52 | (6) e4 = e3 % 190.22/30.52 | % 190.22/30.52 | REDUCE: (4), (6) imply: % 190.22/30.52 | (7) $false % 190.22/30.52 | % 190.22/30.52 | CLOSE: (7) is inconsistent. % 190.22/30.52 | % 190.22/30.52 End of proof % 190.22/30.52 % 190.22/30.52 Sub-proof #317 shows that the following formulas are inconsistent: % 190.22/30.52 ---------------------------------------------------------------- % 190.22/30.52 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.52 (2) all_250_21 = all_22_2 % 190.22/30.52 (3) ~ (all_22_2 = e4) % 190.22/30.52 (4) op(e3, all_48_2) = e0 % 190.22/30.52 (5) ~ (all_22_2 = e0) % 190.22/30.52 (6) ~ (all_22_2 = e2) % 190.22/30.52 (7) op(all_22_2, all_48_2) = e3 % 190.22/30.52 (8) ~ (all_22_2 = e1) % 190.22/30.52 (9) all_250_21 = e4 | all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | % 190.22/30.52 all_250_21 = e0 % 190.22/30.52 % 190.22/30.52 Begin of proof % 190.22/30.52 | % 190.22/30.52 | SIMP: (5) implies: % 190.22/30.52 | (10) ~ (all_22_2 = e0) % 190.22/30.52 | % 190.22/30.52 | BETA: splitting (9) gives: % 190.22/30.52 | % 190.22/30.52 | Case 1: % 190.22/30.52 | | % 190.22/30.52 | | (11) all_250_21 = e4 % 190.22/30.52 | | % 190.22/30.52 | | COMBINE_EQS: (2), (11) imply: % 190.22/30.52 | | (12) all_22_2 = e4 % 190.22/30.52 | | % 190.22/30.52 | | REDUCE: (3), (12) imply: % 190.22/30.52 | | (13) $false % 190.22/30.52 | | % 190.22/30.52 | | CLOSE: (13) is inconsistent. % 190.22/30.52 | | % 190.22/30.52 | Case 2: % 190.22/30.52 | | % 190.22/30.52 | | (14) all_250_21 = e3 | all_250_21 = e2 | all_250_21 = e1 | all_250_21 = % 190.22/30.52 | | e0 % 190.22/30.52 | | % 190.22/30.52 | | BETA: splitting (14) gives: % 190.22/30.52 | | % 190.22/30.52 | | Case 1: % 190.22/30.52 | | | % 190.22/30.52 | | | (15) all_250_21 = e3 % 190.22/30.52 | | | % 190.22/30.52 | | | COMBINE_EQS: (2), (15) imply: % 190.22/30.52 | | | (16) all_22_2 = e3 % 190.22/30.53 | | | % 190.22/30.53 | | | REDUCE: (10), (16) imply: % 190.22/30.53 | | | (17) ~ (e3 = e0) % 190.22/30.53 | | | % 190.22/30.53 | | | REF_CLOSE: (1), (4), (7), (16), (17) are inconsistent by sub-proof #510. % 190.22/30.53 | | | % 190.22/30.53 | | Case 2: % 190.22/30.53 | | | % 190.22/30.53 | | | (18) all_250_21 = e2 | all_250_21 = e1 | all_250_21 = e0 % 190.22/30.53 | | | % 190.22/30.53 | | | BETA: splitting (18) gives: % 190.22/30.53 | | | % 190.22/30.53 | | | Case 1: % 190.22/30.53 | | | | % 190.22/30.53 | | | | (19) all_250_21 = e2 % 190.22/30.53 | | | | % 190.22/30.53 | | | | COMBINE_EQS: (2), (19) imply: % 190.22/30.53 | | | | (20) all_22_2 = e2 % 190.22/30.53 | | | | % 190.22/30.53 | | | | REDUCE: (6), (20) imply: % 190.22/30.53 | | | | (21) $false % 190.22/30.53 | | | | % 190.22/30.53 | | | | CLOSE: (21) is inconsistent. % 190.22/30.53 | | | | % 190.22/30.53 | | | Case 2: % 190.22/30.53 | | | | % 190.22/30.53 | | | | (22) all_250_21 = e1 | all_250_21 = e0 % 190.22/30.53 | | | | % 190.22/30.53 | | | | BETA: splitting (22) gives: % 190.22/30.53 | | | | % 190.22/30.53 | | | | Case 1: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | (23) all_250_21 = e1 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | COMBINE_EQS: (2), (23) imply: % 190.22/30.53 | | | | | (24) all_22_2 = e1 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | REDUCE: (8), (24) imply: % 190.22/30.53 | | | | | (25) $false % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | CLOSE: (25) is inconsistent. % 190.22/30.53 | | | | | % 190.22/30.53 | | | | Case 2: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | (26) all_250_21 = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | COMBINE_EQS: (2), (26) imply: % 190.22/30.53 | | | | | (27) all_22_2 = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | REDUCE: (10), (27) imply: % 190.22/30.53 | | | | | (28) $false % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | CLOSE: (28) is inconsistent. % 190.22/30.53 | | | | | % 190.22/30.53 | | | | End of split % 190.22/30.53 | | | | % 190.22/30.53 | | | End of split % 190.22/30.53 | | | % 190.22/30.53 | | End of split % 190.22/30.53 | | % 190.22/30.53 | End of split % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #318 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) op(e0, e4) = e1 % 190.22/30.53 (3) op(e0, e4) = e0 % 190.22/30.53 (4) ~ (e1 = e0) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | GROUND_INST: instantiating (1) with e1, e0, e4, e0, simplifying with (2), (3) % 190.22/30.53 | gives: % 190.22/30.53 | (5) e1 = e0 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (4), (5) imply: % 190.22/30.53 | (6) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (6) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #319 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) all_252_13 = e0 & op(e1, e3) = e0 % 190.22/30.53 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (3) op(e1, e3) = all_62_2 % 190.22/30.53 (4) ~ (all_62_2 = e0) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | ALPHA: (1) implies: % 190.22/30.53 | (5) op(e1, e3) = e0 % 190.22/30.53 | % 190.22/30.53 | GROUND_INST: instantiating (2) with all_62_2, e0, e3, e1, simplifying with % 190.22/30.53 | (3), (5) gives: % 190.22/30.53 | (6) all_62_2 = e0 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (4), (6) imply: % 190.22/30.53 | (7) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (7) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #320 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) all_252_12 = e0 & op(e1, e4) = e0 % 190.22/30.53 (2) all_252_12 = e2 % 190.22/30.53 (3) ~ (e2 = e0) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | ALPHA: (1) implies: % 190.22/30.53 | (4) all_252_12 = e0 % 190.22/30.53 | % 190.22/30.53 | COMBINE_EQS: (2), (4) imply: % 190.22/30.53 | (5) e2 = e0 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (3), (5) imply: % 190.22/30.53 | (6) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (6) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #321 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) op(e2, e2) = all_244_8 % 190.22/30.53 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (3) ~ (all_36_2 = e0) % 190.22/30.53 (4) op(e0, e2) = all_28_2 % 190.22/30.53 (5) op(e3, e1) = all_36_2 % 190.22/30.53 (6) ~ (e2 = e1) % 190.22/30.53 (7) op(e2, all_38_2) = e1 % 190.22/30.53 (8) ~ (all_26_2 = e0) % 190.22/30.53 (9) op(e1, e1) = all_244_15 % 190.22/30.53 (10) ~ (e4 = e0) % 190.22/30.53 (11) ~ (all_4_2 = e0) % 190.22/30.53 (12) op(e0, e1) = e4 % 190.22/30.53 (13) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.22/30.53 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.22/30.53 $i(all_38_0)))) % 190.22/30.53 (14) ~ (all_8_2 = e0) % 190.22/30.53 (15) op(e0, e0) = all_244_24 % 190.22/30.53 (16) op(e4, e1) = all_26_2 % 190.22/30.53 (17) ~ (all_6_2 = e0) % 190.22/30.53 (18) op(e0, e3) = all_22_2 % 190.22/30.53 (19) op(e3, e2) = all_8_2 % 190.22/30.53 (20) op(all_244_15, all_244_15) = e1 % 190.22/30.53 (21) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.22/30.53 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.22/30.53 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.53 (22) ~ (all_244_24 = e4) % 190.22/30.53 (23) ~ (all_22_2 = e2) % 190.22/30.53 (24) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.22/30.53 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.22/30.53 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.22/30.53 (25) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 190.22/30.53 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 190.22/30.53 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 190.22/30.53 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 190.22/30.53 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 190.22/30.53 op(e0, e1) = e0))) % 190.22/30.53 (26) ~ (e4 = e2) % 190.22/30.53 (27) op(e2, e0) = all_40_2 % 190.22/30.53 (28) op(all_28_2, all_40_2) = e2 % 190.22/30.53 (29) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.22/30.53 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.22/30.53 $i(all_188_0)))) % 190.22/30.53 (30) ~ (e2 = e0) % 190.22/30.53 (31) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.22/30.53 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.22/30.53 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.22/30.53 (32) all_188_2 = all_38_2 % 190.22/30.53 (33) ~ (all_244_24 = e1) % 190.22/30.53 (34) op(e0, e4) = e1 % 190.22/30.53 (35) op(e1, e2) = all_4_2 % 190.22/30.53 (36) op(e4, e2) = all_6_2 % 190.22/30.53 (37) op(e2, e1) = all_38_2 % 190.22/30.53 (38) ~ (all_244_8 = all_38_2) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | BETA: splitting (13) gives: % 190.22/30.53 | % 190.22/30.53 | Case 1: % 190.22/30.53 | | % 190.22/30.53 | | (39) ~ (all_38_2 = e0) % 190.22/30.53 | | % 190.22/30.53 | | BETA: splitting (24) gives: % 190.22/30.53 | | % 190.22/30.53 | | Case 1: % 190.22/30.53 | | | % 190.22/30.53 | | | (40) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) % 190.22/30.53 | | | = e0) % 190.22/30.53 | | | % 190.22/30.53 | | | REF_CLOSE: (2), (3), (5), (8), (16), (40) are inconsistent by sub-proof % 190.22/30.53 | | | #451. % 190.22/30.53 | | | % 190.22/30.53 | | Case 2: % 190.22/30.53 | | | % 190.22/30.53 | | | (41) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, % 190.22/30.53 | | | e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.22/30.53 | | | % 190.22/30.53 | | | BETA: splitting (41) gives: % 190.22/30.53 | | | % 190.22/30.53 | | | Case 1: % 190.22/30.53 | | | | % 190.22/30.53 | | | | (42) all_252_11 = e0 & op(e2, e1) = e0 % 190.22/30.53 | | | | % 190.22/30.53 | | | | ALPHA: (42) implies: % 190.22/30.53 | | | | (43) op(e2, e1) = e0 % 190.22/30.53 | | | | % 190.22/30.53 | | | | REF_CLOSE: (2), (37), (39), (43) are inconsistent by sub-proof #549. % 190.22/30.53 | | | | % 190.22/30.53 | | | Case 2: % 190.22/30.53 | | | | % 190.22/30.53 | | | | (44) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, % 190.22/30.53 | | | | e1) = e0) % 190.22/30.53 | | | | % 190.22/30.53 | | | | BETA: splitting (44) gives: % 190.22/30.53 | | | | % 190.22/30.53 | | | | Case 1: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | (45) all_252_15 = e0 & op(e1, e1) = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | REF_CLOSE: (2), (9), (15), (20), (33), (45) are inconsistent by % 190.22/30.53 | | | | | sub-proof #450. % 190.22/30.53 | | | | | % 190.22/30.53 | | | | Case 2: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | (46) all_252_23 = e0 & op(e0, e1) = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | ALPHA: (46) implies: % 190.22/30.53 | | | | | (47) op(e0, e1) = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | REF_CLOSE: (2), (10), (12), (47) are inconsistent by sub-proof #324. % 190.22/30.53 | | | | | % 190.22/30.53 | | | | End of split % 190.22/30.53 | | | | % 190.22/30.53 | | | End of split % 190.22/30.53 | | | % 190.22/30.53 | | End of split % 190.22/30.53 | | % 190.22/30.53 | Case 2: % 190.22/30.53 | | % 190.22/30.53 | | (48) all_38_2 = e0 % 190.22/30.53 | | (49) op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e4) | ( ~ % 190.22/30.53 | | (all_38_0 = e3) & op(e2, e4) = all_38_0 & $i(all_38_0))) % 190.22/30.53 | | % 190.22/30.53 | | ALPHA: (49) implies: % 190.22/30.53 | | (50) op(e0, e2) = all_38_1 % 190.22/30.53 | | % 190.22/30.53 | | COMBINE_EQS: (32), (48) imply: % 190.22/30.53 | | (51) all_188_2 = e0 % 190.22/30.53 | | % 190.22/30.53 | | REDUCE: (38), (48) imply: % 190.22/30.53 | | (52) ~ (all_244_8 = e0) % 190.22/30.53 | | % 190.22/30.53 | | REDUCE: (7), (48) imply: % 190.22/30.53 | | (53) op(e2, e0) = e1 % 190.22/30.53 | | % 190.22/30.53 | | BETA: splitting (29) gives: % 190.22/30.53 | | % 190.22/30.53 | | Case 1: % 190.22/30.53 | | | % 190.22/30.53 | | | (54) ~ (all_188_2 = e0) % 190.22/30.53 | | | % 190.22/30.53 | | | REDUCE: (51), (54) imply: % 190.22/30.53 | | | (55) $false % 190.22/30.53 | | | % 190.22/30.53 | | | CLOSE: (55) is inconsistent. % 190.22/30.53 | | | % 190.22/30.53 | | Case 2: % 190.22/30.53 | | | % 190.22/30.53 | | | (56) op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ (all_188_1 = e3) | ( % 190.22/30.53 | | | ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & $i(all_188_0))) % 190.22/30.53 | | | % 190.22/30.53 | | | ALPHA: (56) implies: % 190.22/30.53 | | | (57) op(e0, e2) = all_188_1 % 190.22/30.53 | | | % 190.22/30.53 | | | BETA: splitting (21) gives: % 190.22/30.53 | | | % 190.22/30.53 | | | Case 1: % 190.22/30.53 | | | | % 190.22/30.53 | | | | (58) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 190.22/30.53 | | | | e2) = e0) % 190.22/30.53 | | | | % 190.22/30.53 | | | | REF_CLOSE: (2), (14), (17), (19), (36), (58) are inconsistent by % 190.22/30.53 | | | | sub-proof #546. % 190.22/30.53 | | | | % 190.22/30.53 | | | Case 2: % 190.22/30.53 | | | | % 190.22/30.53 | | | | (59) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, % 190.22/30.53 | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.22/30.53 | | | | % 190.22/30.53 | | | | BETA: splitting (59) gives: % 190.22/30.53 | | | | % 190.22/30.53 | | | | Case 1: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | (60) all_252_8 = e0 & op(e2, e2) = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | ALPHA: (60) implies: % 190.22/30.53 | | | | | (61) op(e2, e2) = e0 % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | REF_CLOSE: (1), (2), (52), (61) are inconsistent by sub-proof #448. % 190.22/30.53 | | | | | % 190.22/30.53 | | | | Case 2: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | (62) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 190.22/30.53 | | | | | op(e0, e2) = e0) % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | BETA: splitting (62) gives: % 190.22/30.53 | | | | | % 190.22/30.53 | | | | | Case 1: % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | (63) all_252_14 = e0 & op(e1, e2) = e0 % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | ALPHA: (63) implies: % 190.22/30.53 | | | | | | (64) op(e1, e2) = e0 % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | REF_CLOSE: (2), (11), (35), (64) are inconsistent by sub-proof #545. % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | Case 2: % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | (65) all_252_22 = e0 & op(e0, e2) = e0 % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | ALPHA: (65) implies: % 190.22/30.53 | | | | | | (66) all_252_22 = e0 % 190.22/30.53 | | | | | | (67) op(e0, e2) = e0 % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | BETA: splitting (31) gives: % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | | Case 1: % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | | (68) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & % 190.22/30.53 | | | | | | | op(e0, e3) = e2) % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | | BETA: splitting (68) gives: % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | | Case 1: % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | (69) all_252_20 = e2 & op(e0, e4) = e2 % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | ALPHA: (69) implies: % 190.22/30.53 | | | | | | | | (70) op(e0, e4) = e2 % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | REF_CLOSE: (2), (6), (34), (70) are inconsistent by sub-proof % 190.22/30.53 | | | | | | | | #323. % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | Case 2: % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | (71) all_252_21 = e2 & op(e0, e3) = e2 % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | ALPHA: (71) implies: % 190.22/30.53 | | | | | | | | (72) op(e0, e3) = e2 % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | REF_CLOSE: (2), (18), (23), (72) are inconsistent by sub-proof % 190.22/30.53 | | | | | | | | #543. % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | End of split % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | Case 2: % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | | (73) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & % 190.22/30.53 | | | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | | BETA: splitting (73) gives: % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | | Case 1: % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | (74) all_252_22 = e2 & op(e0, e2) = e2 % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | REF_CLOSE: (30), (66), (74) are inconsistent by sub-proof #447. % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | Case 2: % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | (75) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 190.22/30.53 | | | | | | | | op(e0, e0) = e2) % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | BETA: splitting (75) gives: % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | | Case 1: % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | (76) all_252_23 = e2 & op(e0, e1) = e2 % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | ALPHA: (76) implies: % 190.22/30.53 | | | | | | | | | (77) op(e0, e1) = e2 % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | REF_CLOSE: (2), (12), (26), (77) are inconsistent by sub-proof % 190.22/30.53 | | | | | | | | | #322. % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | Case 2: % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | (78) all_252_24 = e2 & op(e0, e0) = e2 % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | ALPHA: (78) implies: % 190.22/30.53 | | | | | | | | | (79) all_252_24 = e2 % 190.22/30.53 | | | | | | | | | (80) op(e0, e0) = e2 % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | BETA: splitting (25) gives: % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | | Case 1: % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | (81) all_252_24 = e0 & op(e0, e0) = e0 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | REF_CLOSE: (30), (79), (81) are inconsistent by sub-proof % 190.22/30.53 | | | | | | | | | | #445. % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | Case 2: % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | GROUND_INST: instantiating (2) with all_244_24, e2, e0, e0, % 190.22/30.53 | | | | | | | | | | simplifying with (15), (80) gives: % 190.22/30.53 | | | | | | | | | | (82) all_244_24 = e2 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | GROUND_INST: instantiating (2) with all_28_2, all_188_1, e2, % 190.22/30.53 | | | | | | | | | | e0, simplifying with (4), (57) gives: % 190.22/30.53 | | | | | | | | | | (83) all_188_1 = all_28_2 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | GROUND_INST: instantiating (2) with all_38_1, all_188_1, e2, % 190.22/30.53 | | | | | | | | | | e0, simplifying with (50), (57) gives: % 190.22/30.53 | | | | | | | | | | (84) all_188_1 = all_38_1 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | GROUND_INST: instantiating (2) with e0, all_188_1, e2, e0, % 190.22/30.53 | | | | | | | | | | simplifying with (57), (67) gives: % 190.22/30.53 | | | | | | | | | | (85) all_188_1 = e0 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | GROUND_INST: instantiating (2) with all_40_2, e1, e0, e2, % 190.22/30.53 | | | | | | | | | | simplifying with (27), (53) gives: % 190.22/30.53 | | | | | | | | | | (86) all_40_2 = e1 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | COMBINE_EQS: (83), (84) imply: % 190.22/30.53 | | | | | | | | | | (87) all_38_1 = all_28_2 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | COMBINE_EQS: (84), (85) imply: % 190.22/30.53 | | | | | | | | | | (88) all_38_1 = e0 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | COMBINE_EQS: (87), (88) imply: % 190.22/30.53 | | | | | | | | | | (89) all_28_2 = e0 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | REDUCE: (22), (82) imply: % 190.22/30.53 | | | | | | | | | | (90) ~ (e4 = e2) % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | REDUCE: (28), (86), (89) imply: % 190.22/30.53 | | | | | | | | | | (91) op(e0, e1) = e2 % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | | REF_CLOSE: (2), (12), (26), (91) are inconsistent by % 190.22/30.53 | | | | | | | | | | sub-proof #322. % 190.22/30.53 | | | | | | | | | | % 190.22/30.53 | | | | | | | | | End of split % 190.22/30.53 | | | | | | | | | % 190.22/30.53 | | | | | | | | End of split % 190.22/30.53 | | | | | | | | % 190.22/30.53 | | | | | | | End of split % 190.22/30.53 | | | | | | | % 190.22/30.53 | | | | | | End of split % 190.22/30.53 | | | | | | % 190.22/30.53 | | | | | End of split % 190.22/30.53 | | | | | % 190.22/30.53 | | | | End of split % 190.22/30.53 | | | | % 190.22/30.53 | | | End of split % 190.22/30.53 | | | % 190.22/30.53 | | End of split % 190.22/30.53 | | % 190.22/30.53 | End of split % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #322 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) op(e0, e1) = e4 % 190.22/30.53 (3) op(e0, e1) = e2 % 190.22/30.53 (4) ~ (e4 = e2) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | GROUND_INST: instantiating (1) with e4, e2, e1, e0, simplifying with (2), (3) % 190.22/30.53 | gives: % 190.22/30.53 | (5) e4 = e2 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (4), (5) imply: % 190.22/30.53 | (6) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (6) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #323 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) op(e0, e4) = e2 % 190.22/30.53 (3) op(e0, e4) = e1 % 190.22/30.53 (4) ~ (e2 = e1) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | GROUND_INST: instantiating (1) with e1, e2, e4, e0, simplifying with (2), (3) % 190.22/30.53 | gives: % 190.22/30.53 | (5) e2 = e1 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (4), (5) imply: % 190.22/30.53 | (6) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (6) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #324 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) op(e0, e1) = e4 % 190.22/30.53 (3) op(e0, e1) = e0 % 190.22/30.53 (4) ~ (e4 = e0) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | GROUND_INST: instantiating (1) with e4, e0, e1, e0, simplifying with (2), (3) % 190.22/30.53 | gives: % 190.22/30.53 | (5) e4 = e0 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (4), (5) imply: % 190.22/30.53 | (6) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (6) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #325 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) op(e3, e4) = all_100_2 % 190.22/30.53 (3) op(e4, e4) = all_244_0 % 190.22/30.53 (4) (all_252_0 = e2 & op(e4, e4) = e2) | (all_252_2 = e2 & op(e3, e4) = e2) % 190.22/30.53 (5) ~ (all_244_0 = e2) % 190.22/30.53 (6) ~ (all_100_2 = e2) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | BETA: splitting (4) gives: % 190.22/30.53 | % 190.22/30.53 | Case 1: % 190.22/30.53 | | % 190.22/30.53 | | (7) all_252_0 = e2 & op(e4, e4) = e2 % 190.22/30.53 | | % 190.22/30.53 | | ALPHA: (7) implies: % 190.22/30.53 | | (8) op(e4, e4) = e2 % 190.22/30.53 | | % 190.22/30.53 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #500. % 190.22/30.53 | | % 190.22/30.53 | Case 2: % 190.22/30.53 | | % 190.22/30.53 | | (9) all_252_2 = e2 & op(e3, e4) = e2 % 190.22/30.53 | | % 190.22/30.53 | | ALPHA: (9) implies: % 190.22/30.53 | | (10) op(e3, e4) = e2 % 190.22/30.53 | | % 190.22/30.53 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #471. % 190.22/30.53 | | % 190.22/30.53 | End of split % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #326 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ~ (all_16_2 = e2) % 190.22/30.53 (2) ~ (all_16_2 = e0) % 190.22/30.53 (3) all_250_15 = e2 | all_250_15 = e1 | all_250_15 = e0 % 190.22/30.53 (4) all_250_15 = all_16_2 % 190.22/30.53 (5) ~ (all_16_2 = e1) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | BETA: splitting (3) gives: % 190.22/30.53 | % 190.22/30.53 | Case 1: % 190.22/30.53 | | % 190.22/30.53 | | (6) all_250_15 = e2 % 190.22/30.53 | | % 190.22/30.53 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #577. % 190.22/30.53 | | % 190.22/30.53 | Case 2: % 190.22/30.53 | | % 190.22/30.53 | | (7) all_250_15 = e1 | all_250_15 = e0 % 190.22/30.53 | | % 190.22/30.53 | | BETA: splitting (7) gives: % 190.22/30.53 | | % 190.22/30.53 | | Case 1: % 190.22/30.53 | | | % 190.22/30.53 | | | (8) all_250_15 = e1 % 190.22/30.53 | | | % 190.22/30.53 | | | COMBINE_EQS: (4), (8) imply: % 190.22/30.53 | | | (9) all_16_2 = e1 % 190.22/30.53 | | | % 190.22/30.53 | | | SIMP: (9) implies: % 190.22/30.53 | | | (10) all_16_2 = e1 % 190.22/30.53 | | | % 190.22/30.53 | | | REDUCE: (5), (10) imply: % 190.22/30.53 | | | (11) $false % 190.22/30.53 | | | % 190.22/30.53 | | | CLOSE: (11) is inconsistent. % 190.22/30.53 | | | % 190.22/30.53 | | Case 2: % 190.22/30.53 | | | % 190.22/30.53 | | | (12) all_250_15 = e0 % 190.22/30.53 | | | % 190.22/30.53 | | | REF_CLOSE: (2), (4), (12) are inconsistent by sub-proof #574. % 190.22/30.53 | | | % 190.22/30.53 | | End of split % 190.22/30.53 | | % 190.22/30.53 | End of split % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #327 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) ~ (all_244_24 = e2) % 190.22/30.53 (3) op(e0, e0) = all_244_24 % 190.22/30.53 (4) op(e0, e1) = all_20_2 % 190.22/30.53 (5) ~ (all_20_2 = e2) % 190.22/30.53 (6) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | BETA: splitting (6) gives: % 190.22/30.53 | % 190.22/30.53 | Case 1: % 190.22/30.53 | | % 190.22/30.53 | | (7) all_252_23 = e2 & op(e0, e1) = e2 % 190.22/30.53 | | % 190.22/30.53 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #540. % 190.22/30.53 | | % 190.22/30.53 | Case 2: % 190.22/30.53 | | % 190.22/30.53 | | (8) all_252_24 = e2 & op(e0, e0) = e2 % 190.22/30.53 | | % 190.22/30.53 | | ALPHA: (8) implies: % 190.22/30.53 | | (9) op(e0, e0) = e2 % 190.22/30.53 | | % 190.22/30.53 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #477. % 190.22/30.53 | | % 190.22/30.53 | End of split % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #328 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) op(e0, e2) = e4 % 190.22/30.53 (3) op(e0, e2) = e3 % 190.22/30.53 (4) ~ (e4 = e3) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | GROUND_INST: instantiating (1) with e4, e3, e2, e0, simplifying with (2), (3) % 190.22/30.53 | gives: % 190.22/30.53 | (5) e4 = e3 % 190.22/30.53 | % 190.22/30.53 | REDUCE: (4), (5) imply: % 190.22/30.53 | (6) $false % 190.22/30.53 | % 190.22/30.53 | CLOSE: (6) is inconsistent. % 190.22/30.53 | % 190.22/30.53 End of proof % 190.22/30.53 % 190.22/30.53 Sub-proof #329 shows that the following formulas are inconsistent: % 190.22/30.53 ---------------------------------------------------------------- % 190.22/30.53 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.53 (2) ~ (e4 = e0) % 190.22/30.53 (3) (all_252_20 = e4 & op(e0, e4) = e4) | (all_252_21 = e4 & op(e0, e3) = e4) % 190.22/30.53 (4) op(e0, e3) = e2 % 190.22/30.53 (5) all_252_20 = e0 % 190.22/30.53 (6) ~ (e4 = e2) % 190.22/30.53 % 190.22/30.53 Begin of proof % 190.22/30.53 | % 190.22/30.53 | BETA: splitting (3) gives: % 190.22/30.53 | % 190.22/30.53 | Case 1: % 190.22/30.53 | | % 190.22/30.53 | | (7) all_252_20 = e4 & op(e0, e4) = e4 % 190.22/30.53 | | % 190.22/30.53 | | ALPHA: (7) implies: % 190.22/30.53 | | (8) all_252_20 = e4 % 190.22/30.53 | | % 190.22/30.53 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #525. % 190.22/30.53 | | % 190.22/30.53 | Case 2: % 190.22/30.53 | | % 190.22/30.53 | | (9) all_252_21 = e4 & op(e0, e3) = e4 % 190.22/30.53 | | % 190.22/30.53 | | ALPHA: (9) implies: % 190.22/30.53 | | (10) op(e0, e3) = e4 % 190.22/30.54 | | % 190.22/30.54 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #330. % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #330 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) op(e0, e3) = e4 % 190.22/30.54 (3) op(e0, e3) = e2 % 190.22/30.54 (4) ~ (e4 = e2) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (1) with e4, e2, e3, e0, simplifying with (2), (3) % 190.22/30.54 | gives: % 190.22/30.54 | (5) e4 = e2 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (4), (5) imply: % 190.22/30.54 | (6) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (6) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #331 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_24 = e3 % 190.22/30.54 (2) all_252_24 = e0 % 190.22/30.54 (3) ~ (e3 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (1), (2) imply: % 190.22/30.54 | (4) e3 = e0 % 190.22/30.54 | % 190.22/30.54 | SIMP: (4) implies: % 190.22/30.54 | (5) e3 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (5) imply: % 190.22/30.54 | (6) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (6) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #332 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) op(all_26_2, e3) = e1 % 190.22/30.54 (3) all_26_2 = e0 % 190.22/30.54 (4) ~ (all_20_2 = e3) % 190.22/30.54 (5) op(e0, e1) = all_20_2 % 190.22/30.54 (6) op(e0, e3) = all_22_2 % 190.22/30.54 (7) op(e0, all_22_2) = e3 % 190.22/30.54 (8) all_114_1 = all_26_2 % 190.22/30.54 (9) ~ (all_114_1 = e0) | ( ~ (all_114_0 = e2) & op(e1, e0) = all_114_0 & % 190.22/30.54 $i(all_114_0)) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (3), (8) imply: % 190.22/30.54 | (10) all_114_1 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (2), (3) imply: % 190.22/30.54 | (11) op(e0, e3) = e1 % 190.22/30.54 | % 190.22/30.54 | BETA: splitting (9) gives: % 190.22/30.54 | % 190.22/30.54 | Case 1: % 190.22/30.54 | | % 190.22/30.54 | | (12) ~ (all_114_1 = e0) % 190.22/30.54 | | % 190.22/30.54 | | REDUCE: (10), (12) imply: % 190.22/30.54 | | (13) $false % 190.22/30.54 | | % 190.22/30.54 | | CLOSE: (13) is inconsistent. % 190.22/30.54 | | % 190.22/30.54 | Case 2: % 190.22/30.54 | | % 190.22/30.54 | | % 190.22/30.54 | | GROUND_INST: instantiating (1) with all_22_2, e1, e3, e0, simplifying with % 190.22/30.54 | | (6), (11) gives: % 190.22/30.54 | | (14) all_22_2 = e1 % 190.22/30.54 | | % 190.22/30.54 | | REDUCE: (7), (14) imply: % 190.22/30.54 | | (15) op(e0, e1) = e3 % 190.22/30.54 | | % 190.22/30.54 | | REF_CLOSE: (1), (4), (5), (15) are inconsistent by sub-proof #508. % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #333 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_21 = e1 % 190.22/30.54 (2) all_252_21 = e0 % 190.22/30.54 (3) ~ (e1 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (1), (2) imply: % 190.22/30.54 | (4) e1 = e0 % 190.22/30.54 | % 190.22/30.54 | SIMP: (4) implies: % 190.22/30.54 | (5) e1 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (5) imply: % 190.22/30.54 | (6) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (6) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #334 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_21 = e3 % 190.22/30.54 (2) all_252_21 = e0 % 190.22/30.54 (3) ~ (e3 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (1), (2) imply: % 190.22/30.54 | (4) e3 = e0 % 190.22/30.54 | % 190.22/30.54 | SIMP: (4) implies: % 190.22/30.54 | (5) e3 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (5) imply: % 190.22/30.54 | (6) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (6) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #335 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_3 = e0 & op(e3, e3) = e0 % 190.22/30.54 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (3) op(e3, e3) = all_244_3 % 190.22/30.54 (4) ~ (all_244_3 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (1) implies: % 190.22/30.54 | (5) op(e3, e3) = e0 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (2) with all_244_3, e0, e3, e3, simplifying with % 190.22/30.54 | (3), (5) gives: % 190.22/30.54 | (6) all_244_3 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (4), (6) imply: % 190.22/30.54 | (7) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (7) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #336 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) op(e1, e3) = all_62_2 % 190.22/30.54 (3) all_252_13 = e3 & op(e1, e3) = e3 % 190.22/30.54 (4) ~ (e4 = e3) % 190.22/30.54 (5) op(e1, e3) = e4 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (3) implies: % 190.22/30.54 | (6) op(e1, e3) = e3 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (1) with all_62_2, e3, e3, e1, simplifying with % 190.22/30.54 | (2), (6) gives: % 190.22/30.54 | (7) all_62_2 = e3 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (1) with all_62_2, e4, e3, e1, simplifying with % 190.22/30.54 | (2), (5) gives: % 190.22/30.54 | (8) all_62_2 = e4 % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (7), (8) imply: % 190.22/30.54 | (9) e4 = e3 % 190.22/30.54 | % 190.22/30.54 | SIMP: (9) implies: % 190.22/30.54 | (10) e4 = e3 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (4), (10) imply: % 190.22/30.54 | (11) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (11) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #337 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_7 = e3 & op(e2, e3) = e3 % 190.22/30.54 (2) all_252_7 = e2 % 190.22/30.54 (3) ~ (e3 = e2) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (1) implies: % 190.22/30.54 | (4) all_252_7 = e3 % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (2), (4) imply: % 190.22/30.54 | (5) e3 = e2 % 190.22/30.54 | % 190.22/30.54 | SIMP: (5) implies: % 190.22/30.54 | (6) e3 = e2 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (6) imply: % 190.22/30.54 | (7) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (7) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #338 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) (all_252_1 = e3 & op(e4, e3) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 190.22/30.54 (3) op(e4, e3) = all_84_2 % 190.22/30.54 (4) all_252_3 = e1 % 190.22/30.54 (5) ~ (e3 = e0) % 190.22/30.54 (6) ~ (e3 = e1) % 190.22/30.54 (7) op(e4, e3) = e0 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | BETA: splitting (2) gives: % 190.22/30.54 | % 190.22/30.54 | Case 1: % 190.22/30.54 | | % 190.22/30.54 | | (8) all_252_1 = e3 & op(e4, e3) = e3 % 190.22/30.54 | | % 190.22/30.54 | | ALPHA: (8) implies: % 190.22/30.54 | | (9) op(e4, e3) = e3 % 190.22/30.54 | | % 190.22/30.54 | | REF_CLOSE: (1), (3), (5), (7), (9) are inconsistent by sub-proof #431. % 190.22/30.54 | | % 190.22/30.54 | Case 2: % 190.22/30.54 | | % 190.22/30.54 | | (10) all_252_3 = e3 & op(e3, e3) = e3 % 190.22/30.54 | | % 190.22/30.54 | | ALPHA: (10) implies: % 190.22/30.54 | | (11) all_252_3 = e3 % 190.22/30.54 | | % 190.22/30.54 | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #366. % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #339 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ~ (e2 = e1) % 190.22/30.54 (2) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 190.22/30.54 (3) all_252_3 = e1 % 190.22/30.54 (4) all_252_1 = e0 % 190.22/30.54 (5) ~ (e2 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | BETA: splitting (2) gives: % 190.22/30.54 | % 190.22/30.54 | Case 1: % 190.22/30.54 | | % 190.22/30.54 | | (6) all_252_1 = e2 & op(e4, e3) = e2 % 190.22/30.54 | | % 190.22/30.54 | | ALPHA: (6) implies: % 190.22/30.54 | | (7) all_252_1 = e2 % 190.22/30.54 | | % 190.22/30.54 | | COMBINE_EQS: (4), (7) imply: % 190.22/30.54 | | (8) e2 = e0 % 190.22/30.54 | | % 190.22/30.54 | | SIMP: (8) implies: % 190.22/30.54 | | (9) e2 = e0 % 190.22/30.54 | | % 190.22/30.54 | | REDUCE: (5), (9) imply: % 190.22/30.54 | | (10) $false % 190.22/30.54 | | % 190.22/30.54 | | CLOSE: (10) is inconsistent. % 190.22/30.54 | | % 190.22/30.54 | Case 2: % 190.22/30.54 | | % 190.22/30.54 | | (11) all_252_3 = e2 & op(e3, e3) = e2 % 190.22/30.54 | | % 190.22/30.54 | | ALPHA: (11) implies: % 190.22/30.54 | | (12) all_252_3 = e2 % 190.22/30.54 | | % 190.22/30.54 | | COMBINE_EQS: (3), (12) imply: % 190.22/30.54 | | (13) e2 = e1 % 190.22/30.54 | | % 190.22/30.54 | | SIMP: (13) implies: % 190.22/30.54 | | (14) e2 = e1 % 190.22/30.54 | | % 190.22/30.54 | | REDUCE: (1), (14) imply: % 190.22/30.54 | | (15) $false % 190.22/30.54 | | % 190.22/30.54 | | CLOSE: (15) is inconsistent. % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #340 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) ~ (all_26_2 = e0) % 190.22/30.54 (3) all_252_1 = e1 % 190.22/30.54 (4) op(e4, e0) = e3 % 190.22/30.54 (5) op(e4, e1) = all_26_2 % 190.22/30.54 (6) ~ (all_6_2 = e0) % 190.22/30.54 (7) op(e4, e4) = all_244_0 % 190.22/30.54 (8) ~ (e3 = e0) % 190.22/30.54 (9) ~ (all_244_0 = e0) % 190.22/30.54 (10) ~ (e1 = e0) % 190.22/30.54 (11) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = e0) % 190.22/30.54 | (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) = % 190.22/30.54 e0) | (all_252_16 = e0 & op(e4, e0) = e0) % 190.22/30.54 (12) op(e4, e2) = all_6_2 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | BETA: splitting (11) gives: % 190.22/30.54 | % 190.22/30.54 | Case 1: % 190.22/30.54 | | % 190.22/30.54 | | (13) (all_252_0 = e0 & op(e4, e4) = e0) | (all_252_1 = e0 & op(e4, e3) = % 190.22/30.54 | | e0) % 190.22/30.54 | | % 190.22/30.54 | | BETA: splitting (13) gives: % 190.22/30.54 | | % 190.22/30.54 | | Case 1: % 190.22/30.54 | | | % 190.22/30.54 | | | (14) all_252_0 = e0 & op(e4, e4) = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | REF_CLOSE: (1), (7), (9), (14) are inconsistent by sub-proof #343. % 190.22/30.54 | | | % 190.22/30.54 | | Case 2: % 190.22/30.54 | | | % 190.22/30.54 | | | (15) all_252_1 = e0 & op(e4, e3) = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | ALPHA: (15) implies: % 190.22/30.54 | | | (16) all_252_1 = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | COMBINE_EQS: (3), (16) imply: % 190.22/30.54 | | | (17) e1 = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | REDUCE: (10), (17) imply: % 190.22/30.54 | | | (18) $false % 190.22/30.54 | | | % 190.22/30.54 | | | CLOSE: (18) is inconsistent. % 190.22/30.54 | | | % 190.22/30.54 | | End of split % 190.22/30.54 | | % 190.22/30.54 | Case 2: % 190.22/30.54 | | % 190.22/30.54 | | (19) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) = % 190.22/30.54 | | e0) | (all_252_16 = e0 & op(e4, e0) = e0) % 190.22/30.54 | | % 190.22/30.54 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (12), (19) are inconsistent by % 190.22/30.54 | | sub-proof #341. % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #341 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) ~ (all_26_2 = e0) % 190.22/30.54 (3) op(e4, e0) = e3 % 190.22/30.54 (4) op(e4, e1) = all_26_2 % 190.22/30.54 (5) ~ (all_6_2 = e0) % 190.22/30.54 (6) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_9 = e0 & op(e4, e1) = e0) | % 190.22/30.54 (all_252_16 = e0 & op(e4, e0) = e0) % 190.22/30.54 (7) ~ (e3 = e0) % 190.22/30.54 (8) op(e4, e2) = all_6_2 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | BETA: splitting (6) gives: % 190.22/30.54 | % 190.22/30.54 | Case 1: % 190.22/30.54 | | % 190.22/30.54 | | (9) all_252_4 = e0 & op(e4, e2) = e0 % 190.22/30.54 | | % 190.22/30.54 | | ALPHA: (9) implies: % 190.22/30.54 | | (10) op(e4, e2) = e0 % 190.22/30.54 | | % 190.22/30.54 | | REF_CLOSE: (1), (5), (8), (10) are inconsistent by sub-proof #548. % 190.22/30.54 | | % 190.22/30.54 | Case 2: % 190.22/30.54 | | % 190.22/30.54 | | (11) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_16 = e0 & op(e4, e0) = % 190.22/30.54 | | e0) % 190.22/30.54 | | % 190.22/30.54 | | BETA: splitting (11) gives: % 190.22/30.54 | | % 190.22/30.54 | | Case 1: % 190.22/30.54 | | | % 190.22/30.54 | | | (12) all_252_9 = e0 & op(e4, e1) = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | ALPHA: (12) implies: % 190.22/30.54 | | | (13) op(e4, e1) = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | REF_CLOSE: (1), (2), (4), (13) are inconsistent by sub-proof #452. % 190.22/30.54 | | | % 190.22/30.54 | | Case 2: % 190.22/30.54 | | | % 190.22/30.54 | | | (14) all_252_16 = e0 & op(e4, e0) = e0 % 190.22/30.54 | | | % 190.22/30.54 | | | REF_CLOSE: (1), (3), (7), (14) are inconsistent by sub-proof #342. % 190.22/30.54 | | | % 190.22/30.54 | | End of split % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #342 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_16 = e0 & op(e4, e0) = e0 % 190.22/30.54 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (3) op(e4, e0) = e3 % 190.22/30.54 (4) ~ (e3 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (1) implies: % 190.22/30.54 | (5) op(e4, e0) = e0 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (2) with e0, e3, e0, e4, simplifying with (3), (5) % 190.22/30.54 | gives: % 190.22/30.54 | (6) e3 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (4), (6) imply: % 190.22/30.54 | (7) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (7) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #343 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_0 = e0 & op(e4, e4) = e0 % 190.22/30.54 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (3) op(e4, e4) = all_244_0 % 190.22/30.54 (4) ~ (all_244_0 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (1) implies: % 190.22/30.54 | (5) op(e4, e4) = e0 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (2) with all_244_0, e0, e4, e4, simplifying with % 190.22/30.54 | (3), (5) gives: % 190.22/30.54 | (6) all_244_0 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (4), (6) imply: % 190.22/30.54 | (7) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (7) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #344 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) all_36_2 = e0 % 190.22/30.54 (3) ~ (all_30_2 = e3) % 190.22/30.54 (4) op(e4, e0) = all_30_2 % 190.22/30.54 (5) op(e4, all_16_1) = e3 % 190.22/30.54 (6) all_36_2 = all_16_1 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (2), (6) imply: % 190.22/30.54 | (7) all_16_1 = e0 % 190.22/30.54 | % 190.22/30.54 | SIMP: (7) implies: % 190.22/30.54 | (8) all_16_1 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (5), (8) imply: % 190.22/30.54 | (9) op(e4, e0) = e3 % 190.22/30.54 | % 190.22/30.54 | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #539. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #345 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) all_34_2 = e0 % 190.22/30.54 (3) op(e0, all_20_2) = e1 % 190.22/30.54 (4) op(all_34_2, all_20_2) = e0 % 190.22/30.54 (5) ~ (e1 = e0) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | SIMP: (5) implies: % 190.22/30.54 | (6) ~ (e1 = e0) % 190.22/30.54 | % 190.22/30.54 | REDUCE: (2), (4) imply: % 190.22/30.54 | (7) op(e0, all_20_2) = e0 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (1) with e1, e0, all_20_2, e0, simplifying with % 190.22/30.54 | (3), (7) gives: % 190.22/30.54 | (8) e1 = e0 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (6), (8) imply: % 190.22/30.54 | (9) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (9) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #346 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (2) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | % 190.22/30.54 all_250_17 = e0 % 190.22/30.54 (3) ~ (all_4_2 = e4) % 190.22/30.54 (4) op(e2, all_38_2) = e1 % 190.22/30.54 (5) all_74_2 = all_16_1 % 190.22/30.54 (6) ~ (all_74_2 = e2) | (op(e2, e3) = all_74_1 & $i(all_74_1) & ( ~ % 190.22/30.54 (all_74_1 = e0) | ( ~ (all_74_0 = e4) & op(e3, e0) = all_74_0 & % 190.22/30.54 $i(all_74_0)))) % 190.22/30.54 (7) op(e3, all_16_1) = e1 % 190.22/30.54 (8) ~ (all_8_2 = all_4_2) % 190.22/30.54 (9) all_16_1 = e2 % 190.22/30.54 (10) ~ (all_6_2 = all_4_2) % 190.22/30.54 (11) op(all_4_2, all_38_2) = e2 % 190.22/30.54 (12) op(e4, all_16_1) = e3 % 190.22/30.54 (13) ~ (all_16_1 = e2) | ( ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 & % 190.22/30.54 $i(all_16_0)) % 190.22/30.54 (14) op(e3, e2) = all_8_2 % 190.22/30.54 (15) all_250_17 = all_4_2 % 190.22/30.54 (16) op(e1, e2) = all_4_2 % 190.22/30.54 (17) op(e4, e2) = all_6_2 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (5), (9) imply: % 190.22/30.54 | (18) all_74_2 = e2 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (9), (12) imply: % 190.22/30.54 | (19) op(e4, e2) = e3 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (7), (9) imply: % 190.22/30.54 | (20) op(e3, e2) = e1 % 190.22/30.54 | % 190.22/30.54 | BETA: splitting (13) gives: % 190.22/30.54 | % 190.22/30.54 | Case 1: % 190.22/30.54 | | % 190.22/30.54 | | (21) ~ (all_16_1 = e2) % 190.22/30.54 | | % 190.22/30.54 | | REDUCE: (9), (21) imply: % 190.22/30.54 | | (22) $false % 190.22/30.54 | | % 190.22/30.54 | | CLOSE: (22) is inconsistent. % 190.22/30.54 | | % 190.22/30.54 | Case 2: % 190.22/30.54 | | % 190.22/30.54 | | (23) ~ (all_16_0 = e0) & op(e1, e2) = all_16_0 & $i(all_16_0) % 190.22/30.54 | | % 190.22/30.54 | | ALPHA: (23) implies: % 190.22/30.54 | | (24) ~ (all_16_0 = e0) % 190.22/30.54 | | (25) op(e1, e2) = all_16_0 % 190.22/30.54 | | % 190.22/30.54 | | BETA: splitting (6) gives: % 190.22/30.54 | | % 190.22/30.54 | | Case 1: % 190.22/30.54 | | | % 190.22/30.54 | | | (26) ~ (all_74_2 = e2) % 190.22/30.54 | | | % 190.22/30.54 | | | REDUCE: (18), (26) imply: % 190.22/30.54 | | | (27) $false % 190.22/30.54 | | | % 190.22/30.54 | | | CLOSE: (27) is inconsistent. % 190.22/30.54 | | | % 190.22/30.54 | | Case 2: % 190.22/30.54 | | | % 190.22/30.54 | | | % 190.22/30.54 | | | GROUND_INST: instantiating (1) with all_4_2, all_16_0, e2, e1, simplifying % 190.22/30.54 | | | with (16), (25) gives: % 190.22/30.54 | | | (28) all_16_0 = all_4_2 % 190.22/30.54 | | | % 190.22/30.54 | | | GROUND_INST: instantiating (1) with all_8_2, e1, e2, e3, simplifying with % 190.22/30.54 | | | (14), (20) gives: % 190.22/30.54 | | | (29) all_8_2 = e1 % 190.22/30.54 | | | % 190.22/30.54 | | | GROUND_INST: instantiating (1) with all_6_2, e3, e2, e4, simplifying with % 190.22/30.54 | | | (17), (19) gives: % 190.22/30.54 | | | (30) all_6_2 = e3 % 190.22/30.54 | | | % 190.22/30.54 | | | REDUCE: (24), (28) imply: % 190.22/30.54 | | | (31) ~ (all_4_2 = e0) % 190.22/30.54 | | | % 190.22/30.54 | | | REDUCE: (8), (29) imply: % 190.22/30.54 | | | (32) ~ (all_4_2 = e1) % 190.22/30.54 | | | % 190.22/30.54 | | | SIMP: (32) implies: % 190.22/30.54 | | | (33) ~ (all_4_2 = e1) % 190.22/30.54 | | | % 190.22/30.54 | | | REDUCE: (10), (30) imply: % 190.22/30.54 | | | (34) ~ (all_4_2 = e3) % 190.22/30.54 | | | % 190.22/30.54 | | | SIMP: (34) implies: % 190.22/30.54 | | | (35) ~ (all_4_2 = e3) % 190.22/30.54 | | | % 190.22/30.54 | | | REF_CLOSE: (1), (2), (3), (4), (11), (15), (31), (33), (35) are % 190.22/30.54 | | | inconsistent by sub-proof #575. % 190.22/30.54 | | | % 190.22/30.54 | | End of split % 190.22/30.54 | | % 190.22/30.54 | End of split % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #347 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_4 = e2 & op(e4, e2) = e2 % 190.22/30.54 (2) all_252_4 = e3 % 190.22/30.54 (3) ~ (e3 = e2) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (1) implies: % 190.22/30.54 | (4) all_252_4 = e2 % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (2), (4) imply: % 190.22/30.54 | (5) e3 = e2 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (5) imply: % 190.22/30.54 | (6) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (6) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #348 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_4 = e1 & op(e4, e2) = e1 % 190.22/30.54 (2) all_252_4 = e3 % 190.22/30.54 (3) ~ (e3 = e1) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | ALPHA: (1) implies: % 190.22/30.54 | (4) all_252_4 = e1 % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (2), (4) imply: % 190.22/30.54 | (5) e3 = e1 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (5) imply: % 190.22/30.54 | (6) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (6) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #349 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) op(e2, e2) = all_244_8 % 190.22/30.54 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (3) ~ (e4 = e3) % 190.22/30.54 (4) op(e2, e2) = e4 % 190.22/30.54 (5) op(e2, e2) = e3 % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (2) with all_244_8, e3, e2, e2, simplifying with % 190.22/30.54 | (1), (5) gives: % 190.22/30.54 | (6) all_244_8 = e3 % 190.22/30.54 | % 190.22/30.54 | GROUND_INST: instantiating (2) with all_244_8, e4, e2, e2, simplifying with % 190.22/30.54 | (1), (4) gives: % 190.22/30.54 | (7) all_244_8 = e4 % 190.22/30.54 | % 190.22/30.54 | COMBINE_EQS: (6), (7) imply: % 190.22/30.54 | (8) e4 = e3 % 190.22/30.54 | % 190.22/30.54 | REDUCE: (3), (8) imply: % 190.22/30.54 | (9) $false % 190.22/30.54 | % 190.22/30.54 | CLOSE: (9) is inconsistent. % 190.22/30.54 | % 190.22/30.54 End of proof % 190.22/30.54 % 190.22/30.54 Sub-proof #350 shows that the following formulas are inconsistent: % 190.22/30.54 ---------------------------------------------------------------- % 190.22/30.54 (1) all_252_14 = e3 & op(e1, e2) = e3 % 190.22/30.54 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.54 (3) op(e1, e2) = all_4_2 % 190.22/30.54 (4) ~ (all_4_2 = e3) % 190.22/30.54 % 190.22/30.54 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (5) op(e1, e2) = e3 % 190.22/30.55 | % 190.22/30.55 | GROUND_INST: instantiating (2) with all_4_2, e3, e2, e1, simplifying with (3), % 190.22/30.55 | (5) gives: % 190.22/30.55 | (6) all_4_2 = e3 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (4), (6) imply: % 190.22/30.55 | (7) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (7) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #351 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_23 = e1 % 190.22/30.55 (2) all_252_23 = e0 % 190.22/30.55 (3) ~ (e1 = e0) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (1), (2) imply: % 190.22/30.55 | (4) e1 = e0 % 190.22/30.55 | % 190.22/30.55 | SIMP: (4) implies: % 190.22/30.55 | (5) e1 = e0 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (5) imply: % 190.22/30.55 | (6) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (6) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #352 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.55 (2) ~ (all_40_2 = all_34_2) % 190.22/30.55 (3) op(e1, e0) = e1 % 190.22/30.55 (4) op(e2, e0) = all_40_2 % 190.22/30.55 (5) op(e1, e0) = all_34_2 % 190.22/30.55 (6) op(e2, e0) = e1 % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | GROUND_INST: instantiating (1) with all_34_2, e1, e0, e1, simplifying with % 190.22/30.55 | (3), (5) gives: % 190.22/30.55 | (7) all_34_2 = e1 % 190.22/30.55 | % 190.22/30.55 | GROUND_INST: instantiating (1) with all_40_2, e1, e0, e2, simplifying with % 190.22/30.55 | (4), (6) gives: % 190.22/30.55 | (8) all_40_2 = e1 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (2), (7), (8) imply: % 190.22/30.55 | (9) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (9) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #353 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_15 = e0 % 190.22/30.55 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.55 (3) ~ (e2 = e1) % 190.22/30.55 (4) all_252_14 = e2 % 190.22/30.55 (5) all_252_19 = e4 % 190.22/30.55 (6) op(e1, e3) = e4 % 190.22/30.55 (7) all_252_12 = e3 % 190.22/30.55 (8) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1) % 190.22/30.55 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) = % 190.22/30.55 e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.22/30.55 (9) ~ (e1 = e0) % 190.22/30.55 (10) ~ (e3 = e1) % 190.22/30.55 (11) ~ (e4 = e1) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | BETA: splitting (8) gives: % 190.22/30.55 | % 190.22/30.55 | Case 1: % 190.22/30.55 | | % 190.22/30.55 | | (12) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 190.22/30.55 | | = e1) % 190.22/30.55 | | % 190.22/30.55 | | BETA: splitting (12) gives: % 190.22/30.55 | | % 190.22/30.55 | | Case 1: % 190.22/30.55 | | | % 190.22/30.55 | | | (13) all_252_12 = e1 & op(e1, e4) = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | REF_CLOSE: (7), (10), (13) are inconsistent by sub-proof #424. % 190.22/30.55 | | | % 190.22/30.55 | | Case 2: % 190.22/30.55 | | | % 190.22/30.55 | | | (14) all_252_13 = e1 & op(e1, e3) = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | REF_CLOSE: (2), (6), (11), (14) are inconsistent by sub-proof #423. % 190.22/30.55 | | | % 190.22/30.55 | | End of split % 190.22/30.55 | | % 190.22/30.55 | Case 2: % 190.22/30.55 | | % 190.22/30.55 | | (15) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) % 190.22/30.55 | | = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.22/30.55 | | % 190.22/30.55 | | BETA: splitting (15) gives: % 190.22/30.55 | | % 190.22/30.55 | | Case 1: % 190.22/30.55 | | | % 190.22/30.55 | | | (16) all_252_14 = e1 & op(e1, e2) = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #395. % 190.22/30.55 | | | % 190.22/30.55 | | Case 2: % 190.22/30.55 | | | % 190.22/30.55 | | | (17) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 190.22/30.55 | | | e0) = e1) % 190.22/30.55 | | | % 190.22/30.55 | | | BETA: splitting (17) gives: % 190.22/30.55 | | | % 190.22/30.55 | | | Case 1: % 190.22/30.55 | | | | % 190.22/30.55 | | | | (18) all_252_15 = e1 & op(e1, e1) = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | REF_CLOSE: (1), (9), (18) are inconsistent by sub-proof #419. % 190.22/30.55 | | | | % 190.22/30.55 | | | Case 2: % 190.22/30.55 | | | | % 190.22/30.55 | | | | (19) all_252_19 = e1 & op(e1, e0) = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | REF_CLOSE: (5), (11), (19) are inconsistent by sub-proof #354. % 190.22/30.55 | | | | % 190.22/30.55 | | | End of split % 190.22/30.55 | | | % 190.22/30.55 | | End of split % 190.22/30.55 | | % 190.22/30.55 | End of split % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #354 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_19 = e1 & op(e1, e0) = e1 % 190.22/30.55 (2) all_252_19 = e4 % 190.22/30.55 (3) ~ (e4 = e1) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (4) all_252_19 = e1 % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (2), (4) imply: % 190.22/30.55 | (5) e4 = e1 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (5) imply: % 190.22/30.55 | (6) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (6) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #355 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_18 = e3 & op(e2, e0) = e3 % 190.22/30.55 (2) all_252_18 = e4 % 190.22/30.55 (3) ~ (e4 = e3) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (4) all_252_18 = e3 % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (2), (4) imply: % 190.22/30.55 | (5) e4 = e3 % 190.22/30.55 | % 190.22/30.55 | SIMP: (5) implies: % 190.22/30.55 | (6) e4 = e3 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (6) imply: % 190.22/30.55 | (7) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (7) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #356 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_11 = e3 & op(e2, e1) = e3 % 190.22/30.55 (2) all_252_11 = e2 % 190.22/30.55 (3) ~ (e3 = e2) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (4) all_252_11 = e3 % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (2), (4) imply: % 190.22/30.55 | (5) e3 = e2 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (5) imply: % 190.22/30.55 | (6) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (6) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #357 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_11 = e1 & op(e2, e1) = e1 % 190.22/30.55 (2) all_252_11 = e2 % 190.22/30.55 (3) ~ (e2 = e1) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (4) all_252_11 = e1 % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (2), (4) imply: % 190.22/30.55 | (5) e2 = e1 % 190.22/30.55 | % 190.22/30.55 | SIMP: (5) implies: % 190.22/30.55 | (6) e2 = e1 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (6) imply: % 190.22/30.55 | (7) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (7) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #358 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_7 = e3 & op(e2, e3) = e3 % 190.22/30.55 (2) all_252_7 = e0 % 190.22/30.55 (3) ~ (e3 = e0) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (4) all_252_7 = e3 % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (2), (4) imply: % 190.22/30.55 | (5) e3 = e0 % 190.22/30.55 | % 190.22/30.55 | SIMP: (5) implies: % 190.22/30.55 | (6) e3 = e0 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (6) imply: % 190.22/30.55 | (7) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (7) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #359 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) all_252_18 = e0 & op(e2, e0) = e0 % 190.22/30.55 (2) all_252_18 = e4 % 190.22/30.55 (3) ~ (e4 = e0) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | ALPHA: (1) implies: % 190.22/30.55 | (4) all_252_18 = e0 % 190.22/30.55 | % 190.22/30.55 | COMBINE_EQS: (2), (4) imply: % 190.22/30.55 | (5) e4 = e0 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (3), (5) imply: % 190.22/30.55 | (6) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (6) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #360 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.55 (2) op(e2, e4) = e1 % 190.22/30.55 (3) op(e2, e4) = e0 % 190.22/30.55 (4) ~ (e1 = e0) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | GROUND_INST: instantiating (1) with e0, e1, e4, e2, simplifying with (2), (3) % 190.22/30.55 | gives: % 190.22/30.55 | (5) e1 = e0 % 190.22/30.55 | % 190.22/30.55 | REDUCE: (4), (5) imply: % 190.22/30.55 | (6) $false % 190.22/30.55 | % 190.22/30.55 | CLOSE: (6) is inconsistent. % 190.22/30.55 | % 190.22/30.55 End of proof % 190.22/30.55 % 190.22/30.55 Sub-proof #361 shows that the following formulas are inconsistent: % 190.22/30.55 ---------------------------------------------------------------- % 190.22/30.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.22/30.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.22/30.55 (2) ~ (all_36_2 = e0) % 190.22/30.55 (3) op(e3, e1) = all_36_2 % 190.22/30.55 (4) ~ (e2 = e1) % 190.22/30.55 (5) ~ (e4 = e3) % 190.22/30.55 (6) op(e3, e4) = all_100_2 % 190.22/30.55 (7) ~ (all_8_2 = e0) % 190.22/30.55 (8) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = e1) | % 190.22/30.55 (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = e1) % 190.22/30.55 | (all_252_17 = e1 & op(e3, e0) = e1) % 190.22/30.55 (9) ~ (all_100_2 = e3) % 190.22/30.55 (10) ~ (e3 = e0) % 190.22/30.55 (11) op(e3, e2) = all_8_2 % 190.22/30.55 (12) ~ (e3 = e2) % 190.22/30.55 (13) all_252_5 = e4 % 190.22/30.55 (14) all_252_10 = e2 % 190.22/30.55 (15) op(e3, e0) = all_48_2 % 190.22/30.55 (16) ~ (e1 = e0) % 190.22/30.55 (17) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & op(e3, e3) = e3) % 190.22/30.55 | (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & op(e3, e1) = % 190.22/30.55 e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.22/30.55 (18) ~ (e3 = e1) % 190.22/30.55 (19) ~ (e2 = e0) % 190.22/30.55 (20) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, e3) = e0) % 190.22/30.55 | (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = % 190.22/30.55 e0) | (all_252_17 = e0 & op(e3, e0) = e0) % 190.22/30.55 (21) all_252_2 = e2 % 190.22/30.55 (22) ~ (e4 = e1) % 190.22/30.55 % 190.22/30.55 Begin of proof % 190.22/30.55 | % 190.22/30.55 | BETA: splitting (8) gives: % 190.22/30.55 | % 190.22/30.55 | Case 1: % 190.22/30.55 | | % 190.22/30.55 | | (23) (all_252_2 = e1 & op(e3, e4) = e1) | (all_252_3 = e1 & op(e3, e3) = % 190.22/30.55 | | e1) % 190.22/30.55 | | % 190.22/30.55 | | BETA: splitting (23) gives: % 190.22/30.55 | | % 190.22/30.55 | | Case 1: % 190.22/30.55 | | | % 190.22/30.55 | | | (24) all_252_2 = e1 & op(e3, e4) = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | ALPHA: (24) implies: % 190.22/30.55 | | | (25) all_252_2 = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | COMBINE_EQS: (21), (25) imply: % 190.22/30.55 | | | (26) e2 = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | REDUCE: (4), (26) imply: % 190.22/30.55 | | | (27) $false % 190.22/30.55 | | | % 190.22/30.55 | | | CLOSE: (27) is inconsistent. % 190.22/30.55 | | | % 190.22/30.55 | | Case 2: % 190.22/30.55 | | | % 190.22/30.55 | | | (28) all_252_3 = e1 & op(e3, e3) = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | ALPHA: (28) implies: % 190.22/30.55 | | | (29) all_252_3 = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | BETA: splitting (20) gives: % 190.22/30.55 | | | % 190.22/30.55 | | | Case 1: % 190.22/30.55 | | | | % 190.22/30.55 | | | | (30) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, % 190.22/30.55 | | | | e3) = e0) % 190.22/30.55 | | | | % 190.22/30.55 | | | | BETA: splitting (30) gives: % 190.22/30.55 | | | | % 190.22/30.55 | | | | Case 1: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | (31) all_252_2 = e0 & op(e3, e4) = e0 % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | REF_CLOSE: (19), (21), (31) are inconsistent by sub-proof #386. % 190.22/30.55 | | | | | % 190.22/30.55 | | | | Case 2: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | (32) all_252_3 = e0 & op(e3, e3) = e0 % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | REF_CLOSE: (16), (29), (32) are inconsistent by sub-proof #430. % 190.22/30.55 | | | | | % 190.22/30.55 | | | | End of split % 190.22/30.55 | | | | % 190.22/30.55 | | | Case 2: % 190.22/30.55 | | | | % 190.22/30.55 | | | | (33) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, % 190.22/30.55 | | | | e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0) % 190.22/30.55 | | | | % 190.22/30.55 | | | | BETA: splitting (33) gives: % 190.22/30.55 | | | | % 190.22/30.55 | | | | Case 1: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | (34) all_252_5 = e0 & op(e3, e2) = e0 % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | ALPHA: (34) implies: % 190.22/30.55 | | | | | (35) op(e3, e2) = e0 % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | REF_CLOSE: (1), (7), (11), (35) are inconsistent by sub-proof #547. % 190.22/30.55 | | | | | % 190.22/30.55 | | | | Case 2: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | (36) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 190.22/30.55 | | | | | op(e3, e0) = e0) % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | BETA: splitting (36) gives: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | Case 1: % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | (37) all_252_10 = e0 & op(e3, e1) = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | ALPHA: (37) implies: % 190.22/30.55 | | | | | | (38) op(e3, e1) = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | REF_CLOSE: (1), (2), (3), (38) are inconsistent by sub-proof #498. % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | Case 2: % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | (39) all_252_17 = e0 & op(e3, e0) = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | ALPHA: (39) implies: % 190.22/30.55 | | | | | | (40) all_252_17 = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | BETA: splitting (17) gives: % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | Case 1: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | (41) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & % 190.22/30.55 | | | | | | | op(e3, e3) = e3) % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | BETA: splitting (41) gives: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | Case 1: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (42) all_252_2 = e3 & op(e3, e4) = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | REF_CLOSE: (1), (6), (9), (42) are inconsistent by sub-proof % 190.22/30.55 | | | | | | | | #560. % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | Case 2: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (43) all_252_3 = e3 & op(e3, e3) = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | ALPHA: (43) implies: % 190.22/30.55 | | | | | | | | (44) all_252_3 = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | REF_CLOSE: (18), (29), (44) are inconsistent by sub-proof #366. % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | End of split % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | Case 2: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | (45) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & % 190.22/30.55 | | | | | | | op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | BETA: splitting (45) gives: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | Case 1: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (46) all_252_5 = e3 & op(e3, e2) = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | REF_CLOSE: (5), (13), (46) are inconsistent by sub-proof #370. % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | Case 2: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (47) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 190.22/30.55 | | | | | | | | op(e3, e0) = e3) % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | BETA: splitting (47) gives: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | Case 1: % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | (48) all_252_10 = e3 & op(e3, e1) = e3 % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | REF_CLOSE: (12), (14), (48) are inconsistent by sub-proof % 190.22/30.55 | | | | | | | | | #365. % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | Case 2: % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | (49) all_252_17 = e3 & op(e3, e0) = e3 % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | ALPHA: (49) implies: % 190.22/30.55 | | | | | | | | | (50) all_252_17 = e3 % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | COMBINE_EQS: (40), (50) imply: % 190.22/30.55 | | | | | | | | | (51) e3 = e0 % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | REDUCE: (10), (51) imply: % 190.22/30.55 | | | | | | | | | (52) $false % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | CLOSE: (52) is inconsistent. % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | End of split % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | End of split % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | End of split % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | End of split % 190.22/30.55 | | | | | % 190.22/30.55 | | | | End of split % 190.22/30.55 | | | | % 190.22/30.55 | | | End of split % 190.22/30.55 | | | % 190.22/30.55 | | End of split % 190.22/30.55 | | % 190.22/30.55 | Case 2: % 190.22/30.55 | | % 190.22/30.55 | | (53) (all_252_5 = e1 & op(e3, e2) = e1) | (all_252_10 = e1 & op(e3, e1) = % 190.22/30.55 | | e1) | (all_252_17 = e1 & op(e3, e0) = e1) % 190.22/30.55 | | % 190.22/30.55 | | BETA: splitting (53) gives: % 190.22/30.55 | | % 190.22/30.55 | | Case 1: % 190.22/30.55 | | | % 190.22/30.55 | | | (54) all_252_5 = e1 & op(e3, e2) = e1 % 190.22/30.55 | | | % 190.22/30.55 | | | REF_CLOSE: (13), (22), (54) are inconsistent by sub-proof #364. % 190.22/30.55 | | | % 190.22/30.55 | | Case 2: % 190.22/30.55 | | | % 190.22/30.55 | | | (55) (all_252_10 = e1 & op(e3, e1) = e1) | (all_252_17 = e1 & op(e3, % 190.22/30.55 | | | e0) = e1) % 190.22/30.55 | | | % 190.22/30.55 | | | BETA: splitting (55) gives: % 190.22/30.55 | | | % 190.22/30.55 | | | Case 1: % 190.22/30.55 | | | | % 190.22/30.55 | | | | (56) all_252_10 = e1 & op(e3, e1) = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | ALPHA: (56) implies: % 190.22/30.55 | | | | (57) all_252_10 = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | COMBINE_EQS: (14), (57) imply: % 190.22/30.55 | | | | (58) e2 = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | SIMP: (58) implies: % 190.22/30.55 | | | | (59) e2 = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | REDUCE: (4), (59) imply: % 190.22/30.55 | | | | (60) $false % 190.22/30.55 | | | | % 190.22/30.55 | | | | CLOSE: (60) is inconsistent. % 190.22/30.55 | | | | % 190.22/30.55 | | | Case 2: % 190.22/30.55 | | | | % 190.22/30.55 | | | | (61) all_252_17 = e1 & op(e3, e0) = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | ALPHA: (61) implies: % 190.22/30.55 | | | | (62) all_252_17 = e1 % 190.22/30.55 | | | | (63) op(e3, e0) = e1 % 190.22/30.55 | | | | % 190.22/30.55 | | | | BETA: splitting (20) gives: % 190.22/30.55 | | | | % 190.22/30.55 | | | | Case 1: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | (64) (all_252_2 = e0 & op(e3, e4) = e0) | (all_252_3 = e0 & op(e3, % 190.22/30.55 | | | | | e3) = e0) % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | BETA: splitting (64) gives: % 190.22/30.55 | | | | | % 190.22/30.55 | | | | | Case 1: % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | (65) all_252_2 = e0 & op(e3, e4) = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | REF_CLOSE: (19), (21), (65) are inconsistent by sub-proof #386. % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | Case 2: % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | (66) all_252_3 = e0 & op(e3, e3) = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | ALPHA: (66) implies: % 190.22/30.55 | | | | | | (67) all_252_3 = e0 % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | BETA: splitting (17) gives: % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | | Case 1: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | (68) (all_252_2 = e3 & op(e3, e4) = e3) | (all_252_3 = e3 & % 190.22/30.55 | | | | | | | op(e3, e3) = e3) % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | BETA: splitting (68) gives: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | Case 1: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (69) all_252_2 = e3 & op(e3, e4) = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | REF_CLOSE: (1), (6), (9), (69) are inconsistent by sub-proof % 190.22/30.55 | | | | | | | | #560. % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | Case 2: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (70) all_252_3 = e3 & op(e3, e3) = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | REF_CLOSE: (10), (67), (70) are inconsistent by sub-proof #363. % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | End of split % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | Case 2: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | (71) (all_252_5 = e3 & op(e3, e2) = e3) | (all_252_10 = e3 & % 190.22/30.55 | | | | | | | op(e3, e1) = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | BETA: splitting (71) gives: % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | | Case 1: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (72) all_252_5 = e3 & op(e3, e2) = e3 % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | REF_CLOSE: (5), (13), (72) are inconsistent by sub-proof #370. % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | Case 2: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | (73) (all_252_10 = e3 & op(e3, e1) = e3) | (all_252_17 = e3 & % 190.22/30.55 | | | | | | | | op(e3, e0) = e3) % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | BETA: splitting (73) gives: % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | | Case 1: % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | (74) all_252_10 = e3 & op(e3, e1) = e3 % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | REF_CLOSE: (12), (14), (74) are inconsistent by sub-proof % 190.22/30.55 | | | | | | | | | #365. % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | Case 2: % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | (75) all_252_17 = e3 & op(e3, e0) = e3 % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | | REF_CLOSE: (18), (62), (75) are inconsistent by sub-proof % 190.22/30.55 | | | | | | | | | #537. % 190.22/30.55 | | | | | | | | | % 190.22/30.55 | | | | | | | | End of split % 190.22/30.55 | | | | | | | | % 190.22/30.55 | | | | | | | End of split % 190.22/30.55 | | | | | | | % 190.22/30.55 | | | | | | End of split % 190.22/30.55 | | | | | | % 190.22/30.55 | | | | | End of split % 190.22/30.55 | | | | | % 190.22/30.55 | | | | Case 2: % 190.22/30.55 | | | | | % 190.46/30.55 | | | | | (76) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, % 190.46/30.55 | | | | | e1) = e0) | (all_252_17 = e0 & op(e3, e0) = e0) % 190.46/30.55 | | | | | % 190.46/30.55 | | | | | BETA: splitting (76) gives: % 190.46/30.55 | | | | | % 190.46/30.55 | | | | | Case 1: % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | | (77) all_252_5 = e0 & op(e3, e2) = e0 % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | | ALPHA: (77) implies: % 190.46/30.55 | | | | | | (78) op(e3, e2) = e0 % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | | REF_CLOSE: (1), (7), (11), (78) are inconsistent by sub-proof #547. % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | Case 2: % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | | (79) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 = e0 & % 190.46/30.55 | | | | | | op(e3, e0) = e0) % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | | BETA: splitting (79) gives: % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | | Case 1: % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | | (80) all_252_10 = e0 & op(e3, e1) = e0 % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | | ALPHA: (80) implies: % 190.46/30.55 | | | | | | | (81) op(e3, e1) = e0 % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | | REF_CLOSE: (1), (2), (3), (81) are inconsistent by sub-proof #498. % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | Case 2: % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | | (82) all_252_17 = e0 & op(e3, e0) = e0 % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | | ALPHA: (82) implies: % 190.46/30.55 | | | | | | | (83) op(e3, e0) = e0 % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | | REF_CLOSE: (1), (15), (16), (63), (83) are inconsistent by % 190.46/30.55 | | | | | | | sub-proof #362. % 190.46/30.55 | | | | | | | % 190.46/30.55 | | | | | | End of split % 190.46/30.55 | | | | | | % 190.46/30.55 | | | | | End of split % 190.46/30.55 | | | | | % 190.46/30.55 | | | | End of split % 190.46/30.55 | | | | % 190.46/30.55 | | | End of split % 190.46/30.55 | | | % 190.46/30.55 | | End of split % 190.46/30.55 | | % 190.46/30.55 | End of split % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #362 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.55 (2) op(e3, e0) = e0 % 190.46/30.55 (3) op(e3, e0) = e1 % 190.46/30.55 (4) op(e3, e0) = all_48_2 % 190.46/30.55 (5) ~ (e1 = e0) % 190.46/30.55 % 190.46/30.55 Begin of proof % 190.46/30.55 | % 190.46/30.55 | GROUND_INST: instantiating (1) with all_48_2, e0, e0, e3, simplifying with % 190.46/30.55 | (2), (4) gives: % 190.46/30.55 | (6) all_48_2 = e0 % 190.46/30.55 | % 190.46/30.55 | GROUND_INST: instantiating (1) with all_48_2, e1, e0, e3, simplifying with % 190.46/30.55 | (3), (4) gives: % 190.46/30.55 | (7) all_48_2 = e1 % 190.46/30.55 | % 190.46/30.55 | COMBINE_EQS: (6), (7) imply: % 190.46/30.55 | (8) e1 = e0 % 190.46/30.55 | % 190.46/30.55 | SIMP: (8) implies: % 190.46/30.55 | (9) e1 = e0 % 190.46/30.55 | % 190.46/30.55 | REDUCE: (5), (9) imply: % 190.46/30.55 | (10) $false % 190.46/30.55 | % 190.46/30.55 | CLOSE: (10) is inconsistent. % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #363 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) all_252_3 = e3 & op(e3, e3) = e3 % 190.46/30.55 (2) all_252_3 = e0 % 190.46/30.55 (3) ~ (e3 = e0) % 190.46/30.55 % 190.46/30.55 Begin of proof % 190.46/30.55 | % 190.46/30.55 | ALPHA: (1) implies: % 190.46/30.55 | (4) all_252_3 = e3 % 190.46/30.55 | % 190.46/30.55 | COMBINE_EQS: (2), (4) imply: % 190.46/30.55 | (5) e3 = e0 % 190.46/30.55 | % 190.46/30.55 | SIMP: (5) implies: % 190.46/30.55 | (6) e3 = e0 % 190.46/30.55 | % 190.46/30.55 | REDUCE: (3), (6) imply: % 190.46/30.55 | (7) $false % 190.46/30.55 | % 190.46/30.55 | CLOSE: (7) is inconsistent. % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #364 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) all_252_5 = e1 & op(e3, e2) = e1 % 190.46/30.55 (2) all_252_5 = e4 % 190.46/30.55 (3) ~ (e4 = e1) % 190.46/30.55 % 190.46/30.55 Begin of proof % 190.46/30.55 | % 190.46/30.55 | ALPHA: (1) implies: % 190.46/30.55 | (4) all_252_5 = e1 % 190.46/30.55 | % 190.46/30.55 | COMBINE_EQS: (2), (4) imply: % 190.46/30.55 | (5) e4 = e1 % 190.46/30.55 | % 190.46/30.55 | REDUCE: (3), (5) imply: % 190.46/30.55 | (6) $false % 190.46/30.55 | % 190.46/30.55 | CLOSE: (6) is inconsistent. % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #365 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) all_252_10 = e3 & op(e3, e1) = e3 % 190.46/30.55 (2) all_252_10 = e2 % 190.46/30.55 (3) ~ (e3 = e2) % 190.46/30.55 % 190.46/30.55 Begin of proof % 190.46/30.55 | % 190.46/30.55 | ALPHA: (1) implies: % 190.46/30.55 | (4) all_252_10 = e3 % 190.46/30.55 | % 190.46/30.55 | COMBINE_EQS: (2), (4) imply: % 190.46/30.55 | (5) e3 = e2 % 190.46/30.55 | % 190.46/30.55 | SIMP: (5) implies: % 190.46/30.55 | (6) e3 = e2 % 190.46/30.55 | % 190.46/30.55 | REDUCE: (3), (6) imply: % 190.46/30.55 | (7) $false % 190.46/30.55 | % 190.46/30.55 | CLOSE: (7) is inconsistent. % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #366 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) all_252_3 = e3 % 190.46/30.55 (2) all_252_3 = e1 % 190.46/30.55 (3) ~ (e3 = e1) % 190.46/30.55 % 190.46/30.55 Begin of proof % 190.46/30.55 | % 190.46/30.55 | COMBINE_EQS: (1), (2) imply: % 190.46/30.55 | (4) e3 = e1 % 190.46/30.55 | % 190.46/30.55 | SIMP: (4) implies: % 190.46/30.55 | (5) e3 = e1 % 190.46/30.55 | % 190.46/30.55 | REDUCE: (3), (5) imply: % 190.46/30.55 | (6) $false % 190.46/30.55 | % 190.46/30.55 | CLOSE: (6) is inconsistent. % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #367 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) all_252_9 = e3 % 190.46/30.55 (2) all_252_9 = e2 % 190.46/30.55 (3) ~ (e3 = e2) % 190.46/30.55 % 190.46/30.55 Begin of proof % 190.46/30.55 | % 190.46/30.55 | COMBINE_EQS: (1), (2) imply: % 190.46/30.55 | (4) e3 = e2 % 190.46/30.55 | % 190.46/30.55 | SIMP: (4) implies: % 190.46/30.55 | (5) e3 = e2 % 190.46/30.55 | % 190.46/30.55 | REDUCE: (3), (5) imply: % 190.46/30.55 | (6) $false % 190.46/30.55 | % 190.46/30.55 | CLOSE: (6) is inconsistent. % 190.46/30.55 | % 190.46/30.55 End of proof % 190.46/30.55 % 190.46/30.55 Sub-proof #368 shows that the following formulas are inconsistent: % 190.46/30.55 ---------------------------------------------------------------- % 190.46/30.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.55 (2) ~ (e4 = e3) % 190.46/30.55 (3) ~ (all_4_2 = e0) % 190.46/30.55 (4) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = e3) | % 190.46/30.55 (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = e3) % 190.46/30.55 | (all_252_22 = e3 & op(e0, e2) = e3) % 190.46/30.55 (5) ~ (all_8_2 = e0) % 190.46/30.55 (6) all_252_8 = e1 % 190.46/30.55 (7) ~ (all_6_2 = e0) % 190.46/30.55 (8) ~ (e3 = e0) % 190.46/30.55 (9) op(e1, e2) = e2 % 190.46/30.55 (10) op(e3, e2) = all_8_2 % 190.46/30.55 (11) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.46/30.55 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.46/30.55 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.46/30.55 (12) ~ (e3 = e2) % 190.46/30.55 (13) all_252_5 = e4 % 190.46/30.55 (14) ~ (e1 = e0) % 190.46/30.55 (15) ~ (all_6_2 = e3) % 190.46/30.55 (16) ~ (e3 = e1) % 190.46/30.56 (17) op(e1, e2) = all_4_2 % 190.46/30.56 (18) op(e4, e2) = all_6_2 % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (4) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (19) (all_252_4 = e3 & op(e4, e2) = e3) | (all_252_5 = e3 & op(e3, e2) = % 190.46/30.56 | | e3) % 190.46/30.56 | | % 190.46/30.56 | | BETA: splitting (19) gives: % 190.46/30.56 | | % 190.46/30.56 | | Case 1: % 190.46/30.56 | | | % 190.46/30.56 | | | (20) all_252_4 = e3 & op(e4, e2) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (20) implies: % 190.46/30.56 | | | (21) op(e4, e2) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (1), (15), (18), (21) are inconsistent by sub-proof #494. % 190.46/30.56 | | | % 190.46/30.56 | | Case 2: % 190.46/30.56 | | | % 190.46/30.56 | | | (22) all_252_5 = e3 & op(e3, e2) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (2), (13), (22) are inconsistent by sub-proof #370. % 190.46/30.56 | | | % 190.46/30.56 | | End of split % 190.46/30.56 | | % 190.46/30.56 | Case 2: % 190.46/30.56 | | % 190.46/30.56 | | (23) (all_252_8 = e3 & op(e2, e2) = e3) | (all_252_14 = e3 & op(e1, e2) = % 190.46/30.56 | | e3) | (all_252_22 = e3 & op(e0, e2) = e3) % 190.46/30.56 | | % 190.46/30.56 | | BETA: splitting (23) gives: % 190.46/30.56 | | % 190.46/30.56 | | Case 1: % 190.46/30.56 | | | % 190.46/30.56 | | | (24) all_252_8 = e3 & op(e2, e2) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (24) implies: % 190.46/30.56 | | | (25) all_252_8 = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (6), (16), (25) are inconsistent by sub-proof #369. % 190.46/30.56 | | | % 190.46/30.56 | | Case 2: % 190.46/30.56 | | | % 190.46/30.56 | | | (26) (all_252_14 = e3 & op(e1, e2) = e3) | (all_252_22 = e3 & op(e0, % 190.46/30.56 | | | e2) = e3) % 190.46/30.56 | | | % 190.46/30.56 | | | BETA: splitting (26) gives: % 190.46/30.56 | | | % 190.46/30.56 | | | Case 1: % 190.46/30.56 | | | | % 190.46/30.56 | | | | (27) all_252_14 = e3 & op(e1, e2) = e3 % 190.46/30.56 | | | | % 190.46/30.56 | | | | ALPHA: (27) implies: % 190.46/30.56 | | | | (28) op(e1, e2) = e3 % 190.46/30.56 | | | | % 190.46/30.56 | | | | REF_CLOSE: (1), (9), (12), (17), (28) are inconsistent by sub-proof % 190.46/30.56 | | | | #439. % 190.46/30.56 | | | | % 190.46/30.56 | | | Case 2: % 190.46/30.56 | | | | % 190.46/30.56 | | | | (29) all_252_22 = e3 & op(e0, e2) = e3 % 190.46/30.56 | | | | % 190.46/30.56 | | | | ALPHA: (29) implies: % 190.46/30.56 | | | | (30) all_252_22 = e3 % 190.46/30.56 | | | | % 190.46/30.56 | | | | BETA: splitting (11) gives: % 190.46/30.56 | | | | % 190.46/30.56 | | | | Case 1: % 190.46/30.56 | | | | | % 190.46/30.56 | | | | | (31) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 190.46/30.56 | | | | | e2) = e0) % 190.46/30.56 | | | | | % 190.46/30.56 | | | | | REF_CLOSE: (1), (5), (7), (10), (18), (31) are inconsistent by % 190.46/30.56 | | | | | sub-proof #546. % 190.46/30.56 | | | | | % 190.46/30.56 | | | | Case 2: % 190.46/30.56 | | | | | % 190.46/30.56 | | | | | (32) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, % 190.46/30.56 | | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.46/30.56 | | | | | % 190.46/30.56 | | | | | BETA: splitting (32) gives: % 190.46/30.56 | | | | | % 190.46/30.56 | | | | | Case 1: % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | | (33) all_252_8 = e0 & op(e2, e2) = e0 % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | | REF_CLOSE: (6), (14), (33) are inconsistent by sub-proof #550. % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | Case 2: % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | | (34) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 190.46/30.56 | | | | | | op(e0, e2) = e0) % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | | BETA: splitting (34) gives: % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | | Case 1: % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | | (35) all_252_14 = e0 & op(e1, e2) = e0 % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | | ALPHA: (35) implies: % 190.46/30.56 | | | | | | | (36) op(e1, e2) = e0 % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | | REF_CLOSE: (1), (3), (17), (36) are inconsistent by sub-proof % 190.46/30.56 | | | | | | | #545. % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | Case 2: % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | | (37) all_252_22 = e0 & op(e0, e2) = e0 % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | | ALPHA: (37) implies: % 190.46/30.56 | | | | | | | (38) all_252_22 = e0 % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | | REF_CLOSE: (8), (30), (38) are inconsistent by sub-proof #389. % 190.46/30.56 | | | | | | | % 190.46/30.56 | | | | | | End of split % 190.46/30.56 | | | | | | % 190.46/30.56 | | | | | End of split % 190.46/30.56 | | | | | % 190.46/30.56 | | | | End of split % 190.46/30.56 | | | | % 190.46/30.56 | | | End of split % 190.46/30.56 | | | % 190.46/30.56 | | End of split % 190.46/30.56 | | % 190.46/30.56 | End of split % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #369 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_8 = e3 % 190.46/30.56 (2) all_252_8 = e1 % 190.46/30.56 (3) ~ (e3 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (1), (2) imply: % 190.46/30.56 | (4) e3 = e1 % 190.46/30.56 | % 190.46/30.56 | SIMP: (4) implies: % 190.46/30.56 | (5) e3 = e1 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #370 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_5 = e3 & op(e3, e2) = e3 % 190.46/30.56 (2) all_252_5 = e4 % 190.46/30.56 (3) ~ (e4 = e3) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_5 = e3 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e4 = e3 % 190.46/30.56 | % 190.46/30.56 | SIMP: (5) implies: % 190.46/30.56 | (6) e4 = e3 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #371 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_12 = e2 & op(e1, e4) = e2 % 190.46/30.56 (2) all_252_12 = e3 % 190.46/30.56 (3) ~ (e3 = e2) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_12 = e2 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e3 = e2 % 190.46/30.56 | % 190.46/30.56 | SIMP: (5) implies: % 190.46/30.56 | (6) e3 = e2 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #372 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) ~ (all_36_2 = e0) % 190.46/30.56 (3) op(e3, e1) = all_36_2 % 190.46/30.56 (4) all_252_17 = e3 % 190.46/30.56 (5) (all_252_5 = e0 & op(e3, e2) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.46/30.56 | (all_252_17 = e0 & op(e3, e0) = e0) % 190.46/30.56 (6) ~ (all_8_2 = e0) % 190.46/30.56 (7) ~ (e3 = e0) % 190.46/30.56 (8) op(e3, e2) = all_8_2 % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (5) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (9) all_252_5 = e0 & op(e3, e2) = e0 % 190.46/30.56 | | % 190.46/30.56 | | ALPHA: (9) implies: % 190.46/30.56 | | (10) op(e3, e2) = e0 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (1), (6), (8), (10) are inconsistent by sub-proof #547. % 190.46/30.56 | | % 190.46/30.56 | Case 2: % 190.46/30.56 | | % 190.46/30.56 | | (11) (all_252_10 = e0 & op(e3, e1) = e0) | (all_252_17 = e0 & op(e3, e0) % 190.46/30.56 | | = e0) % 190.46/30.56 | | % 190.46/30.56 | | BETA: splitting (11) gives: % 190.46/30.56 | | % 190.46/30.56 | | Case 1: % 190.46/30.56 | | | % 190.46/30.56 | | | (12) all_252_10 = e0 & op(e3, e1) = e0 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (12) implies: % 190.46/30.56 | | | (13) op(e3, e1) = e0 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #498. % 190.46/30.56 | | | % 190.46/30.56 | | Case 2: % 190.46/30.56 | | | % 190.46/30.56 | | | (14) all_252_17 = e0 & op(e3, e0) = e0 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (14) implies: % 190.46/30.56 | | | (15) all_252_17 = e0 % 190.46/30.56 | | | % 190.46/30.56 | | | COMBINE_EQS: (4), (15) imply: % 190.46/30.56 | | | (16) e3 = e0 % 190.46/30.56 | | | % 190.46/30.56 | | | SIMP: (16) implies: % 190.46/30.56 | | | (17) e3 = e0 % 190.46/30.56 | | | % 190.46/30.56 | | | REDUCE: (7), (17) imply: % 190.46/30.56 | | | (18) $false % 190.46/30.56 | | | % 190.46/30.56 | | | CLOSE: (18) is inconsistent. % 190.46/30.56 | | | % 190.46/30.56 | | End of split % 190.46/30.56 | | % 190.46/30.56 | End of split % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #373 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.46/30.56 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (3) op(e0, e3) = all_22_2 % 190.46/30.56 (4) op(e1, e3) = e4 % 190.46/30.56 (5) ~ (all_22_2 = e2) % 190.46/30.56 (6) ~ (e4 = e2) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (1) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (7) all_252_13 = e2 & op(e1, e3) = e2 % 190.46/30.56 | | % 190.46/30.56 | | ALPHA: (7) implies: % 190.46/30.56 | | (8) op(e1, e3) = e2 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #529. % 190.46/30.56 | | % 190.46/30.56 | Case 2: % 190.46/30.56 | | % 190.46/30.56 | | (9) all_252_21 = e2 & op(e0, e3) = e2 % 190.46/30.56 | | % 190.46/30.56 | | ALPHA: (9) implies: % 190.46/30.56 | | (10) op(e0, e3) = e2 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #543. % 190.46/30.56 | | % 190.46/30.56 | End of split % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #374 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_1 = e2 & op(e4, e3) = e2 % 190.46/30.56 (2) all_252_1 = e1 % 190.46/30.56 (3) ~ (e2 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_1 = e2 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e2 = e1 % 190.46/30.56 | % 190.46/30.56 | SIMP: (5) implies: % 190.46/30.56 | (6) e2 = e1 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #375 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) op(e0, e2) = all_28_2 % 190.46/30.56 (3) ~ (all_20_2 = e3) % 190.46/30.56 (4) op(e0, e1) = all_20_2 % 190.46/30.56 (5) all_252_24 = e2 % 190.46/30.56 (6) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) = e3) % 190.46/30.56 | (all_252_24 = e3 & op(e0, e0) = e3) % 190.46/30.56 (7) ~ (e3 = e2) % 190.46/30.56 (8) ~ (all_28_2 = e3) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (6) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (9) all_252_22 = e3 & op(e0, e2) = e3 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (1), (2), (8), (9) are inconsistent by sub-proof #509. % 190.46/30.56 | | % 190.46/30.56 | Case 2: % 190.46/30.56 | | % 190.46/30.56 | | (10) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) % 190.46/30.56 | | = e3) % 190.46/30.56 | | % 190.46/30.56 | | BETA: splitting (10) gives: % 190.46/30.56 | | % 190.46/30.56 | | Case 1: % 190.46/30.56 | | | % 190.46/30.56 | | | (11) all_252_23 = e3 & op(e0, e1) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (11) implies: % 190.46/30.56 | | | (12) op(e0, e1) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #508. % 190.46/30.56 | | | % 190.46/30.56 | | Case 2: % 190.46/30.56 | | | % 190.46/30.56 | | | (13) all_252_24 = e3 & op(e0, e0) = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (13) implies: % 190.46/30.56 | | | (14) all_252_24 = e3 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (5), (7), (14) are inconsistent by sub-proof #376. % 190.46/30.56 | | | % 190.46/30.56 | | End of split % 190.46/30.56 | | % 190.46/30.56 | End of split % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #376 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_24 = e3 % 190.46/30.56 (2) all_252_24 = e2 % 190.46/30.56 (3) ~ (e3 = e2) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (1), (2) imply: % 190.46/30.56 | (4) e3 = e2 % 190.46/30.56 | % 190.46/30.56 | SIMP: (4) implies: % 190.46/30.56 | (5) e3 = e2 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #377 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_24 = e1 & op(e0, e0) = e1 % 190.46/30.56 (2) all_252_24 = e2 % 190.46/30.56 (3) ~ (e2 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_24 = e1 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e2 = e1 % 190.46/30.56 | % 190.46/30.56 | SIMP: (5) implies: % 190.46/30.56 | (6) e2 = e1 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #378 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_17 = e0 & op(e3, e0) = e0 % 190.46/30.56 (2) all_252_17 = e3 % 190.46/30.56 (3) ~ (e3 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_17 = e0 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e3 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #379 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) (all_252_7 = e1 & op(e2, e3) = e1) | (all_252_13 = e1 & op(e1, e3) = e1) % 190.46/30.56 | (all_252_21 = e1 & op(e0, e3) = e1) % 190.46/30.56 (3) op(e2, e3) = all_10_2 % 190.46/30.56 (4) ~ (all_10_2 = e1) % 190.46/30.56 (5) op(e0, e3) = all_22_2 % 190.46/30.56 (6) op(e1, e3) = e4 % 190.46/30.56 (7) op(e0, e3) = e3 % 190.46/30.56 (8) ~ (e3 = e1) % 190.46/30.56 (9) ~ (e4 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (2) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (10) all_252_7 = e1 & op(e2, e3) = e1 % 190.46/30.56 | | % 190.46/30.56 | | ALPHA: (10) implies: % 190.46/30.56 | | (11) op(e2, e3) = e1 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (1), (3), (4), (11) are inconsistent by sub-proof #554. % 190.46/30.56 | | % 190.46/30.56 | Case 2: % 190.46/30.56 | | % 190.46/30.56 | | (12) (all_252_13 = e1 & op(e1, e3) = e1) | (all_252_21 = e1 & op(e0, e3) % 190.46/30.56 | | = e1) % 190.46/30.56 | | % 190.46/30.56 | | BETA: splitting (12) gives: % 190.46/30.56 | | % 190.46/30.56 | | Case 1: % 190.46/30.56 | | | % 190.46/30.56 | | | (13) all_252_13 = e1 & op(e1, e3) = e1 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (1), (6), (9), (13) are inconsistent by sub-proof #423. % 190.46/30.56 | | | % 190.46/30.56 | | Case 2: % 190.46/30.56 | | | % 190.46/30.56 | | | (14) all_252_21 = e1 & op(e0, e3) = e1 % 190.46/30.56 | | | % 190.46/30.56 | | | ALPHA: (14) implies: % 190.46/30.56 | | | (15) op(e0, e3) = e1 % 190.46/30.56 | | | % 190.46/30.56 | | | REF_CLOSE: (1), (5), (7), (8), (15) are inconsistent by sub-proof #454. % 190.46/30.56 | | | % 190.46/30.56 | | End of split % 190.46/30.56 | | % 190.46/30.56 | End of split % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #380 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_3 = e1 & op(e3, e3) = e1 % 190.46/30.56 (2) all_252_3 = e0 % 190.46/30.56 (3) ~ (e1 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_3 = e1 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e1 = e0 % 190.46/30.56 | % 190.46/30.56 | SIMP: (5) implies: % 190.46/30.56 | (6) e1 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #381 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_12 = e3 % 190.46/30.56 (2) all_252_12 = e0 % 190.46/30.56 (3) ~ (e3 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (1), (2) imply: % 190.46/30.56 | (4) e3 = e0 % 190.46/30.56 | % 190.46/30.56 | SIMP: (4) implies: % 190.46/30.56 | (5) e3 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #382 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) op(e2, e4) = all_64_2 % 190.46/30.56 (3) op(e2, e4) = e0 % 190.46/30.56 (4) ~ (all_64_2 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | GROUND_INST: instantiating (1) with all_64_2, e0, e4, e2, simplifying with % 190.46/30.56 | (2), (3) gives: % 190.46/30.56 | (5) all_64_2 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (4), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #383 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_16 = e4 & op(e4, e0) = e4 % 190.46/30.56 (2) all_252_16 = e1 % 190.46/30.56 (3) ~ (e4 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_16 = e4 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e4 = e1 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #384 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_9 = e4 % 190.46/30.56 (2) all_252_9 = e3 % 190.46/30.56 (3) ~ (e4 = e3) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (1), (2) imply: % 190.46/30.56 | (4) e4 = e3 % 190.46/30.56 | % 190.46/30.56 | SIMP: (4) implies: % 190.46/30.56 | (5) e4 = e3 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #385 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_0 = e4 & op(e4, e4) = e4 % 190.46/30.56 (2) all_252_0 = e0 % 190.46/30.56 (3) ~ (e4 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_0 = e4 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e4 = e0 % 190.46/30.56 | % 190.46/30.56 | SIMP: (5) implies: % 190.46/30.56 | (6) e4 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #386 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_2 = e0 & op(e3, e4) = e0 % 190.46/30.56 (2) all_252_2 = e2 % 190.46/30.56 (3) ~ (e2 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (4) all_252_2 = e0 % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (2), (4) imply: % 190.46/30.56 | (5) e2 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #387 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) op(e4, e0) = e3 % 190.46/30.56 (3) op(e4, e0) = e1 % 190.46/30.56 (4) ~ (e3 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | GROUND_INST: instantiating (1) with e1, e3, e0, e4, simplifying with (2), (3) % 190.46/30.56 | gives: % 190.46/30.56 | (5) e3 = e1 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (4), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #388 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_4 = e4 & op(e4, e2) = e4 % 190.46/30.56 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (3) op(e4, e2) = all_6_2 % 190.46/30.56 (4) ~ (all_6_2 = e4) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | ALPHA: (1) implies: % 190.46/30.56 | (5) op(e4, e2) = e4 % 190.46/30.56 | % 190.46/30.56 | GROUND_INST: instantiating (2) with all_6_2, e4, e2, e4, simplifying with (3), % 190.46/30.56 | (5) gives: % 190.46/30.56 | (6) all_6_2 = e4 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (4), (6) imply: % 190.46/30.56 | (7) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (7) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #389 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_22 = e3 % 190.46/30.56 (2) all_252_22 = e0 % 190.46/30.56 (3) ~ (e3 = e0) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (1), (2) imply: % 190.46/30.56 | (4) e3 = e0 % 190.46/30.56 | % 190.46/30.56 | SIMP: (4) implies: % 190.46/30.56 | (5) e3 = e0 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #390 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 190.46/30.56 (3) op(e0, e3) = all_22_2 % 190.46/30.56 (4) op(e0, e3) = e3 % 190.46/30.56 (5) ~ (all_12_2 = e1) % 190.46/30.56 (6) op(e0, e4) = all_12_2 % 190.46/30.56 (7) ~ (e3 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (2) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (8) all_252_20 = e1 & op(e0, e4) = e1 % 190.46/30.56 | | % 190.46/30.56 | | ALPHA: (8) implies: % 190.46/30.56 | | (9) op(e0, e4) = e1 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #530. % 190.46/30.56 | | % 190.46/30.56 | Case 2: % 190.46/30.56 | | % 190.46/30.56 | | (10) all_252_21 = e1 & op(e0, e3) = e1 % 190.46/30.56 | | % 190.46/30.56 | | ALPHA: (10) implies: % 190.46/30.56 | | (11) op(e0, e3) = e1 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (1), (3), (4), (7), (11) are inconsistent by sub-proof #454. % 190.46/30.56 | | % 190.46/30.56 | End of split % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #391 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) all_252_14 = e2 % 190.46/30.56 (2) all_252_14 = e1 % 190.46/30.56 (3) ~ (e2 = e1) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | COMBINE_EQS: (1), (2) imply: % 190.46/30.56 | (4) e2 = e1 % 190.46/30.56 | % 190.46/30.56 | SIMP: (4) implies: % 190.46/30.56 | (5) e2 = e1 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (3), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #392 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (2) op(e2, e1) = e4 % 190.46/30.56 (3) op(e2, e1) = e2 % 190.46/30.56 (4) ~ (e4 = e2) % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | GROUND_INST: instantiating (1) with e2, e4, e1, e2, simplifying with (2), (3) % 190.46/30.56 | gives: % 190.46/30.56 | (5) e4 = e2 % 190.46/30.56 | % 190.46/30.56 | REDUCE: (4), (5) imply: % 190.46/30.56 | (6) $false % 190.46/30.56 | % 190.46/30.56 | CLOSE: (6) is inconsistent. % 190.46/30.56 | % 190.46/30.56 End of proof % 190.46/30.56 % 190.46/30.56 Sub-proof #393 shows that the following formulas are inconsistent: % 190.46/30.56 ---------------------------------------------------------------- % 190.46/30.56 (1) ~ (all_26_2 = e2) % 190.46/30.56 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.56 (3) ~ (all_16_1 = e2) % 190.46/30.56 (4) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 190.46/30.56 (5) op(e4, e1) = all_26_2 % 190.46/30.56 (6) op(e3, e1) = all_16_1 % 190.46/30.56 % 190.46/30.56 Begin of proof % 190.46/30.56 | % 190.46/30.56 | BETA: splitting (4) gives: % 190.46/30.56 | % 190.46/30.56 | Case 1: % 190.46/30.56 | | % 190.46/30.56 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 190.46/30.56 | | % 190.46/30.56 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #558. % 190.46/30.56 | | % 190.46/30.57 | Case 2: % 190.46/30.57 | | % 190.46/30.57 | | (8) all_252_10 = e2 & op(e3, e1) = e2 % 190.46/30.57 | | % 190.46/30.57 | | ALPHA: (8) implies: % 190.46/30.57 | | (9) op(e3, e1) = e2 % 190.46/30.57 | | % 190.46/30.57 | | GROUND_INST: instantiating (2) with all_16_1, e2, e1, e3, simplifying with % 190.46/30.57 | | (6), (9) gives: % 190.46/30.57 | | (10) all_16_1 = e2 % 190.46/30.57 | | % 190.46/30.57 | | REDUCE: (3), (10) imply: % 190.46/30.57 | | (11) $false % 190.46/30.57 | | % 190.46/30.57 | | CLOSE: (11) is inconsistent. % 190.46/30.57 | | % 190.46/30.57 | End of split % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #394 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_15 = e1 & op(e1, e1) = e1 % 190.46/30.57 (2) all_252_15 = e4 % 190.46/30.57 (3) ~ (e4 = e1) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_15 = e1 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e4 = e1 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #395 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_14 = e1 & op(e1, e2) = e1 % 190.46/30.57 (2) all_252_14 = e2 % 190.46/30.57 (3) ~ (e2 = e1) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_14 = e1 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e2 = e1 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #396 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_15 = e2 & op(e1, e1) = e2 % 190.46/30.57 (2) all_252_15 = e4 % 190.46/30.57 (3) ~ (e4 = e2) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_15 = e2 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e4 = e2 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #397 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_14 = e2 & op(e1, e2) = e2 % 190.46/30.57 (2) all_252_14 = e0 % 190.46/30.57 (3) ~ (e2 = e0) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_14 = e2 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e2 = e0 % 190.46/30.57 | % 190.46/30.57 | SIMP: (5) implies: % 190.46/30.57 | (6) e2 = e0 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (6) imply: % 190.46/30.57 | (7) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (7) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #398 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_9 = e3 & op(e4, e1) = e3 % 190.46/30.57 (2) all_252_9 = e4 % 190.46/30.57 (3) ~ (e4 = e3) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_9 = e3 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e4 = e3 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #399 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_24 = e1 & op(e0, e0) = e1 % 190.46/30.57 (2) all_252_24 = e3 % 190.46/30.57 (3) ~ (e3 = e1) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_24 = e1 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e3 = e1 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #400 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (2) (all_252_23 = e4 & op(e0, e1) = e4) | (all_252_24 = e4 & op(e0, e0) = e4) % 190.46/30.57 (3) ~ (e4 = e3) % 190.46/30.57 (4) op(e0, e1) = all_20_2 % 190.46/30.57 (5) all_252_24 = e3 % 190.46/30.57 (6) op(e0, e1) = e1 % 190.46/30.57 (7) ~ (e4 = e1) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | BETA: splitting (2) gives: % 190.46/30.57 | % 190.46/30.57 | Case 1: % 190.46/30.57 | | % 190.46/30.57 | | (8) all_252_23 = e4 & op(e0, e1) = e4 % 190.46/30.57 | | % 190.46/30.57 | | ALPHA: (8) implies: % 190.46/30.57 | | (9) op(e0, e1) = e4 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (1), (4), (6), (7), (9) are inconsistent by sub-proof #401. % 190.46/30.57 | | % 190.46/30.57 | Case 2: % 190.46/30.57 | | % 190.46/30.57 | | (10) all_252_24 = e4 & op(e0, e0) = e4 % 190.46/30.57 | | % 190.46/30.57 | | ALPHA: (10) implies: % 190.46/30.57 | | (11) all_252_24 = e4 % 190.46/30.57 | | % 190.46/30.57 | | COMBINE_EQS: (5), (11) imply: % 190.46/30.57 | | (12) e4 = e3 % 190.46/30.57 | | % 190.46/30.57 | | SIMP: (12) implies: % 190.46/30.57 | | (13) e4 = e3 % 190.46/30.57 | | % 190.46/30.57 | | REDUCE: (3), (13) imply: % 190.46/30.57 | | (14) $false % 190.46/30.57 | | % 190.46/30.57 | | CLOSE: (14) is inconsistent. % 190.46/30.57 | | % 190.46/30.57 | End of split % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #401 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (2) op(e0, e1) = e4 % 190.46/30.57 (3) op(e0, e1) = all_20_2 % 190.46/30.57 (4) op(e0, e1) = e1 % 190.46/30.57 (5) ~ (e4 = e1) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | GROUND_INST: instantiating (1) with all_20_2, e1, e1, e0, simplifying with % 190.46/30.57 | (3), (4) gives: % 190.46/30.57 | (6) all_20_2 = e1 % 190.46/30.57 | % 190.46/30.57 | GROUND_INST: instantiating (1) with all_20_2, e4, e1, e0, simplifying with % 190.46/30.57 | (2), (3) gives: % 190.46/30.57 | (7) all_20_2 = e4 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (6), (7) imply: % 190.46/30.57 | (8) e4 = e1 % 190.46/30.57 | % 190.46/30.57 | SIMP: (8) implies: % 190.46/30.57 | (9) e4 = e1 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (5), (9) imply: % 190.46/30.57 | (10) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (10) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #402 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (2) op(e0, e3) = e4 % 190.46/30.57 (3) op(e0, e3) = e0 % 190.46/30.57 (4) ~ (e4 = e0) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | GROUND_INST: instantiating (1) with e4, e0, e3, e0, simplifying with (2), (3) % 190.46/30.57 | gives: % 190.46/30.57 | (5) e4 = e0 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (4), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #403 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_23 = e0 & op(e0, e1) = e0 % 190.46/30.57 (2) all_252_23 = e1 % 190.46/30.57 (3) ~ (e1 = e0) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_23 = e0 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e1 = e0 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #404 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_15 = e0 % 190.46/30.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (3) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.46/30.57 (4) ~ (e2 = e0) % 190.46/30.57 (5) op(e1, e0) = all_34_2 % 190.46/30.57 (6) ~ (all_34_2 = e2) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | BETA: splitting (3) gives: % 190.46/30.57 | % 190.46/30.57 | Case 1: % 190.46/30.57 | | % 190.46/30.57 | | (7) all_252_15 = e2 & op(e1, e1) = e2 % 190.46/30.57 | | % 190.46/30.57 | | ALPHA: (7) implies: % 190.46/30.57 | | (8) all_252_15 = e2 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #405. % 190.46/30.57 | | % 190.46/30.57 | Case 2: % 190.46/30.57 | | % 190.46/30.57 | | (9) all_252_19 = e2 & op(e1, e0) = e2 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #438. % 190.46/30.57 | | % 190.46/30.57 | End of split % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #405 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_15 = e2 % 190.46/30.57 (2) all_252_15 = e0 % 190.46/30.57 (3) ~ (e2 = e0) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (1), (2) imply: % 190.46/30.57 | (4) e2 = e0 % 190.46/30.57 | % 190.46/30.57 | SIMP: (4) implies: % 190.46/30.57 | (5) e2 = e0 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #406 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.46/30.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (3) ~ (all_4_2 = e0) % 190.46/30.57 (4) all_252_22 = e2 % 190.46/30.57 (5) ~ (e2 = e0) % 190.46/30.57 (6) op(e1, e2) = all_4_2 % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | BETA: splitting (1) gives: % 190.46/30.57 | % 190.46/30.57 | Case 1: % 190.46/30.57 | | % 190.46/30.57 | | (7) all_252_14 = e0 & op(e1, e2) = e0 % 190.46/30.57 | | % 190.46/30.57 | | ALPHA: (7) implies: % 190.46/30.57 | | (8) op(e1, e2) = e0 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #545. % 190.46/30.57 | | % 190.46/30.57 | Case 2: % 190.46/30.57 | | % 190.46/30.57 | | (9) all_252_22 = e0 & op(e0, e2) = e0 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #407. % 190.46/30.57 | | % 190.46/30.57 | End of split % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #407 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_22 = e0 & op(e0, e2) = e0 % 190.46/30.57 (2) all_252_22 = e2 % 190.46/30.57 (3) ~ (e2 = e0) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | ALPHA: (1) implies: % 190.46/30.57 | (4) all_252_22 = e0 % 190.46/30.57 | % 190.46/30.57 | COMBINE_EQS: (2), (4) imply: % 190.46/30.57 | (5) e2 = e0 % 190.46/30.57 | % 190.46/30.57 | REDUCE: (3), (5) imply: % 190.46/30.57 | (6) $false % 190.46/30.57 | % 190.46/30.57 | CLOSE: (6) is inconsistent. % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #408 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_15 = e0 % 190.46/30.57 (2) ~ (all_28_2 = e1) % 190.46/30.57 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (4) op(e0, e2) = all_28_2 % 190.46/30.57 (5) ~ (e2 = e1) % 190.46/30.57 (6) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.46/30.57 | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) = % 190.46/30.57 e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.46/30.57 (7) op(e1, e3) = e4 % 190.46/30.57 (8) all_252_12 = e3 % 190.46/30.57 (9) ~ (e3 = e2) % 190.46/30.57 (10) ~ (e4 = e2) % 190.46/30.57 (11) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_22 = e1 & op(e0, e2) = % 190.46/30.57 e1) % 190.46/30.57 (12) ~ (e2 = e0) % 190.46/30.57 (13) op(e1, e0) = all_34_2 % 190.46/30.57 (14) ~ (all_34_2 = e2) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | BETA: splitting (11) gives: % 190.46/30.57 | % 190.46/30.57 | Case 1: % 190.46/30.57 | | % 190.46/30.57 | | (15) all_252_14 = e1 & op(e1, e2) = e1 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15) % 190.46/30.57 | | are inconsistent by sub-proof #420. % 190.46/30.57 | | % 190.46/30.57 | Case 2: % 190.46/30.57 | | % 190.46/30.57 | | (16) all_252_22 = e1 & op(e0, e2) = e1 % 190.46/30.57 | | % 190.46/30.57 | | ALPHA: (16) implies: % 190.46/30.57 | | (17) op(e0, e2) = e1 % 190.46/30.57 | | % 190.46/30.57 | | REF_CLOSE: (2), (3), (4), (17) are inconsistent by sub-proof #502. % 190.46/30.57 | | % 190.46/30.57 | End of split % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #409 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.46/30.57 (1) all_252_15 = e0 % 190.46/30.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.46/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.46/30.57 (3) ~ (e2 = e1) % 190.46/30.57 (4) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.46/30.57 | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) = % 190.46/30.57 e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.46/30.57 (5) op(e1, e3) = e4 % 190.46/30.57 (6) all_252_12 = e3 % 190.46/30.57 (7) all_252_19 = e0 % 190.46/30.57 (8) ~ (e3 = e2) % 190.46/30.57 (9) ~ (e4 = e2) % 190.46/30.57 (10) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 190.46/30.57 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 190.46/30.57 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.46/30.57 (11) ~ (e1 = e0) % 190.46/30.57 (12) ~ (e3 = e1) % 190.46/30.57 (13) ~ (e2 = e0) % 190.46/30.57 (14) op(e1, e0) = all_34_2 % 190.46/30.57 (15) ~ (all_34_2 = e2) % 190.46/30.57 (16) ~ (e4 = e1) % 190.46/30.57 % 190.46/30.57 Begin of proof % 190.46/30.57 | % 190.46/30.57 | BETA: splitting (10) gives: % 190.46/30.57 | % 190.46/30.57 | Case 1: % 190.46/30.57 | | % 190.46/30.57 | | (17) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 190.46/30.57 | | = e1) % 190.46/30.57 | | % 190.46/30.57 | | BETA: splitting (17) gives: % 190.46/30.57 | | % 190.46/30.57 | | Case 1: % 190.46/30.57 | | | % 190.46/30.57 | | | (18) all_252_12 = e1 & op(e1, e4) = e1 % 190.46/30.57 | | | % 190.46/30.57 | | | REF_CLOSE: (6), (12), (18) are inconsistent by sub-proof #410. % 190.46/30.57 | | | % 190.46/30.57 | | Case 2: % 190.46/30.57 | | | % 190.46/30.57 | | | (19) all_252_13 = e1 & op(e1, e3) = e1 % 190.46/30.57 | | | % 190.46/30.57 | | | REF_CLOSE: (2), (5), (16), (19) are inconsistent by sub-proof #423. % 190.46/30.57 | | | % 190.46/30.57 | | End of split % 190.46/30.57 | | % 190.46/30.57 | Case 2: % 190.46/30.57 | | % 190.46/30.57 | | (20) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) % 190.46/30.57 | | = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.46/30.57 | | % 190.46/30.57 | | BETA: splitting (20) gives: % 190.46/30.57 | | % 190.46/30.57 | | Case 1: % 190.46/30.57 | | | % 190.46/30.57 | | | (21) all_252_14 = e1 & op(e1, e2) = e1 % 190.46/30.57 | | | % 190.46/30.57 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (13), (14), (15), (21) % 190.46/30.57 | | | are inconsistent by sub-proof #420. % 190.46/30.57 | | | % 190.46/30.57 | | Case 2: % 190.46/30.57 | | | % 190.46/30.57 | | | (22) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 190.46/30.57 | | | e0) = e1) % 190.46/30.57 | | | % 190.46/30.57 | | | BETA: splitting (22) gives: % 190.46/30.57 | | | % 190.46/30.57 | | | Case 1: % 190.46/30.57 | | | | % 190.46/30.57 | | | | (23) all_252_15 = e1 & op(e1, e1) = e1 % 190.46/30.57 | | | | % 190.46/30.57 | | | | ALPHA: (23) implies: % 190.46/30.57 | | | | (24) all_252_15 = e1 % 190.46/30.57 | | | | % 190.46/30.57 | | | | COMBINE_EQS: (1), (24) imply: % 190.46/30.57 | | | | (25) e1 = e0 % 190.46/30.57 | | | | % 190.46/30.57 | | | | REDUCE: (11), (25) imply: % 190.46/30.57 | | | | (26) $false % 190.46/30.57 | | | | % 190.46/30.57 | | | | CLOSE: (26) is inconsistent. % 190.46/30.57 | | | | % 190.46/30.57 | | | Case 2: % 190.46/30.57 | | | | % 190.46/30.57 | | | | (27) all_252_19 = e1 & op(e1, e0) = e1 % 190.46/30.57 | | | | % 190.46/30.57 | | | | REF_CLOSE: (7), (11), (27) are inconsistent by sub-proof #414. % 190.46/30.57 | | | | % 190.46/30.57 | | | End of split % 190.46/30.57 | | | % 190.46/30.57 | | End of split % 190.46/30.57 | | % 190.46/30.57 | End of split % 190.46/30.57 | % 190.46/30.57 End of proof % 190.46/30.57 % 190.46/30.57 Sub-proof #410 shows that the following formulas are inconsistent: % 190.46/30.57 ---------------------------------------------------------------- % 190.52/30.57 (1) all_252_12 = e1 & op(e1, e4) = e1 % 190.52/30.57 (2) all_252_12 = e3 % 190.52/30.57 (3) ~ (e3 = e1) % 190.52/30.57 % 190.52/30.57 Begin of proof % 190.52/30.57 | % 190.52/30.57 | ALPHA: (1) implies: % 190.52/30.57 | (4) all_252_12 = e1 % 190.52/30.57 | % 190.52/30.57 | COMBINE_EQS: (2), (4) imply: % 190.52/30.57 | (5) e3 = e1 % 190.52/30.57 | % 190.52/30.57 | SIMP: (5) implies: % 190.52/30.57 | (6) e3 = e1 % 190.52/30.57 | % 190.52/30.57 | REDUCE: (3), (6) imply: % 190.52/30.57 | (7) $false % 190.52/30.57 | % 190.52/30.57 | CLOSE: (7) is inconsistent. % 190.52/30.57 | % 190.52/30.57 End of proof % 190.52/30.57 % 190.52/30.57 Sub-proof #411 shows that the following formulas are inconsistent: % 190.52/30.57 ---------------------------------------------------------------- % 190.52/30.57 (1) all_252_22 = e4 & op(e0, e2) = e4 % 190.52/30.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.57 (3) op(e0, e2) = all_28_2 % 190.52/30.57 (4) ~ (all_28_2 = e4) % 190.52/30.57 % 190.52/30.57 Begin of proof % 190.52/30.57 | % 190.52/30.57 | ALPHA: (1) implies: % 190.52/30.57 | (5) op(e0, e2) = e4 % 190.52/30.57 | % 190.52/30.57 | GROUND_INST: instantiating (2) with all_28_2, e4, e2, e0, simplifying with % 190.52/30.57 | (3), (5) gives: % 190.52/30.57 | (6) all_28_2 = e4 % 190.52/30.57 | % 190.52/30.57 | REDUCE: (4), (6) imply: % 190.52/30.57 | (7) $false % 190.52/30.57 | % 190.52/30.57 | CLOSE: (7) is inconsistent. % 190.52/30.57 | % 190.52/30.57 End of proof % 190.52/30.57 % 190.52/30.57 Sub-proof #412 shows that the following formulas are inconsistent: % 190.52/30.57 ---------------------------------------------------------------- % 190.52/30.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.57 (2) ~ (e2 = e1) % 190.52/30.57 (3) ~ (e4 = e0) % 190.52/30.57 (4) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 190.52/30.57 | (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.52/30.57 e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 190.52/30.57 (5) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.52/30.57 | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) = % 190.52/30.57 e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.52/30.57 (6) op(e1, e3) = e4 % 190.52/30.57 (7) ~ (e3 = e0) % 190.52/30.57 (8) all_252_14 = e4 & op(e1, e2) = e4 % 190.52/30.57 (9) all_252_12 = e3 % 190.52/30.57 (10) ~ (e3 = e2) % 190.52/30.57 (11) ~ (e4 = e2) % 190.52/30.57 (12) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = % 190.52/30.57 e1) | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, % 190.52/30.57 e1) = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.52/30.57 (13) ~ (e1 = e0) % 190.52/30.57 (14) ~ (e3 = e1) % 190.52/30.57 (15) ~ (e2 = e0) % 190.52/30.57 (16) op(e1, e0) = all_34_2 % 190.52/30.57 (17) ~ (all_34_2 = e2) % 190.52/30.57 (18) ~ (e4 = e1) % 190.52/30.57 % 190.52/30.57 Begin of proof % 190.52/30.57 | % 190.52/30.57 | ALPHA: (8) implies: % 190.52/30.58 | (19) all_252_14 = e4 % 190.52/30.58 | % 190.52/30.58 | BETA: splitting (5) gives: % 190.52/30.58 | % 190.52/30.58 | Case 1: % 190.52/30.58 | | % 190.52/30.58 | | (20) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 190.52/30.58 | | = e2) % 190.52/30.58 | | % 190.52/30.58 | | REF_CLOSE: (1), (6), (9), (10), (11), (20) are inconsistent by sub-proof % 190.52/30.58 | | #425. % 190.52/30.58 | | % 190.52/30.58 | Case 2: % 190.52/30.58 | | % 190.52/30.58 | | (21) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) % 190.52/30.58 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.52/30.58 | | % 190.52/30.58 | | BETA: splitting (21) gives: % 190.52/30.58 | | % 190.52/30.58 | | Case 1: % 190.52/30.58 | | | % 190.52/30.58 | | | (22) all_252_14 = e2 & op(e1, e2) = e2 % 190.52/30.58 | | | % 190.52/30.58 | | | ALPHA: (22) implies: % 190.52/30.58 | | | (23) all_252_14 = e2 % 190.52/30.58 | | | % 190.52/30.58 | | | COMBINE_EQS: (19), (23) imply: % 190.52/30.58 | | | (24) e4 = e2 % 190.52/30.58 | | | % 190.52/30.58 | | | REDUCE: (11), (24) imply: % 190.52/30.58 | | | (25) $false % 190.52/30.58 | | | % 190.52/30.58 | | | CLOSE: (25) is inconsistent. % 190.52/30.58 | | | % 190.52/30.58 | | Case 2: % 190.52/30.58 | | | % 190.52/30.58 | | | (26) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, % 190.52/30.58 | | | e0) = e2) % 190.52/30.58 | | | % 190.52/30.58 | | | BETA: splitting (26) gives: % 190.52/30.58 | | | % 190.52/30.58 | | | Case 1: % 190.52/30.58 | | | | % 190.52/30.58 | | | | (27) all_252_15 = e2 & op(e1, e1) = e2 % 190.52/30.58 | | | | % 190.52/30.58 | | | | ALPHA: (27) implies: % 190.52/30.58 | | | | (28) all_252_15 = e2 % 190.52/30.58 | | | | % 190.52/30.58 | | | | BETA: splitting (4) gives: % 190.52/30.58 | | | | % 190.52/30.58 | | | | Case 1: % 190.52/30.58 | | | | | % 190.52/30.58 | | | | | (29) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & % 190.52/30.58 | | | | | op(e1, e3) = e0) % 190.52/30.58 | | | | | % 190.52/30.58 | | | | | BETA: splitting (29) gives: % 190.52/30.58 | | | | | % 190.52/30.58 | | | | | Case 1: % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | (30) all_252_12 = e0 & op(e1, e4) = e0 % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | REF_CLOSE: (7), (9), (30) are inconsistent by sub-proof #417. % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | Case 2: % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | (31) all_252_13 = e0 & op(e1, e3) = e0 % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | REF_CLOSE: (1), (3), (6), (31) are inconsistent by sub-proof #428. % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | End of split % 190.52/30.58 | | | | | % 190.52/30.58 | | | | Case 2: % 190.52/30.58 | | | | | % 190.52/30.58 | | | | | (32) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_15 = e0 & % 190.52/30.58 | | | | | op(e1, e1) = e0) | (all_252_19 = e0 & op(e1, e0) = e0) % 190.52/30.58 | | | | | % 190.52/30.58 | | | | | BETA: splitting (32) gives: % 190.52/30.58 | | | | | % 190.52/30.58 | | | | | Case 1: % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | (33) all_252_14 = e0 & op(e1, e2) = e0 % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | ALPHA: (33) implies: % 190.52/30.58 | | | | | | (34) all_252_14 = e0 % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | COMBINE_EQS: (19), (34) imply: % 190.52/30.58 | | | | | | (35) e4 = e0 % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | REDUCE: (3), (35) imply: % 190.52/30.58 | | | | | | (36) $false % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | CLOSE: (36) is inconsistent. % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | Case 2: % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | (37) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_19 = e0 & % 190.52/30.58 | | | | | | op(e1, e0) = e0) % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | BETA: splitting (37) gives: % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | | Case 1: % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | | (38) all_252_15 = e0 & op(e1, e1) = e0 % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | | REF_CLOSE: (15), (28), (38) are inconsistent by sub-proof #416. % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | Case 2: % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | | (39) all_252_19 = e0 & op(e1, e0) = e0 % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | | ALPHA: (39) implies: % 190.52/30.58 | | | | | | | (40) all_252_19 = e0 % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | | REF_CLOSE: (1), (2), (6), (9), (12), (13), (14), (18), (19), (28), % 190.52/30.58 | | | | | | | (40) are inconsistent by sub-proof #413. % 190.52/30.58 | | | | | | | % 190.52/30.58 | | | | | | End of split % 190.52/30.58 | | | | | | % 190.52/30.58 | | | | | End of split % 190.52/30.58 | | | | | % 190.52/30.58 | | | | End of split % 190.52/30.58 | | | | % 190.52/30.58 | | | Case 2: % 190.52/30.58 | | | | % 190.52/30.58 | | | | (41) all_252_19 = e2 & op(e1, e0) = e2 % 190.52/30.58 | | | | % 190.52/30.58 | | | | REF_CLOSE: (1), (16), (17), (41) are inconsistent by sub-proof #438. % 190.52/30.58 | | | | % 190.52/30.58 | | | End of split % 190.52/30.58 | | | % 190.52/30.58 | | End of split % 190.52/30.58 | | % 190.52/30.58 | End of split % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #413 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (2) ~ (e2 = e1) % 190.52/30.58 (3) all_252_15 = e2 % 190.52/30.58 (4) all_252_14 = e4 % 190.52/30.58 (5) op(e1, e3) = e4 % 190.52/30.58 (6) all_252_12 = e3 % 190.52/30.58 (7) all_252_19 = e0 % 190.52/30.58 (8) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) = e1) % 190.52/30.58 | (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) = % 190.52/30.58 e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.52/30.58 (9) ~ (e1 = e0) % 190.52/30.58 (10) ~ (e3 = e1) % 190.52/30.58 (11) ~ (e4 = e1) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | BETA: splitting (8) gives: % 190.52/30.58 | % 190.52/30.58 | Case 1: % 190.52/30.58 | | % 190.52/30.58 | | (12) (all_252_12 = e1 & op(e1, e4) = e1) | (all_252_13 = e1 & op(e1, e3) % 190.52/30.58 | | = e1) % 190.52/30.58 | | % 190.52/30.58 | | BETA: splitting (12) gives: % 190.52/30.58 | | % 190.52/30.58 | | Case 1: % 190.52/30.58 | | | % 190.52/30.58 | | | (13) all_252_12 = e1 & op(e1, e4) = e1 % 190.52/30.58 | | | % 190.52/30.58 | | | REF_CLOSE: (6), (10), (13) are inconsistent by sub-proof #424. % 190.52/30.58 | | | % 190.52/30.58 | | Case 2: % 190.52/30.58 | | | % 190.52/30.58 | | | (14) all_252_13 = e1 & op(e1, e3) = e1 % 190.52/30.58 | | | % 190.52/30.58 | | | REF_CLOSE: (1), (5), (11), (14) are inconsistent by sub-proof #423. % 190.52/30.58 | | | % 190.52/30.58 | | End of split % 190.52/30.58 | | % 190.52/30.58 | Case 2: % 190.52/30.58 | | % 190.52/30.58 | | (15) (all_252_14 = e1 & op(e1, e2) = e1) | (all_252_15 = e1 & op(e1, e1) % 190.52/30.58 | | = e1) | (all_252_19 = e1 & op(e1, e0) = e1) % 190.52/30.58 | | % 190.52/30.58 | | BETA: splitting (15) gives: % 190.52/30.58 | | % 190.52/30.58 | | Case 1: % 190.52/30.58 | | | % 190.52/30.58 | | | (16) all_252_14 = e1 & op(e1, e2) = e1 % 190.52/30.58 | | | % 190.52/30.58 | | | ALPHA: (16) implies: % 190.52/30.58 | | | (17) all_252_14 = e1 % 190.52/30.58 | | | % 190.52/30.58 | | | COMBINE_EQS: (4), (17) imply: % 190.52/30.58 | | | (18) e4 = e1 % 190.52/30.58 | | | % 190.52/30.58 | | | REDUCE: (11), (18) imply: % 190.52/30.58 | | | (19) $false % 190.52/30.58 | | | % 190.52/30.58 | | | CLOSE: (19) is inconsistent. % 190.52/30.58 | | | % 190.52/30.58 | | Case 2: % 190.52/30.58 | | | % 190.52/30.58 | | | (20) (all_252_15 = e1 & op(e1, e1) = e1) | (all_252_19 = e1 & op(e1, % 190.52/30.58 | | | e0) = e1) % 190.52/30.58 | | | % 190.52/30.58 | | | BETA: splitting (20) gives: % 190.52/30.58 | | | % 190.52/30.58 | | | Case 1: % 190.52/30.58 | | | | % 190.52/30.58 | | | | (21) all_252_15 = e1 & op(e1, e1) = e1 % 190.52/30.58 | | | | % 190.52/30.58 | | | | REF_CLOSE: (2), (3), (21) are inconsistent by sub-proof #415. % 190.52/30.58 | | | | % 190.52/30.58 | | | Case 2: % 190.52/30.58 | | | | % 190.52/30.58 | | | | (22) all_252_19 = e1 & op(e1, e0) = e1 % 190.52/30.58 | | | | % 190.52/30.58 | | | | REF_CLOSE: (7), (9), (22) are inconsistent by sub-proof #414. % 190.52/30.58 | | | | % 190.52/30.58 | | | End of split % 190.52/30.58 | | | % 190.52/30.58 | | End of split % 190.52/30.58 | | % 190.52/30.58 | End of split % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #414 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_19 = e1 & op(e1, e0) = e1 % 190.52/30.58 (2) all_252_19 = e0 % 190.52/30.58 (3) ~ (e1 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_19 = e1 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e1 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #415 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_15 = e1 & op(e1, e1) = e1 % 190.52/30.58 (2) all_252_15 = e2 % 190.52/30.58 (3) ~ (e2 = e1) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_15 = e1 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e2 = e1 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #416 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_15 = e0 & op(e1, e1) = e0 % 190.52/30.58 (2) all_252_15 = e2 % 190.52/30.58 (3) ~ (e2 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_15 = e0 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e2 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #417 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_12 = e0 & op(e1, e4) = e0 % 190.52/30.58 (2) all_252_12 = e3 % 190.52/30.58 (3) ~ (e3 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_12 = e0 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e3 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #418 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_8 = e4 & op(e2, e2) = e4 % 190.52/30.58 (2) all_252_8 = e0 % 190.52/30.58 (3) ~ (e4 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_8 = e4 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e4 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #419 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_15 = e1 & op(e1, e1) = e1 % 190.52/30.58 (2) all_252_15 = e0 % 190.52/30.58 (3) ~ (e1 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_15 = e1 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e1 = e0 % 190.52/30.58 | % 190.52/30.58 | SIMP: (5) implies: % 190.52/30.58 | (6) e1 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (6) imply: % 190.52/30.58 | (7) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (7) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #420 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_15 = e0 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) ~ (e2 = e1) % 190.52/30.58 (4) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.52/30.58 | (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) = % 190.52/30.58 e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.52/30.58 (5) op(e1, e3) = e4 % 190.52/30.58 (6) all_252_12 = e3 % 190.52/30.58 (7) ~ (e3 = e2) % 190.52/30.58 (8) ~ (e4 = e2) % 190.52/30.58 (9) all_252_14 = e1 & op(e1, e2) = e1 % 190.52/30.58 (10) ~ (e2 = e0) % 190.52/30.58 (11) op(e1, e0) = all_34_2 % 190.52/30.58 (12) ~ (all_34_2 = e2) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (9) implies: % 190.52/30.58 | (13) all_252_14 = e1 % 190.52/30.58 | % 190.52/30.58 | BETA: splitting (4) gives: % 190.52/30.58 | % 190.52/30.58 | Case 1: % 190.52/30.58 | | % 190.52/30.58 | | (14) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) % 190.52/30.58 | | = e2) % 190.52/30.58 | | % 190.52/30.58 | | REF_CLOSE: (2), (5), (6), (7), (8), (14) are inconsistent by sub-proof #425. % 190.52/30.58 | | % 190.52/30.58 | Case 2: % 190.52/30.58 | | % 190.52/30.58 | | (15) (all_252_14 = e2 & op(e1, e2) = e2) | (all_252_15 = e2 & op(e1, e1) % 190.52/30.58 | | = e2) | (all_252_19 = e2 & op(e1, e0) = e2) % 190.52/30.58 | | % 190.52/30.58 | | BETA: splitting (15) gives: % 190.52/30.58 | | % 190.52/30.58 | | Case 1: % 190.52/30.58 | | | % 190.52/30.58 | | | (16) all_252_14 = e2 & op(e1, e2) = e2 % 190.52/30.58 | | | % 190.52/30.58 | | | REF_CLOSE: (3), (13), (16) are inconsistent by sub-proof #422. % 190.52/30.58 | | | % 190.52/30.58 | | Case 2: % 190.52/30.58 | | | % 190.52/30.58 | | | (17) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_19 = e2 & op(e1, % 190.52/30.58 | | | e0) = e2) % 190.52/30.58 | | | % 190.52/30.58 | | | BETA: splitting (17) gives: % 190.52/30.58 | | | % 190.52/30.58 | | | Case 1: % 190.52/30.58 | | | | % 190.52/30.58 | | | | (18) all_252_15 = e2 & op(e1, e1) = e2 % 190.52/30.58 | | | | % 190.52/30.58 | | | | REF_CLOSE: (1), (10), (18) are inconsistent by sub-proof #421. % 190.52/30.58 | | | | % 190.52/30.58 | | | Case 2: % 190.52/30.58 | | | | % 190.52/30.58 | | | | (19) all_252_19 = e2 & op(e1, e0) = e2 % 190.52/30.58 | | | | % 190.52/30.58 | | | | REF_CLOSE: (2), (11), (12), (19) are inconsistent by sub-proof #438. % 190.52/30.58 | | | | % 190.52/30.58 | | | End of split % 190.52/30.58 | | | % 190.52/30.58 | | End of split % 190.52/30.58 | | % 190.52/30.58 | End of split % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #421 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_15 = e2 & op(e1, e1) = e2 % 190.52/30.58 (2) all_252_15 = e0 % 190.52/30.58 (3) ~ (e2 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_15 = e2 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e2 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #422 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_14 = e2 & op(e1, e2) = e2 % 190.52/30.58 (2) all_252_14 = e1 % 190.52/30.58 (3) ~ (e2 = e1) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_14 = e2 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e2 = e1 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #423 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_13 = e1 & op(e1, e3) = e1 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) op(e1, e3) = e4 % 190.52/30.58 (4) ~ (e4 = e1) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (5) op(e1, e3) = e1 % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (2) with e4, e1, e3, e1, simplifying with (3), (5) % 190.52/30.58 | gives: % 190.52/30.58 | (6) e4 = e1 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (4), (6) imply: % 190.52/30.58 | (7) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (7) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #424 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_12 = e1 & op(e1, e4) = e1 % 190.52/30.58 (2) all_252_12 = e3 % 190.52/30.58 (3) ~ (e3 = e1) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_12 = e1 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e3 = e1 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #425 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (2) (all_252_12 = e2 & op(e1, e4) = e2) | (all_252_13 = e2 & op(e1, e3) = e2) % 190.52/30.58 (3) op(e1, e3) = e4 % 190.52/30.58 (4) all_252_12 = e3 % 190.52/30.58 (5) ~ (e3 = e2) % 190.52/30.58 (6) ~ (e4 = e2) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | BETA: splitting (2) gives: % 190.52/30.58 | % 190.52/30.58 | Case 1: % 190.52/30.58 | | % 190.52/30.58 | | (7) all_252_12 = e2 & op(e1, e4) = e2 % 190.52/30.58 | | % 190.52/30.58 | | ALPHA: (7) implies: % 190.52/30.58 | | (8) all_252_12 = e2 % 190.52/30.58 | | % 190.52/30.58 | | COMBINE_EQS: (4), (8) imply: % 190.52/30.58 | | (9) e3 = e2 % 190.52/30.58 | | % 190.52/30.58 | | REDUCE: (5), (9) imply: % 190.52/30.58 | | (10) $false % 190.52/30.58 | | % 190.52/30.58 | | CLOSE: (10) is inconsistent. % 190.52/30.58 | | % 190.52/30.58 | Case 2: % 190.52/30.58 | | % 190.52/30.58 | | (11) all_252_13 = e2 & op(e1, e3) = e2 % 190.52/30.58 | | % 190.52/30.58 | | ALPHA: (11) implies: % 190.52/30.58 | | (12) op(e1, e3) = e2 % 190.52/30.58 | | % 190.52/30.58 | | REF_CLOSE: (1), (3), (6), (12) are inconsistent by sub-proof #529. % 190.52/30.58 | | % 190.52/30.58 | End of split % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #426 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (2) op(e0, e4) = e4 % 190.52/30.58 (3) op(e0, e4) = e2 % 190.52/30.58 (4) ~ (e4 = e2) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (1) with e2, e4, e4, e0, simplifying with (2), (3) % 190.52/30.58 | gives: % 190.52/30.58 | (5) e4 = e2 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (4), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #427 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (2) op(e4, e1) = e4 % 190.52/30.58 (3) op(e4, e1) = e0 % 190.52/30.58 (4) ~ (e4 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (1) with e0, e4, e1, e4, simplifying with (2), (3) % 190.52/30.58 | gives: % 190.52/30.58 | (5) e4 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (4), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #428 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_13 = e0 & op(e1, e3) = e0 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) op(e1, e3) = e4 % 190.52/30.58 (4) ~ (e4 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (5) op(e1, e3) = e0 % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (2) with e4, e0, e3, e1, simplifying with (3), (5) % 190.52/30.58 | gives: % 190.52/30.58 | (6) e4 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (4), (6) imply: % 190.52/30.58 | (7) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (7) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #429 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_7 = e0 & op(e2, e3) = e0 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) op(e2, e3) = all_10_2 % 190.52/30.58 (4) ~ (all_10_2 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (5) op(e2, e3) = e0 % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (2) with all_10_2, e0, e3, e2, simplifying with % 190.52/30.58 | (3), (5) gives: % 190.52/30.58 | (6) all_10_2 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (4), (6) imply: % 190.52/30.58 | (7) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (7) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #430 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_3 = e0 & op(e3, e3) = e0 % 190.52/30.58 (2) all_252_3 = e1 % 190.52/30.58 (3) ~ (e1 = e0) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (4) all_252_3 = e0 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (2), (4) imply: % 190.52/30.58 | (5) e1 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (5) imply: % 190.52/30.58 | (6) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (6) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #431 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (2) op(e4, e3) = all_84_2 % 190.52/30.58 (3) ~ (e3 = e0) % 190.52/30.58 (4) op(e4, e3) = e3 % 190.52/30.58 (5) op(e4, e3) = e0 % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (1) with all_84_2, e0, e3, e4, simplifying with % 190.52/30.58 | (2), (5) gives: % 190.52/30.58 | (6) all_84_2 = e0 % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (1) with all_84_2, e3, e3, e4, simplifying with % 190.52/30.58 | (2), (4) gives: % 190.52/30.58 | (7) all_84_2 = e3 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (6), (7) imply: % 190.52/30.58 | (8) e3 = e0 % 190.52/30.58 | % 190.52/30.58 | SIMP: (8) implies: % 190.52/30.58 | (9) e3 = e0 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (3), (9) imply: % 190.52/30.58 | (10) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (10) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #432 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) all_252_6 = e3 & op(e2, e4) = e3 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) op(e2, e4) = all_64_2 % 190.52/30.58 (4) ~ (all_64_2 = e3) % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | ALPHA: (1) implies: % 190.52/30.58 | (5) op(e2, e4) = e3 % 190.52/30.58 | % 190.52/30.58 | GROUND_INST: instantiating (2) with all_64_2, e3, e4, e2, simplifying with % 190.52/30.58 | (3), (5) gives: % 190.52/30.58 | (6) all_64_2 = e3 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (4), (6) imply: % 190.52/30.58 | (7) $false % 190.52/30.58 | % 190.52/30.58 | CLOSE: (7) is inconsistent. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #433 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) op(e2, e2) = all_244_8 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) all_210_2 = all_12_2 % 190.52/30.58 (4) op(e0, e2) = all_28_2 % 190.52/30.58 (5) ~ (e4 = e0) % 190.52/30.58 (6) ~ (all_244_24 = all_12_2) % 190.52/30.58 (7) ~ (all_4_2 = e0) % 190.52/30.58 (8) op(e0, all_12_2) = e4 % 190.52/30.58 (9) ~ (all_206_2 = e4) | (op(e4, e0) = all_206_1 & $i(all_206_1) & ( ~ % 190.52/30.58 (all_206_1 = e3) | ( ~ (all_206_0 = e1) & op(e0, e3) = all_206_0 & % 190.52/30.58 $i(all_206_0)))) % 190.52/30.58 (10) ~ (all_8_2 = e0) % 190.52/30.58 (11) op(e0, e0) = all_244_24 % 190.52/30.58 (12) all_18_2 = all_12_2 % 190.52/30.58 (13) ~ (all_6_2 = e0) % 190.52/30.58 (14) op(e3, e2) = all_8_2 % 190.52/30.58 (15) op(all_244_8, all_244_8) = e2 % 190.52/30.58 (16) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.52/30.58 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.52/30.58 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.58 (17) ~ (all_210_2 = e2) | (op(e2, e0) = all_210_1 & $i(all_210_1) & ( ~ % 190.52/30.58 (all_210_1 = e1) | ( ~ (all_210_0 = e3) & op(e0, e1) = all_210_0 & % 190.52/30.58 $i(all_210_0)))) % 190.52/30.58 (18) all_206_2 = all_28_2 % 190.52/30.58 (19) all_18_2 = e2 % 190.52/30.58 (20) op(e1, e2) = all_4_2 % 190.52/30.58 (21) op(e4, e2) = all_6_2 % 190.52/30.58 % 190.52/30.58 Begin of proof % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (12), (19) imply: % 190.52/30.58 | (22) all_12_2 = e2 % 190.52/30.58 | % 190.52/30.58 | SIMP: (22) implies: % 190.52/30.58 | (23) all_12_2 = e2 % 190.52/30.58 | % 190.52/30.58 | COMBINE_EQS: (3), (23) imply: % 190.52/30.58 | (24) all_210_2 = e2 % 190.52/30.58 | % 190.52/30.58 | REDUCE: (6), (23) imply: % 190.52/30.58 | (25) ~ (all_244_24 = e2) % 190.52/30.58 | % 190.52/30.58 | REDUCE: (8), (23) imply: % 190.52/30.58 | (26) op(e0, e2) = e4 % 190.52/30.58 | % 190.52/30.58 | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (13), (14), (15), (16), % 190.52/30.58 | (17), (18), (20), (21), (24), (25), (26) are inconsistent by % 190.52/30.58 | sub-proof #434. % 190.52/30.58 | % 190.52/30.58 End of proof % 190.52/30.58 % 190.52/30.58 Sub-proof #434 shows that the following formulas are inconsistent: % 190.52/30.58 ---------------------------------------------------------------- % 190.52/30.58 (1) op(e2, e2) = all_244_8 % 190.52/30.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.58 (3) op(e0, e2) = e4 % 190.52/30.58 (4) op(e0, e2) = all_28_2 % 190.52/30.58 (5) ~ (all_244_24 = e2) % 190.52/30.58 (6) all_210_2 = e2 % 190.52/30.58 (7) ~ (e4 = e0) % 190.52/30.58 (8) ~ (all_4_2 = e0) % 190.52/30.59 (9) ~ (all_206_2 = e4) | (op(e4, e0) = all_206_1 & $i(all_206_1) & ( ~ % 190.52/30.59 (all_206_1 = e3) | ( ~ (all_206_0 = e1) & op(e0, e3) = all_206_0 & % 190.52/30.59 $i(all_206_0)))) % 190.52/30.59 (10) ~ (all_8_2 = e0) % 190.52/30.59 (11) op(e0, e0) = all_244_24 % 190.52/30.59 (12) ~ (all_6_2 = e0) % 190.52/30.59 (13) op(e3, e2) = all_8_2 % 190.52/30.59 (14) op(all_244_8, all_244_8) = e2 % 190.52/30.59 (15) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.52/30.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.52/30.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.59 (16) ~ (all_210_2 = e2) | (op(e2, e0) = all_210_1 & $i(all_210_1) & ( ~ % 190.52/30.59 (all_210_1 = e1) | ( ~ (all_210_0 = e3) & op(e0, e1) = all_210_0 & % 190.52/30.59 $i(all_210_0)))) % 190.52/30.59 (17) all_206_2 = all_28_2 % 190.52/30.59 (18) op(e1, e2) = all_4_2 % 190.52/30.59 (19) op(e4, e2) = all_6_2 % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | BETA: splitting (16) gives: % 190.52/30.59 | % 190.52/30.59 | Case 1: % 190.52/30.59 | | % 190.52/30.59 | | (20) ~ (all_210_2 = e2) % 190.52/30.59 | | % 190.52/30.59 | | REDUCE: (6), (20) imply: % 190.52/30.59 | | (21) $false % 190.52/30.59 | | % 190.52/30.59 | | CLOSE: (21) is inconsistent. % 190.52/30.59 | | % 190.52/30.59 | Case 2: % 190.52/30.59 | | % 190.52/30.59 | | % 190.52/30.59 | | GROUND_INST: instantiating (2) with all_28_2, e4, e2, e0, simplifying with % 190.52/30.59 | | (3), (4) gives: % 190.52/30.59 | | (22) all_28_2 = e4 % 190.52/30.59 | | % 190.52/30.59 | | COMBINE_EQS: (17), (22) imply: % 190.52/30.59 | | (23) all_206_2 = e4 % 190.52/30.59 | | % 190.52/30.59 | | BETA: splitting (15) gives: % 190.52/30.59 | | % 190.52/30.59 | | Case 1: % 190.52/30.59 | | | % 190.52/30.59 | | | (24) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) % 190.52/30.59 | | | = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | REF_CLOSE: (2), (10), (12), (13), (19), (24) are inconsistent by sub-proof % 190.52/30.59 | | | #546. % 190.52/30.59 | | | % 190.52/30.59 | | Case 2: % 190.52/30.59 | | | % 190.52/30.59 | | | (25) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) % 190.52/30.59 | | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | BETA: splitting (25) gives: % 190.52/30.59 | | | % 190.52/30.59 | | | Case 1: % 190.52/30.59 | | | | % 190.52/30.59 | | | | (26) all_252_8 = e0 & op(e2, e2) = e0 % 190.52/30.59 | | | | % 190.52/30.59 | | | | ALPHA: (26) implies: % 190.52/30.59 | | | | (27) op(e2, e2) = e0 % 190.52/30.59 | | | | % 190.52/30.59 | | | | BETA: splitting (9) gives: % 190.52/30.59 | | | | % 190.52/30.59 | | | | Case 1: % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | (28) ~ (all_206_2 = e4) % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REDUCE: (23), (28) imply: % 190.52/30.59 | | | | | (29) $false % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | CLOSE: (29) is inconsistent. % 190.52/30.59 | | | | | % 190.52/30.59 | | | | Case 2: % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | GROUND_INST: instantiating (2) with all_244_8, e0, e2, e2, simplifying % 190.52/30.59 | | | | | with (1), (27) gives: % 190.52/30.59 | | | | | (30) all_244_8 = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REDUCE: (14), (30) imply: % 190.52/30.59 | | | | | (31) op(e0, e0) = e2 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REF_CLOSE: (2), (5), (11), (31) are inconsistent by sub-proof #477. % 190.52/30.59 | | | | | % 190.52/30.59 | | | | End of split % 190.52/30.59 | | | | % 190.52/30.59 | | | Case 2: % 190.52/30.59 | | | | % 190.52/30.59 | | | | (32) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, % 190.52/30.59 | | | | e2) = e0) % 190.52/30.59 | | | | % 190.52/30.59 | | | | BETA: splitting (32) gives: % 190.52/30.59 | | | | % 190.52/30.59 | | | | Case 1: % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | (33) all_252_14 = e0 & op(e1, e2) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | ALPHA: (33) implies: % 190.52/30.59 | | | | | (34) op(e1, e2) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REF_CLOSE: (2), (8), (18), (34) are inconsistent by sub-proof #545. % 190.52/30.59 | | | | | % 190.52/30.59 | | | | Case 2: % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | (35) all_252_22 = e0 & op(e0, e2) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | ALPHA: (35) implies: % 190.52/30.59 | | | | | (36) op(e0, e2) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REF_CLOSE: (2), (3), (7), (36) are inconsistent by sub-proof #520. % 190.52/30.59 | | | | | % 190.52/30.59 | | | | End of split % 190.52/30.59 | | | | % 190.52/30.59 | | | End of split % 190.52/30.59 | | | % 190.52/30.59 | | End of split % 190.52/30.59 | | % 190.52/30.59 | End of split % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #435 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ~ (all_28_2 = e1) % 190.52/30.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (3) op(e0, e2) = all_28_2 % 190.52/30.59 (4) op(e0, e0) = all_244_24 % 190.52/30.59 (5) all_252_23 = e3 % 190.52/30.59 (6) ~ (e3 = e1) % 190.52/30.59 (7) ~ (all_244_24 = e1) % 190.52/30.59 (8) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) = e1) % 190.52/30.59 | (all_252_24 = e1 & op(e0, e0) = e1) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | BETA: splitting (8) gives: % 190.52/30.59 | % 190.52/30.59 | Case 1: % 190.52/30.59 | | % 190.52/30.59 | | (9) all_252_22 = e1 & op(e0, e2) = e1 % 190.52/30.59 | | % 190.52/30.59 | | ALPHA: (9) implies: % 190.52/30.59 | | (10) op(e0, e2) = e1 % 190.52/30.59 | | % 190.52/30.59 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #502. % 190.52/30.59 | | % 190.52/30.59 | Case 2: % 190.52/30.59 | | % 190.52/30.59 | | (11) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) % 190.52/30.59 | | = e1) % 190.52/30.59 | | % 190.52/30.59 | | REF_CLOSE: (2), (4), (5), (6), (7), (11) are inconsistent by sub-proof #436. % 190.52/30.59 | | % 190.52/30.59 | End of split % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #436 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (2) op(e0, e0) = all_244_24 % 190.52/30.59 (3) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.52/30.59 (4) all_252_23 = e3 % 190.52/30.59 (5) ~ (e3 = e1) % 190.52/30.59 (6) ~ (all_244_24 = e1) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | BETA: splitting (3) gives: % 190.52/30.59 | % 190.52/30.59 | Case 1: % 190.52/30.59 | | % 190.52/30.59 | | (7) all_252_23 = e1 & op(e0, e1) = e1 % 190.52/30.59 | | % 190.52/30.59 | | ALPHA: (7) implies: % 190.52/30.59 | | (8) all_252_23 = e1 % 190.52/30.59 | | % 190.52/30.59 | | COMBINE_EQS: (4), (8) imply: % 190.52/30.59 | | (9) e3 = e1 % 190.52/30.59 | | % 190.52/30.59 | | REDUCE: (5), (9) imply: % 190.52/30.59 | | (10) $false % 190.52/30.59 | | % 190.52/30.59 | | CLOSE: (10) is inconsistent. % 190.52/30.59 | | % 190.52/30.59 | Case 2: % 190.52/30.59 | | % 190.52/30.59 | | (11) all_252_24 = e1 & op(e0, e0) = e1 % 190.52/30.59 | | % 190.52/30.59 | | ALPHA: (11) implies: % 190.52/30.59 | | (12) op(e0, e0) = e1 % 190.52/30.59 | | % 190.52/30.59 | | REF_CLOSE: (1), (2), (6), (12) are inconsistent by sub-proof #474. % 190.52/30.59 | | % 190.52/30.59 | End of split % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #437 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (2) op(e1, all_34_2) = e0 % 190.52/30.59 (3) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | % 190.52/30.59 all_250_20 = e0 % 190.52/30.59 (4) all_250_20 = all_12_2 % 190.52/30.59 (5) ~ (all_12_2 = e2) % 190.52/30.59 (6) all_232_2 = all_34_2 % 190.52/30.59 (7) op(all_12_2, all_30_2) = e4 % 190.52/30.59 (8) ~ (all_16_2 = all_12_2) % 190.52/30.59 (9) op(e1, e4) = all_16_2 % 190.52/30.59 (10) op(e4, all_30_2) = e0 % 190.52/30.59 (11) ~ (all_232_2 = e4) | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 190.52/30.59 (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 & % 190.52/30.59 $i(all_232_0)))) % 190.52/30.59 (12) ~ (all_12_2 = e1) % 190.52/30.59 (13) all_34_2 = e4 % 190.52/30.59 (14) ~ (all_12_2 = e3) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | COMBINE_EQS: (6), (13) imply: % 190.52/30.59 | (15) all_232_2 = e4 % 190.52/30.59 | % 190.52/30.59 | REDUCE: (2), (13) imply: % 190.52/30.59 | (16) op(e1, e4) = e0 % 190.52/30.59 | % 190.52/30.59 | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14), (15), % 190.52/30.59 | (16) are inconsistent by sub-proof #483. % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #438 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) all_252_19 = e2 & op(e1, e0) = e2 % 190.52/30.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (3) op(e1, e0) = all_34_2 % 190.52/30.59 (4) ~ (all_34_2 = e2) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | ALPHA: (1) implies: % 190.52/30.59 | (5) op(e1, e0) = e2 % 190.52/30.59 | % 190.52/30.59 | GROUND_INST: instantiating (2) with all_34_2, e2, e0, e1, simplifying with % 190.52/30.59 | (3), (5) gives: % 190.52/30.59 | (6) all_34_2 = e2 % 190.52/30.59 | % 190.52/30.59 | REDUCE: (4), (6) imply: % 190.52/30.59 | (7) $false % 190.52/30.59 | % 190.52/30.59 | CLOSE: (7) is inconsistent. % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #439 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (2) op(e1, e2) = e3 % 190.52/30.59 (3) op(e1, e2) = e2 % 190.52/30.59 (4) ~ (e3 = e2) % 190.52/30.59 (5) op(e1, e2) = all_4_2 % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | GROUND_INST: instantiating (1) with all_4_2, e2, e2, e1, simplifying with (3), % 190.52/30.59 | (5) gives: % 190.52/30.59 | (6) all_4_2 = e2 % 190.52/30.59 | % 190.52/30.59 | GROUND_INST: instantiating (1) with all_4_2, e3, e2, e1, simplifying with (2), % 190.52/30.59 | (5) gives: % 190.52/30.59 | (7) all_4_2 = e3 % 190.52/30.59 | % 190.52/30.59 | COMBINE_EQS: (6), (7) imply: % 190.52/30.59 | (8) e3 = e2 % 190.52/30.59 | % 190.52/30.59 | REDUCE: (4), (8) imply: % 190.52/30.59 | (9) $false % 190.52/30.59 | % 190.52/30.59 | CLOSE: (9) is inconsistent. % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #440 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (2) op(e1, e1) = all_244_15 % 190.52/30.59 (3) op(e1, e1) = e0 % 190.52/30.59 (4) ~ (all_244_15 = e0) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | GROUND_INST: instantiating (1) with all_244_15, e0, e1, e1, simplifying with % 190.52/30.59 | (2), (3) gives: % 190.52/30.59 | (5) all_244_15 = e0 % 190.52/30.59 | % 190.52/30.59 | REDUCE: (4), (5) imply: % 190.52/30.59 | (6) $false % 190.52/30.59 | % 190.52/30.59 | CLOSE: (6) is inconsistent. % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #441 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (2) op(e3, e1) = all_36_2 % 190.52/30.59 (3) op(e4, e1) = e0 % 190.52/30.59 (4) ~ (all_36_2 = e2) % 190.52/30.59 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 190.52/30.59 (6) ~ (e2 = e0) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | BETA: splitting (5) gives: % 190.52/30.59 | % 190.52/30.59 | Case 1: % 190.52/30.59 | | % 190.52/30.59 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 190.52/30.59 | | % 190.52/30.59 | | ALPHA: (7) implies: % 190.52/30.59 | | (8) op(e4, e1) = e2 % 190.52/30.59 | | % 190.52/30.59 | | GROUND_INST: instantiating (1) with e0, e2, e1, e4, simplifying with (3), % 190.52/30.59 | | (8) gives: % 190.52/30.59 | | (9) e2 = e0 % 190.52/30.59 | | % 190.52/30.59 | | REDUCE: (6), (9) imply: % 190.52/30.59 | | (10) $false % 190.52/30.59 | | % 190.52/30.59 | | CLOSE: (10) is inconsistent. % 190.52/30.59 | | % 190.52/30.59 | Case 2: % 190.52/30.59 | | % 190.52/30.59 | | (11) all_252_10 = e2 & op(e3, e1) = e2 % 190.52/30.59 | | % 190.52/30.59 | | ALPHA: (11) implies: % 190.52/30.59 | | (12) op(e3, e1) = e2 % 190.52/30.59 | | % 190.52/30.59 | | REF_CLOSE: (1), (2), (4), (12) are inconsistent by sub-proof #557. % 190.52/30.59 | | % 190.52/30.59 | End of split % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #442 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ~ (all_244_24 = e3) % 190.52/30.59 (2) op(e2, e2) = all_244_8 % 190.52/30.59 (3) ~ (all_36_2 = e0) | (op(e0, e3) = all_36_1 & $i(all_36_1) & ( ~ % 190.52/30.59 (all_36_1 = e4) | ( ~ (all_36_0 = e2) & op(e3, e4) = all_36_0 & % 190.52/30.59 $i(all_36_0)))) % 190.52/30.59 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (5) op(e0, e2) = all_28_2 % 190.52/30.59 (6) op(e3, e1) = all_36_2 % 190.52/30.59 (7) ~ (e2 = e1) % 190.52/30.59 (8) op(e2, all_38_2) = e1 % 190.52/30.59 (9) ~ (all_26_2 = e0) % 190.52/30.59 (10) op(e1, e1) = all_244_15 % 190.52/30.59 (11) ~ (all_4_2 = e0) % 190.52/30.59 (12) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.52/30.59 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.52/30.59 $i(all_38_0)))) % 190.52/30.59 (13) ~ (all_12_2 = e2) % 190.52/30.59 (14) ~ (all_46_2 = e0) | (op(e0, e3) = all_46_1 & $i(all_46_1) & ( ~ % 190.52/30.59 (all_46_1 = e2) | ( ~ (all_46_0 = e4) & op(e3, e2) = all_46_0 & % 190.52/30.59 $i(all_46_0)))) % 190.52/30.59 (15) ~ (all_8_2 = e0) % 190.52/30.59 (16) op(e0, e0) = all_244_24 % 190.52/30.59 (17) op(e4, e1) = all_26_2 % 190.52/30.59 (18) ~ (all_6_2 = e0) % 190.52/30.59 (19) ~ (e3 = e0) % 190.52/30.59 (20) op(e3, e2) = all_8_2 % 190.52/30.59 (21) ~ (all_244_15 = e3) % 190.52/30.59 (22) op(all_244_15, all_244_15) = e1 % 190.52/30.59 (23) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.52/30.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.52/30.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.59 (24) op(e0, e1) = e3 % 190.52/30.59 (25) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.52/30.59 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.52/30.59 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.52/30.59 (26) ~ (e3 = e2) % 190.52/30.59 (27) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 190.52/30.59 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 190.52/30.59 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 190.52/30.59 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 190.52/30.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 190.52/30.59 op(e0, e1) = e0))) % 190.52/30.59 (28) op(e2, e0) = all_40_2 % 190.52/30.59 (29) op(all_28_2, all_40_2) = e2 % 190.52/30.59 (30) all_46_2 = all_36_2 % 190.52/30.59 (31) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.52/30.59 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.52/30.59 $i(all_188_0)))) % 190.52/30.59 (32) op(e1, all_20_1) = e3 % 190.52/30.59 (33) op(e0, e4) = all_12_2 % 190.52/30.59 (34) op(e3, all_36_2) = e1 % 190.52/30.59 (35) ~ (e2 = e0) % 190.52/30.59 (36) all_252_21 = e1 % 190.52/30.59 (37) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.52/30.59 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.52/30.59 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.52/30.59 (38) all_188_2 = all_38_2 % 190.52/30.59 (39) ~ (all_244_24 = e1) % 190.52/30.59 (40) op(e1, e2) = all_4_2 % 190.52/30.59 (41) op(e4, e2) = all_6_2 % 190.52/30.59 (42) op(e2, e1) = all_38_2 % 190.52/30.59 (43) op(e3, e0) = all_20_1 % 190.52/30.59 (44) ~ (all_244_8 = all_38_2) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | BETA: splitting (3) gives: % 190.52/30.59 | % 190.52/30.59 | Case 1: % 190.52/30.59 | | % 190.52/30.59 | | (45) ~ (all_36_2 = e0) % 190.52/30.59 | | % 190.52/30.59 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), % 190.52/30.59 | | (15), (16), (17), (18), (19), (20), (22), (23), (24), (25), (26), % 190.52/30.59 | | (27), (28), (29), (31), (33), (35), (36), (37), (38), (39), (40), % 190.52/30.59 | | (41), (42), (44), (45) are inconsistent by sub-proof #444. % 190.52/30.59 | | % 190.52/30.59 | Case 2: % 190.52/30.59 | | % 190.52/30.59 | | (46) all_36_2 = e0 % 190.52/30.59 | | % 190.52/30.59 | | COMBINE_EQS: (30), (46) imply: % 190.52/30.59 | | (47) all_46_2 = e0 % 190.52/30.59 | | % 190.52/30.59 | | REDUCE: (34), (46) imply: % 190.52/30.59 | | (48) op(e3, e0) = e1 % 190.52/30.59 | | % 190.52/30.59 | | BETA: splitting (14) gives: % 190.52/30.59 | | % 190.52/30.59 | | Case 1: % 190.52/30.59 | | | % 190.52/30.59 | | | (49) ~ (all_46_2 = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | REDUCE: (47), (49) imply: % 190.52/30.59 | | | (50) $false % 190.52/30.59 | | | % 190.52/30.59 | | | CLOSE: (50) is inconsistent. % 190.52/30.59 | | | % 190.52/30.59 | | Case 2: % 190.52/30.59 | | | % 190.52/30.59 | | | % 190.52/30.59 | | | GROUND_INST: instantiating (4) with all_20_1, e1, e0, e3, simplifying with % 190.52/30.59 | | | (43), (48) gives: % 190.52/30.59 | | | (51) all_20_1 = e1 % 190.52/30.59 | | | % 190.52/30.59 | | | REDUCE: (32), (51) imply: % 190.52/30.59 | | | (52) op(e1, e1) = e3 % 190.52/30.59 | | | % 190.52/30.59 | | | REF_CLOSE: (4), (10), (21), (52) are inconsistent by sub-proof #443. % 190.52/30.59 | | | % 190.52/30.59 | | End of split % 190.52/30.59 | | % 190.52/30.59 | End of split % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #443 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (2) op(e1, e1) = all_244_15 % 190.52/30.59 (3) op(e1, e1) = e3 % 190.52/30.59 (4) ~ (all_244_15 = e3) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | GROUND_INST: instantiating (1) with all_244_15, e3, e1, e1, simplifying with % 190.52/30.59 | (2), (3) gives: % 190.52/30.59 | (5) all_244_15 = e3 % 190.52/30.59 | % 190.52/30.59 | REDUCE: (4), (5) imply: % 190.52/30.59 | (6) $false % 190.52/30.59 | % 190.52/30.59 | CLOSE: (6) is inconsistent. % 190.52/30.59 | % 190.52/30.59 End of proof % 190.52/30.59 % 190.52/30.59 Sub-proof #444 shows that the following formulas are inconsistent: % 190.52/30.59 ---------------------------------------------------------------- % 190.52/30.59 (1) ~ (all_244_24 = e3) % 190.52/30.59 (2) op(e2, e2) = all_244_8 % 190.52/30.59 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.59 (4) ~ (all_36_2 = e0) % 190.52/30.59 (5) op(e0, e2) = all_28_2 % 190.52/30.59 (6) op(e3, e1) = all_36_2 % 190.52/30.59 (7) ~ (e2 = e1) % 190.52/30.59 (8) op(e2, all_38_2) = e1 % 190.52/30.59 (9) ~ (all_26_2 = e0) % 190.52/30.59 (10) op(e1, e1) = all_244_15 % 190.52/30.59 (11) ~ (all_4_2 = e0) % 190.52/30.59 (12) ~ (all_38_2 = e0) | (op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ % 190.52/30.59 (all_38_1 = e4) | ( ~ (all_38_0 = e3) & op(e2, e4) = all_38_0 & % 190.52/30.59 $i(all_38_0)))) % 190.52/30.59 (13) ~ (all_12_2 = e2) % 190.52/30.59 (14) ~ (all_8_2 = e0) % 190.52/30.59 (15) op(e0, e0) = all_244_24 % 190.52/30.59 (16) op(e4, e1) = all_26_2 % 190.52/30.59 (17) ~ (all_6_2 = e0) % 190.52/30.59 (18) ~ (e3 = e0) % 190.52/30.59 (19) op(e3, e2) = all_8_2 % 190.52/30.59 (20) op(all_244_15, all_244_15) = e1 % 190.52/30.59 (21) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.52/30.59 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.52/30.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.59 (22) op(e0, e1) = e3 % 190.52/30.59 (23) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.52/30.59 | (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, e1) = % 190.52/30.59 e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.52/30.59 (24) ~ (e3 = e2) % 190.52/30.59 (25) (all_252_24 = e0 & op(e0, e0) = e0) | (((all_252_16 = e0 & op(e4, e0) = % 190.52/30.59 e0) | (all_252_17 = e0 & op(e3, e0) = e0) | (all_252_18 = e0 & % 190.52/30.59 op(e2, e0) = e0) | (all_252_19 = e0 & op(e1, e0) = e0)) & % 190.52/30.59 ((all_252_20 = e0 & op(e0, e4) = e0) | (all_252_21 = e0 & op(e0, e3) = % 190.52/30.59 e0) | (all_252_22 = e0 & op(e0, e2) = e0) | (all_252_23 = e0 & % 190.52/30.59 op(e0, e1) = e0))) % 190.52/30.59 (26) op(e2, e0) = all_40_2 % 190.52/30.59 (27) op(all_28_2, all_40_2) = e2 % 190.52/30.59 (28) ~ (all_188_2 = e0) | (op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ % 190.52/30.59 (all_188_1 = e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.52/30.59 $i(all_188_0)))) % 190.52/30.59 (29) op(e0, e4) = all_12_2 % 190.52/30.59 (30) ~ (e2 = e0) % 190.52/30.59 (31) all_252_21 = e1 % 190.52/30.59 (32) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = % 190.52/30.59 e2) | (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & op(e0, % 190.52/30.59 e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.52/30.59 (33) all_188_2 = all_38_2 % 190.52/30.59 (34) ~ (all_244_24 = e1) % 190.52/30.59 (35) op(e1, e2) = all_4_2 % 190.52/30.59 (36) op(e4, e2) = all_6_2 % 190.52/30.59 (37) op(e2, e1) = all_38_2 % 190.52/30.59 (38) ~ (all_244_8 = all_38_2) % 190.52/30.59 % 190.52/30.59 Begin of proof % 190.52/30.59 | % 190.52/30.59 | BETA: splitting (12) gives: % 190.52/30.59 | % 190.52/30.59 | Case 1: % 190.52/30.59 | | % 190.52/30.59 | | (39) ~ (all_38_2 = e0) % 190.52/30.59 | | % 190.52/30.59 | | BETA: splitting (23) gives: % 190.52/30.59 | | % 190.52/30.59 | | Case 1: % 190.52/30.59 | | | % 190.52/30.59 | | | (40) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) % 190.52/30.59 | | | = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | REF_CLOSE: (3), (4), (6), (9), (16), (40) are inconsistent by sub-proof % 190.52/30.59 | | | #451. % 190.52/30.59 | | | % 190.52/30.59 | | Case 2: % 190.52/30.59 | | | % 190.52/30.59 | | | (41) (all_252_11 = e0 & op(e2, e1) = e0) | (all_252_15 = e0 & op(e1, % 190.52/30.59 | | | e1) = e0) | (all_252_23 = e0 & op(e0, e1) = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | BETA: splitting (41) gives: % 190.52/30.59 | | | % 190.52/30.59 | | | Case 1: % 190.52/30.59 | | | | % 190.52/30.59 | | | | (42) all_252_11 = e0 & op(e2, e1) = e0 % 190.52/30.59 | | | | % 190.52/30.59 | | | | ALPHA: (42) implies: % 190.52/30.59 | | | | (43) op(e2, e1) = e0 % 190.52/30.59 | | | | % 190.52/30.59 | | | | REF_CLOSE: (3), (37), (39), (43) are inconsistent by sub-proof #549. % 190.52/30.59 | | | | % 190.52/30.59 | | | Case 2: % 190.52/30.59 | | | | % 190.52/30.59 | | | | (44) (all_252_15 = e0 & op(e1, e1) = e0) | (all_252_23 = e0 & op(e0, % 190.52/30.59 | | | | e1) = e0) % 190.52/30.59 | | | | % 190.52/30.59 | | | | BETA: splitting (44) gives: % 190.52/30.59 | | | | % 190.52/30.59 | | | | Case 1: % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | (45) all_252_15 = e0 & op(e1, e1) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REF_CLOSE: (3), (10), (15), (20), (34), (45) are inconsistent by % 190.52/30.59 | | | | | sub-proof #450. % 190.52/30.59 | | | | | % 190.52/30.59 | | | | Case 2: % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | (46) all_252_23 = e0 & op(e0, e1) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | ALPHA: (46) implies: % 190.52/30.59 | | | | | (47) op(e0, e1) = e0 % 190.52/30.59 | | | | | % 190.52/30.59 | | | | | REF_CLOSE: (3), (18), (22), (47) are inconsistent by sub-proof #449. % 190.52/30.59 | | | | | % 190.52/30.59 | | | | End of split % 190.52/30.59 | | | | % 190.52/30.59 | | | End of split % 190.52/30.59 | | | % 190.52/30.59 | | End of split % 190.52/30.59 | | % 190.52/30.59 | Case 2: % 190.52/30.59 | | % 190.52/30.59 | | (48) all_38_2 = e0 % 190.52/30.59 | | (49) op(e0, e2) = all_38_1 & $i(all_38_1) & ( ~ (all_38_1 = e4) | ( ~ % 190.52/30.59 | | (all_38_0 = e3) & op(e2, e4) = all_38_0 & $i(all_38_0))) % 190.52/30.59 | | % 190.52/30.59 | | ALPHA: (49) implies: % 190.52/30.59 | | (50) op(e0, e2) = all_38_1 % 190.52/30.59 | | % 190.52/30.59 | | COMBINE_EQS: (33), (48) imply: % 190.52/30.59 | | (51) all_188_2 = e0 % 190.52/30.59 | | % 190.52/30.59 | | REDUCE: (38), (48) imply: % 190.52/30.59 | | (52) ~ (all_244_8 = e0) % 190.52/30.59 | | % 190.52/30.59 | | REDUCE: (8), (48) imply: % 190.52/30.59 | | (53) op(e2, e0) = e1 % 190.52/30.59 | | % 190.52/30.59 | | BETA: splitting (21) gives: % 190.52/30.59 | | % 190.52/30.59 | | Case 1: % 190.52/30.59 | | | % 190.52/30.59 | | | (54) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) % 190.52/30.59 | | | = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | REF_CLOSE: (3), (14), (17), (19), (36), (54) are inconsistent by sub-proof % 190.52/30.59 | | | #546. % 190.52/30.59 | | | % 190.52/30.59 | | Case 2: % 190.52/30.59 | | | % 190.52/30.59 | | | (55) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) % 190.52/30.59 | | | = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.59 | | | % 190.52/30.59 | | | BETA: splitting (55) gives: % 190.52/30.59 | | | % 190.52/30.59 | | | Case 1: % 190.52/30.59 | | | | % 190.52/30.59 | | | | (56) all_252_8 = e0 & op(e2, e2) = e0 % 190.52/30.59 | | | | % 190.52/30.59 | | | | ALPHA: (56) implies: % 190.52/30.59 | | | | (57) op(e2, e2) = e0 % 190.52/30.59 | | | | % 190.52/30.59 | | | | REF_CLOSE: (2), (3), (52), (57) are inconsistent by sub-proof #448. % 190.52/30.59 | | | | % 190.52/30.59 | | | Case 2: % 190.52/30.59 | | | | % 190.52/30.60 | | | | (58) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & op(e0, % 190.52/30.60 | | | | e2) = e0) % 190.52/30.60 | | | | % 190.52/30.60 | | | | BETA: splitting (58) gives: % 190.52/30.60 | | | | % 190.52/30.60 | | | | Case 1: % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | (59) all_252_14 = e0 & op(e1, e2) = e0 % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | ALPHA: (59) implies: % 190.52/30.60 | | | | | (60) op(e1, e2) = e0 % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | REF_CLOSE: (3), (11), (35), (60) are inconsistent by sub-proof #545. % 190.52/30.60 | | | | | % 190.52/30.60 | | | | Case 2: % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | (61) all_252_22 = e0 & op(e0, e2) = e0 % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | ALPHA: (61) implies: % 190.52/30.60 | | | | | (62) all_252_22 = e0 % 190.52/30.60 | | | | | (63) op(e0, e2) = e0 % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | BETA: splitting (28) gives: % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | Case 1: % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | (64) ~ (all_188_2 = e0) % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | REDUCE: (51), (64) imply: % 190.52/30.60 | | | | | | (65) $false % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | CLOSE: (65) is inconsistent. % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | Case 2: % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | (66) op(e0, e2) = all_188_1 & $i(all_188_1) & ( ~ (all_188_1 = % 190.52/30.60 | | | | | | e3) | ( ~ (all_188_0 = e4) & op(e2, e3) = all_188_0 & % 190.52/30.60 | | | | | | $i(all_188_0))) % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | ALPHA: (66) implies: % 190.52/30.60 | | | | | | (67) op(e0, e2) = all_188_1 % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | BETA: splitting (32) gives: % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | Case 1: % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | | (68) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & % 190.52/30.60 | | | | | | | op(e0, e3) = e2) % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | | BETA: splitting (68) gives: % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | | Case 1: % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | (69) all_252_20 = e2 & op(e0, e4) = e2 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | ALPHA: (69) implies: % 190.52/30.60 | | | | | | | | (70) op(e0, e4) = e2 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | REF_CLOSE: (3), (13), (29), (70) are inconsistent by sub-proof % 190.52/30.60 | | | | | | | | #544. % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | Case 2: % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | (71) all_252_21 = e2 & op(e0, e3) = e2 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | ALPHA: (71) implies: % 190.52/30.60 | | | | | | | | (72) all_252_21 = e2 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | COMBINE_EQS: (31), (72) imply: % 190.52/30.60 | | | | | | | | (73) e2 = e1 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | SIMP: (73) implies: % 190.52/30.60 | | | | | | | | (74) e2 = e1 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | REDUCE: (7), (74) imply: % 190.52/30.60 | | | | | | | | (75) $false % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | CLOSE: (75) is inconsistent. % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | End of split % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | Case 2: % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | | (76) (all_252_22 = e2 & op(e0, e2) = e2) | (all_252_23 = e2 & % 190.52/30.60 | | | | | | | op(e0, e1) = e2) | (all_252_24 = e2 & op(e0, e0) = e2) % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | | BETA: splitting (76) gives: % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | | Case 1: % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | (77) all_252_22 = e2 & op(e0, e2) = e2 % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | REF_CLOSE: (30), (62), (77) are inconsistent by sub-proof #447. % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | Case 2: % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | (78) (all_252_23 = e2 & op(e0, e1) = e2) | (all_252_24 = e2 & % 190.52/30.60 | | | | | | | | op(e0, e0) = e2) % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | BETA: splitting (78) gives: % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | | Case 1: % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | (79) all_252_23 = e2 & op(e0, e1) = e2 % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | ALPHA: (79) implies: % 190.52/30.60 | | | | | | | | | (80) op(e0, e1) = e2 % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | REF_CLOSE: (3), (22), (24), (80) are inconsistent by sub-proof % 190.52/30.60 | | | | | | | | | #446. % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | Case 2: % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | (81) all_252_24 = e2 & op(e0, e0) = e2 % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | ALPHA: (81) implies: % 190.52/30.60 | | | | | | | | | (82) all_252_24 = e2 % 190.52/30.60 | | | | | | | | | (83) op(e0, e0) = e2 % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | BETA: splitting (25) gives: % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | | Case 1: % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | (84) all_252_24 = e0 & op(e0, e0) = e0 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | REF_CLOSE: (30), (82), (84) are inconsistent by sub-proof % 190.52/30.60 | | | | | | | | | | #445. % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | Case 2: % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | GROUND_INST: instantiating (3) with all_244_24, e2, e0, e0, % 190.52/30.60 | | | | | | | | | | simplifying with (15), (83) gives: % 190.52/30.60 | | | | | | | | | | (85) all_244_24 = e2 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | GROUND_INST: instantiating (3) with e0, all_38_1, e2, e0, % 190.52/30.60 | | | | | | | | | | simplifying with (50), (63) gives: % 190.52/30.60 | | | | | | | | | | (86) all_38_1 = e0 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | GROUND_INST: instantiating (3) with all_28_2, all_188_1, e2, % 190.52/30.60 | | | | | | | | | | e0, simplifying with (5), (67) gives: % 190.52/30.60 | | | | | | | | | | (87) all_188_1 = all_28_2 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | GROUND_INST: instantiating (3) with all_38_1, all_188_1, e2, % 190.52/30.60 | | | | | | | | | | e0, simplifying with (50), (67) gives: % 190.52/30.60 | | | | | | | | | | (88) all_188_1 = all_38_1 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | GROUND_INST: instantiating (3) with all_40_2, e1, e0, e2, % 190.52/30.60 | | | | | | | | | | simplifying with (26), (53) gives: % 190.52/30.60 | | | | | | | | | | (89) all_40_2 = e1 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | COMBINE_EQS: (87), (88) imply: % 190.52/30.60 | | | | | | | | | | (90) all_38_1 = all_28_2 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | SIMP: (90) implies: % 190.52/30.60 | | | | | | | | | | (91) all_38_1 = all_28_2 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | COMBINE_EQS: (86), (91) imply: % 190.52/30.60 | | | | | | | | | | (92) all_28_2 = e0 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | REDUCE: (1), (85) imply: % 190.52/30.60 | | | | | | | | | | (93) ~ (e3 = e2) % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | REDUCE: (27), (89), (92) imply: % 190.52/30.60 | | | | | | | | | | (94) op(e0, e1) = e2 % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | | REF_CLOSE: (3), (22), (24), (94) are inconsistent by % 190.52/30.60 | | | | | | | | | | sub-proof #446. % 190.52/30.60 | | | | | | | | | | % 190.52/30.60 | | | | | | | | | End of split % 190.52/30.60 | | | | | | | | | % 190.52/30.60 | | | | | | | | End of split % 190.52/30.60 | | | | | | | | % 190.52/30.60 | | | | | | | End of split % 190.52/30.60 | | | | | | | % 190.52/30.60 | | | | | | End of split % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | End of split % 190.52/30.60 | | | | | % 190.52/30.60 | | | | End of split % 190.52/30.60 | | | | % 190.52/30.60 | | | End of split % 190.52/30.60 | | | % 190.52/30.60 | | End of split % 190.52/30.60 | | % 190.52/30.60 | End of split % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #445 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) all_252_24 = e0 & op(e0, e0) = e0 % 190.52/30.60 (2) all_252_24 = e2 % 190.52/30.60 (3) ~ (e2 = e0) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | ALPHA: (1) implies: % 190.52/30.60 | (4) all_252_24 = e0 % 190.52/30.60 | % 190.52/30.60 | COMBINE_EQS: (2), (4) imply: % 190.52/30.60 | (5) e2 = e0 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (3), (5) imply: % 190.52/30.60 | (6) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (6) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #446 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e0, e1) = e3 % 190.52/30.60 (3) op(e0, e1) = e2 % 190.52/30.60 (4) ~ (e3 = e2) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with e2, e3, e1, e0, simplifying with (2), (3) % 190.52/30.60 | gives: % 190.52/30.60 | (5) e3 = e2 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (4), (5) imply: % 190.52/30.60 | (6) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (6) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #447 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) all_252_22 = e2 & op(e0, e2) = e2 % 190.52/30.60 (2) all_252_22 = e0 % 190.52/30.60 (3) ~ (e2 = e0) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | ALPHA: (1) implies: % 190.52/30.60 | (4) all_252_22 = e2 % 190.52/30.60 | % 190.52/30.60 | COMBINE_EQS: (2), (4) imply: % 190.52/30.60 | (5) e2 = e0 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (3), (5) imply: % 190.52/30.60 | (6) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (6) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #448 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e2, e2) = all_244_8 % 190.52/30.60 (3) op(e2, e2) = e0 % 190.52/30.60 (4) ~ (all_244_8 = e0) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with all_244_8, e0, e2, e2, simplifying with % 190.52/30.60 | (2), (3) gives: % 190.52/30.60 | (5) all_244_8 = e0 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (4), (5) imply: % 190.52/30.60 | (6) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (6) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #449 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e0, e1) = e3 % 190.52/30.60 (3) op(e0, e1) = e0 % 190.52/30.60 (4) ~ (e3 = e0) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with e0, e3, e1, e0, simplifying with (2), (3) % 190.52/30.60 | gives: % 190.52/30.60 | (5) e3 = e0 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (4), (5) imply: % 190.52/30.60 | (6) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (6) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #450 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e1, e1) = all_244_15 % 190.52/30.60 (3) op(e0, e0) = all_244_24 % 190.52/30.60 (4) op(all_244_15, all_244_15) = e1 % 190.52/30.60 (5) ~ (all_244_24 = e1) % 190.52/30.60 (6) all_252_15 = e0 & op(e1, e1) = e0 % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | ALPHA: (6) implies: % 190.52/30.60 | (7) op(e1, e1) = e0 % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with all_244_15, e0, e1, e1, simplifying with % 190.52/30.60 | (2), (7) gives: % 190.52/30.60 | (8) all_244_15 = e0 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (4), (8) imply: % 190.52/30.60 | (9) op(e0, e0) = e1 % 190.52/30.60 | % 190.52/30.60 | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #474. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #451 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) ~ (all_36_2 = e0) % 190.52/30.60 (3) op(e3, e1) = all_36_2 % 190.52/30.60 (4) ~ (all_26_2 = e0) % 190.52/30.60 (5) (all_252_9 = e0 & op(e4, e1) = e0) | (all_252_10 = e0 & op(e3, e1) = e0) % 190.52/30.60 (6) op(e4, e1) = all_26_2 % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | BETA: splitting (5) gives: % 190.52/30.60 | % 190.52/30.60 | Case 1: % 190.52/30.60 | | % 190.52/30.60 | | (7) all_252_9 = e0 & op(e4, e1) = e0 % 190.52/30.60 | | % 190.52/30.60 | | ALPHA: (7) implies: % 190.52/30.60 | | (8) op(e4, e1) = e0 % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #452. % 190.52/30.60 | | % 190.52/30.60 | Case 2: % 190.52/30.60 | | % 190.52/30.60 | | (9) all_252_10 = e0 & op(e3, e1) = e0 % 190.52/30.60 | | % 190.52/30.60 | | ALPHA: (9) implies: % 190.52/30.60 | | (10) op(e3, e1) = e0 % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #498. % 190.52/30.60 | | % 190.52/30.60 | End of split % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #452 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e4, e1) = all_26_2 % 190.52/30.60 (3) op(e4, e1) = e0 % 190.52/30.60 (4) ~ (all_26_2 = e0) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with all_26_2, e0, e1, e4, simplifying with % 190.52/30.60 | (2), (3) gives: % 190.52/30.60 | (5) all_26_2 = e0 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (4), (5) imply: % 190.52/30.60 | (6) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (6) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #453 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e0, e3) = e1 % 190.52/30.60 (3) op(e0, e3) = all_22_2 % 190.52/30.60 (4) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 190.52/30.60 (5) op(e0, e4) = all_12_2 % 190.52/30.60 (6) ~ (e3 = e1) % 190.52/30.60 (7) ~ (all_12_2 = e3) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | BETA: splitting (4) gives: % 190.52/30.60 | % 190.52/30.60 | Case 1: % 190.52/30.60 | | % 190.52/30.60 | | (8) all_252_20 = e3 & op(e0, e4) = e3 % 190.52/30.60 | | % 190.52/30.60 | | ALPHA: (8) implies: % 190.52/30.60 | | (9) op(e0, e4) = e3 % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (1), (5), (7), (9) are inconsistent by sub-proof #512. % 190.52/30.60 | | % 190.52/30.60 | Case 2: % 190.52/30.60 | | % 190.52/30.60 | | (10) all_252_21 = e3 & op(e0, e3) = e3 % 190.52/30.60 | | % 190.52/30.60 | | ALPHA: (10) implies: % 190.52/30.60 | | (11) op(e0, e3) = e3 % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (1), (2), (3), (6), (11) are inconsistent by sub-proof #454. % 190.52/30.60 | | % 190.52/30.60 | End of split % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #454 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) op(e0, e3) = e1 % 190.52/30.60 (3) op(e0, e3) = all_22_2 % 190.52/30.60 (4) op(e0, e3) = e3 % 190.52/30.60 (5) ~ (e3 = e1) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with all_22_2, e1, e3, e0, simplifying with % 190.52/30.60 | (2), (3) gives: % 190.52/30.60 | (6) all_22_2 = e1 % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (1) with all_22_2, e3, e3, e0, simplifying with % 190.52/30.60 | (3), (4) gives: % 190.52/30.60 | (7) all_22_2 = e3 % 190.52/30.60 | % 190.52/30.60 | COMBINE_EQS: (6), (7) imply: % 190.52/30.60 | (8) e3 = e1 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (5), (8) imply: % 190.52/30.60 | (9) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (9) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #455 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) op(e2, e2) = all_244_8 % 190.52/30.60 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (3) op(e0, e2) = all_28_2 % 190.52/30.60 (4) ~ (all_244_24 = e2) % 190.52/30.60 (5) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 190.52/30.60 (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 190.52/30.60 $i(all_158_0)))) % 190.52/30.60 (6) all_158_2 = all_28_2 % 190.52/30.60 (7) ~ (all_28_2 = all_12_2) % 190.52/30.60 (8) ~ (all_4_2 = e0) % 190.52/30.60 (9) ~ (all_28_2 = all_20_2) % 190.52/30.60 (10) ~ (all_8_2 = e0) % 190.52/30.60 (11) op(e0, e0) = all_244_24 % 190.52/30.60 (12) op(e0, e1) = all_20_2 % 190.52/30.60 (13) ~ (all_6_2 = e0) % 190.52/30.60 (14) ~ (e3 = e0) % 190.52/30.60 (15) op(e3, e2) = all_8_2 % 190.52/30.60 (16) op(all_244_8, all_244_8) = e2 % 190.52/30.60 (17) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.52/30.60 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.52/30.60 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.60 (18) ~ (all_244_24 = all_28_2) % 190.52/30.60 (19) op(e0, e2) = e3 % 190.52/30.60 (20) op(e0, e4) = all_12_2 % 190.52/30.60 (21) all_252_21 = e2 % 190.52/30.60 (22) ~ (all_28_2 = e2) % 190.52/30.60 (23) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 190.52/30.60 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.52/30.60 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.52/30.60 (24) op(e1, e2) = all_4_2 % 190.52/30.60 (25) op(e4, e2) = all_6_2 % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (2) with all_28_2, e3, e2, e0, simplifying with % 190.52/30.60 | (3), (19) gives: % 190.52/30.60 | (26) all_28_2 = e3 % 190.52/30.60 | % 190.52/30.60 | COMBINE_EQS: (6), (26) imply: % 190.52/30.60 | (27) all_158_2 = e3 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (18), (26) imply: % 190.52/30.60 | (28) ~ (all_244_24 = e3) % 190.52/30.60 | % 190.52/30.60 | REDUCE: (9), (26) imply: % 190.52/30.60 | (29) ~ (all_20_2 = e3) % 190.52/30.60 | % 190.52/30.60 | SIMP: (29) implies: % 190.52/30.60 | (30) ~ (all_20_2 = e3) % 190.52/30.60 | % 190.52/30.60 | REDUCE: (7), (26) imply: % 190.52/30.60 | (31) ~ (all_12_2 = e3) % 190.52/30.60 | % 190.52/30.60 | SIMP: (31) implies: % 190.52/30.60 | (32) ~ (all_12_2 = e3) % 190.52/30.60 | % 190.52/30.60 | REDUCE: (22), (26) imply: % 190.52/30.60 | (33) ~ (e3 = e2) % 190.52/30.60 | % 190.52/30.60 | BETA: splitting (23) gives: % 190.52/30.60 | % 190.52/30.60 | Case 1: % 190.52/30.60 | | % 190.52/30.60 | | (34) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) % 190.52/30.60 | | = e3) % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (2), (20), (21), (32), (33), (34) are inconsistent by sub-proof % 190.52/30.60 | | #457. % 190.52/30.60 | | % 190.52/30.60 | Case 2: % 190.52/30.60 | | % 190.52/30.60 | | (35) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, e1) % 190.52/30.60 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.52/30.60 | | % 190.52/30.60 | | BETA: splitting (35) gives: % 190.52/30.60 | | % 190.52/30.60 | | Case 1: % 190.52/30.60 | | | % 190.52/30.60 | | | (36) all_252_22 = e3 & op(e0, e2) = e3 % 190.52/30.60 | | | % 190.52/30.60 | | | ALPHA: (36) implies: % 190.52/30.60 | | | (37) all_252_22 = e3 % 190.52/30.60 | | | % 190.52/30.60 | | | BETA: splitting (17) gives: % 190.52/30.60 | | | % 190.52/30.60 | | | Case 1: % 190.52/30.60 | | | | % 190.52/30.60 | | | | (38) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 190.52/30.60 | | | | e2) = e0) % 190.52/30.60 | | | | % 190.52/30.60 | | | | REF_CLOSE: (2), (10), (13), (15), (25), (38) are inconsistent by % 190.52/30.60 | | | | sub-proof #546. % 190.52/30.60 | | | | % 190.52/30.60 | | | Case 2: % 190.52/30.60 | | | | % 190.52/30.60 | | | | (39) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, % 190.52/30.60 | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.60 | | | | % 190.52/30.60 | | | | BETA: splitting (39) gives: % 190.52/30.60 | | | | % 190.52/30.60 | | | | Case 1: % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | (40) all_252_8 = e0 & op(e2, e2) = e0 % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | REF_CLOSE: (1), (2), (4), (5), (11), (16), (27), (40) are inconsistent % 190.52/30.60 | | | | | by sub-proof #456. % 190.52/30.60 | | | | | % 190.52/30.60 | | | | Case 2: % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | (41) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 190.52/30.60 | | | | | op(e0, e2) = e0) % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | BETA: splitting (41) gives: % 190.52/30.60 | | | | | % 190.52/30.60 | | | | | Case 1: % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | (42) all_252_14 = e0 & op(e1, e2) = e0 % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | ALPHA: (42) implies: % 190.52/30.60 | | | | | | (43) op(e1, e2) = e0 % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | REF_CLOSE: (2), (8), (24), (43) are inconsistent by sub-proof #545. % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | Case 2: % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | (44) all_252_22 = e0 & op(e0, e2) = e0 % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | ALPHA: (44) implies: % 190.52/30.60 | | | | | | (45) all_252_22 = e0 % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | COMBINE_EQS: (37), (45) imply: % 190.52/30.60 | | | | | | (46) e3 = e0 % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | REDUCE: (14), (46) imply: % 190.52/30.60 | | | | | | (47) $false % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | | CLOSE: (47) is inconsistent. % 190.52/30.60 | | | | | | % 190.52/30.60 | | | | | End of split % 190.52/30.60 | | | | | % 190.52/30.60 | | | | End of split % 190.52/30.60 | | | | % 190.52/30.60 | | | End of split % 190.52/30.60 | | | % 190.52/30.60 | | Case 2: % 190.52/30.60 | | | % 190.52/30.60 | | | (48) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, % 190.52/30.60 | | | e0) = e3) % 190.52/30.60 | | | % 190.52/30.60 | | | REF_CLOSE: (2), (11), (12), (28), (30), (48) are inconsistent by sub-proof % 190.52/30.60 | | | #506. % 190.52/30.60 | | | % 190.52/30.60 | | End of split % 190.52/30.60 | | % 190.52/30.60 | End of split % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #456 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) op(e2, e2) = all_244_8 % 190.52/30.60 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (3) ~ (all_244_24 = e2) % 190.52/30.60 (4) ~ (all_158_2 = e3) | (op(e3, e0) = all_158_1 & $i(all_158_1) & ( ~ % 190.52/30.60 (all_158_1 = e4) | ( ~ (all_158_0 = e1) & op(e0, e4) = all_158_0 & % 190.52/30.60 $i(all_158_0)))) % 190.52/30.60 (5) all_252_8 = e0 & op(e2, e2) = e0 % 190.52/30.60 (6) all_158_2 = e3 % 190.52/30.60 (7) op(e0, e0) = all_244_24 % 190.52/30.60 (8) op(all_244_8, all_244_8) = e2 % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | ALPHA: (5) implies: % 190.52/30.60 | (9) op(e2, e2) = e0 % 190.52/30.60 | % 190.52/30.60 | BETA: splitting (4) gives: % 190.52/30.60 | % 190.52/30.60 | Case 1: % 190.52/30.60 | | % 190.52/30.60 | | (10) ~ (all_158_2 = e3) % 190.52/30.60 | | % 190.52/30.60 | | REDUCE: (6), (10) imply: % 190.52/30.60 | | (11) $false % 190.52/30.60 | | % 190.52/30.60 | | CLOSE: (11) is inconsistent. % 190.52/30.60 | | % 190.52/30.60 | Case 2: % 190.52/30.60 | | % 190.52/30.60 | | % 190.52/30.60 | | GROUND_INST: instantiating (2) with all_244_8, e0, e2, e2, simplifying with % 190.52/30.60 | | (1), (9) gives: % 190.52/30.60 | | (12) all_244_8 = e0 % 190.52/30.60 | | % 190.52/30.60 | | REDUCE: (8), (12) imply: % 190.52/30.60 | | (13) op(e0, e0) = e2 % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (2), (3), (7), (13) are inconsistent by sub-proof #477. % 190.52/30.60 | | % 190.52/30.60 | End of split % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #457 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = e3) % 190.52/30.60 (3) ~ (e3 = e2) % 190.52/30.60 (4) op(e0, e4) = all_12_2 % 190.52/30.60 (5) all_252_21 = e2 % 190.52/30.60 (6) ~ (all_12_2 = e3) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | BETA: splitting (2) gives: % 190.52/30.60 | % 190.52/30.60 | Case 1: % 190.52/30.60 | | % 190.52/30.60 | | (7) all_252_20 = e3 & op(e0, e4) = e3 % 190.52/30.60 | | % 190.52/30.60 | | ALPHA: (7) implies: % 190.52/30.60 | | (8) op(e0, e4) = e3 % 190.52/30.60 | | % 190.52/30.60 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #512. % 190.52/30.60 | | % 190.52/30.60 | Case 2: % 190.52/30.60 | | % 190.52/30.60 | | (9) all_252_21 = e3 & op(e0, e3) = e3 % 190.52/30.60 | | % 190.52/30.60 | | ALPHA: (9) implies: % 190.52/30.60 | | (10) all_252_21 = e3 % 190.52/30.60 | | % 190.52/30.60 | | COMBINE_EQS: (5), (10) imply: % 190.52/30.60 | | (11) e3 = e2 % 190.52/30.60 | | % 190.52/30.60 | | SIMP: (11) implies: % 190.52/30.60 | | (12) e3 = e2 % 190.52/30.60 | | % 190.52/30.60 | | REDUCE: (3), (12) imply: % 190.52/30.60 | | (13) $false % 190.52/30.60 | | % 190.52/30.60 | | CLOSE: (13) is inconsistent. % 190.52/30.60 | | % 190.52/30.60 | End of split % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #458 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) all_252_7 = e2 & op(e2, e3) = e2 % 190.52/30.60 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (3) op(e2, e3) = all_10_2 % 190.52/30.60 (4) ~ (all_10_2 = e2) % 190.52/30.60 % 190.52/30.60 Begin of proof % 190.52/30.60 | % 190.52/30.60 | ALPHA: (1) implies: % 190.52/30.60 | (5) op(e2, e3) = e2 % 190.52/30.60 | % 190.52/30.60 | GROUND_INST: instantiating (2) with all_10_2, e2, e3, e2, simplifying with % 190.52/30.60 | (3), (5) gives: % 190.52/30.60 | (6) all_10_2 = e2 % 190.52/30.60 | % 190.52/30.60 | REDUCE: (4), (6) imply: % 190.52/30.60 | (7) $false % 190.52/30.60 | % 190.52/30.60 | CLOSE: (7) is inconsistent. % 190.52/30.60 | % 190.52/30.60 End of proof % 190.52/30.60 % 190.52/30.60 Sub-proof #459 shows that the following formulas are inconsistent: % 190.52/30.60 ---------------------------------------------------------------- % 190.52/30.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.60 (2) all_32_2 = e4 % 190.52/30.60 (3) op(e0, all_20_2) = e1 % 190.52/30.60 (4) all_32_2 = all_20_2 % 190.52/30.61 (5) ~ (all_12_2 = e1) % 190.52/30.61 (6) op(e0, e4) = all_12_2 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (2), (4) imply: % 190.52/30.61 | (7) all_20_2 = e4 % 190.52/30.61 | % 190.52/30.61 | SIMP: (7) implies: % 190.52/30.61 | (8) all_20_2 = e4 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (3), (8) imply: % 190.52/30.61 | (9) op(e0, e4) = e1 % 190.52/30.61 | % 190.52/30.61 | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #530. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #460 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e1, e1) = all_244_15 % 190.52/30.61 (3) op(e1, e1) = e4 % 190.52/30.61 (4) ~ (all_244_15 = e4) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_244_15, e4, e1, e1, simplifying with % 190.52/30.61 | (2), (3) gives: % 190.52/30.61 | (5) all_244_15 = e4 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #461 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) all_252_11 = e4 % 190.52/30.61 (2) all_252_11 = e1 % 190.52/30.61 (3) ~ (e4 = e1) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (1), (2) imply: % 190.52/30.61 | (4) e4 = e1 % 190.52/30.61 | % 190.52/30.61 | SIMP: (4) implies: % 190.52/30.61 | (5) e4 = e1 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (3), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #462 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) all_252_10 = e4 & op(e3, e1) = e4 % 190.52/30.61 (2) all_252_10 = e2 % 190.52/30.61 (3) ~ (e4 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | ALPHA: (1) implies: % 190.52/30.61 | (4) all_252_10 = e4 % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (2), (4) imply: % 190.52/30.61 | (5) e4 = e2 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (3), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #463 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) ~ (e4 = e3) % 190.52/30.61 (3) op(e4, e1) = all_26_2 % 190.52/30.61 (4) op(e4, e1) = e3 % 190.52/30.61 (5) op(e4, e1) = e4 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_26_2, e3, e1, e4, simplifying with % 190.52/30.61 | (3), (4) gives: % 190.52/30.61 | (6) all_26_2 = e3 % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_26_2, e4, e1, e4, simplifying with % 190.52/30.61 | (3), (5) gives: % 190.52/30.61 | (7) all_26_2 = e4 % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (6), (7) imply: % 190.52/30.61 | (8) e4 = e3 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (2), (8) imply: % 190.52/30.61 | (9) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (9) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #464 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) ~ (e2 = e1) % 190.52/30.61 (3) op(e3, e2) = e1 % 190.52/30.61 (4) op(e3, e2) = all_8_2 % 190.52/30.61 (5) op(e3, e2) = e2 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_8_2, e1, e2, e3, simplifying with (3), % 190.52/30.61 | (4) gives: % 190.52/30.61 | (6) all_8_2 = e1 % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_8_2, e2, e2, e3, simplifying with (4), % 190.52/30.61 | (5) gives: % 190.52/30.61 | (7) all_8_2 = e2 % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (6), (7) imply: % 190.52/30.61 | (8) e2 = e1 % 190.52/30.61 | % 190.52/30.61 | SIMP: (8) implies: % 190.52/30.61 | (9) e2 = e1 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (2), (9) imply: % 190.52/30.61 | (10) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (10) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #465 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e3, e3) = all_244_3 % 190.52/30.61 (3) ~ (all_244_3 = e2) % 190.52/30.61 (4) op(e3, e4) = all_100_2 % 190.52/30.61 (5) (all_252_2 = e2 & op(e3, e4) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 190.52/30.61 (6) ~ (all_100_2 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | BETA: splitting (5) gives: % 190.52/30.61 | % 190.52/30.61 | Case 1: % 190.52/30.61 | | % 190.52/30.61 | | (7) all_252_2 = e2 & op(e3, e4) = e2 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (7) implies: % 190.52/30.61 | | (8) op(e3, e4) = e2 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #471. % 190.52/30.61 | | % 190.52/30.61 | Case 2: % 190.52/30.61 | | % 190.52/30.61 | | (9) all_252_3 = e2 & op(e3, e3) = e2 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #496. % 190.52/30.61 | | % 190.52/30.61 | End of split % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #466 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e0, all_28_2) = e2 % 190.52/30.61 (3) op(e0, e3) = all_22_2 % 190.52/30.61 (4) ~ (all_22_2 = e2) % 190.52/30.61 (5) all_82_2 = all_28_2 % 190.52/30.61 (6) all_82_2 = e3 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (5), (6) imply: % 190.52/30.61 | (7) all_28_2 = e3 % 190.52/30.61 | % 190.52/30.61 | SIMP: (7) implies: % 190.52/30.61 | (8) all_28_2 = e3 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (2), (8) imply: % 190.52/30.61 | (9) op(e0, e3) = e2 % 190.52/30.61 | % 190.52/30.61 | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #543. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #467 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) all_252_6 = e2 & op(e2, e4) = e2 % 190.52/30.61 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (3) op(e2, e4) = all_64_2 % 190.52/30.61 (4) ~ (all_64_2 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | ALPHA: (1) implies: % 190.52/30.61 | (5) op(e2, e4) = e2 % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (2) with all_64_2, e2, e4, e2, simplifying with % 190.52/30.61 | (3), (5) gives: % 190.52/30.61 | (6) all_64_2 = e2 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (6) imply: % 190.52/30.61 | (7) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (7) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #468 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) op(e2, e2) = all_244_8 % 190.52/30.61 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (3) op(e2, e2) = e0 % 190.52/30.61 (4) ~ (e3 = e0) % 190.52/30.61 (5) op(e2, e2) = e3 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (2) with all_244_8, e0, e2, e2, simplifying with % 190.52/30.61 | (1), (3) gives: % 190.52/30.61 | (6) all_244_8 = e0 % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (2) with all_244_8, e3, e2, e2, simplifying with % 190.52/30.61 | (1), (5) gives: % 190.52/30.61 | (7) all_244_8 = e3 % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (6), (7) imply: % 190.52/30.61 | (8) e3 = e0 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (8) imply: % 190.52/30.61 | (9) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (9) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #469 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e3, e1) = all_36_2 % 190.52/30.61 (3) ~ (all_36_2 = e2) % 190.52/30.61 (4) (all_252_10 = e2 & op(e3, e1) = e2) | (all_252_17 = e2 & op(e3, e0) = e2) % 190.52/30.61 (5) op(e3, e0) = all_48_2 % 190.52/30.61 (6) ~ (all_48_2 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | BETA: splitting (4) gives: % 190.52/30.61 | % 190.52/30.61 | Case 1: % 190.52/30.61 | | % 190.52/30.61 | | (7) all_252_10 = e2 & op(e3, e1) = e2 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (7) implies: % 190.52/30.61 | | (8) op(e3, e1) = e2 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #557. % 190.52/30.61 | | % 190.52/30.61 | Case 2: % 190.52/30.61 | | % 190.52/30.61 | | (9) all_252_17 = e2 & op(e3, e0) = e2 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (9) implies: % 190.52/30.61 | | (10) op(e3, e0) = e2 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #470. % 190.52/30.61 | | % 190.52/30.61 | End of split % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #470 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e3, e0) = all_48_2 % 190.52/30.61 (3) op(e3, e0) = e2 % 190.52/30.61 (4) ~ (all_48_2 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_48_2, e2, e0, e3, simplifying with % 190.52/30.61 | (2), (3) gives: % 190.52/30.61 | (5) all_48_2 = e2 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #471 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e3, e4) = all_100_2 % 190.52/30.61 (3) op(e3, e4) = e2 % 190.52/30.61 (4) ~ (all_100_2 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_100_2, e2, e4, e3, simplifying with % 190.52/30.61 | (2), (3) gives: % 190.52/30.61 | (5) all_100_2 = e2 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #472 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) all_28_2 = e1 % 190.52/30.61 (2) op(e2, e2) = all_244_8 % 190.52/30.61 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (4) ~ (e2 = e1) % 190.52/30.61 (5) ~ (all_28_2 = all_12_2) % 190.52/30.61 (6) ~ (all_4_2 = e0) % 190.52/30.61 (7) ~ (all_244_24 = all_20_2) % 190.52/30.61 (8) ~ (all_8_2 = e0) % 190.52/30.61 (9) op(e0, e0) = all_244_24 % 190.52/30.61 (10) op(e0, e1) = all_20_2 % 190.52/30.61 (11) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = % 190.52/30.61 e1) | (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, % 190.52/30.61 e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.52/30.61 (12) op(e0, all_28_2) = e2 % 190.52/30.61 (13) ~ (all_6_2 = e0) % 190.52/30.61 (14) op(e0, e3) = all_22_2 % 190.52/30.61 (15) op(e3, e2) = all_8_2 % 190.52/30.61 (16) op(all_244_8, all_244_8) = e2 % 190.52/30.61 (17) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.52/30.61 | (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, e2) = % 190.52/30.61 e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.61 (18) ~ (all_244_24 = all_28_2) % 190.52/30.61 (19) ~ (e1 = e0) % 190.52/30.61 (20) op(e0, e4) = all_12_2 % 190.52/30.61 (21) ~ (all_28_2 = all_22_2) % 190.52/30.61 (22) op(e1, e2) = all_4_2 % 190.52/30.61 (23) op(e4, e2) = all_6_2 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | REDUCE: (1), (18) imply: % 190.52/30.61 | (24) ~ (all_244_24 = e1) % 190.52/30.61 | % 190.52/30.61 | REDUCE: (1), (21) imply: % 190.52/30.61 | (25) ~ (all_22_2 = e1) % 190.52/30.61 | % 190.52/30.61 | SIMP: (25) implies: % 190.52/30.61 | (26) ~ (all_22_2 = e1) % 190.52/30.61 | % 190.52/30.61 | REDUCE: (1), (5) imply: % 190.52/30.61 | (27) ~ (all_12_2 = e1) % 190.52/30.61 | % 190.52/30.61 | SIMP: (27) implies: % 190.52/30.61 | (28) ~ (all_12_2 = e1) % 190.52/30.61 | % 190.52/30.61 | REDUCE: (1), (12) imply: % 190.52/30.61 | (29) op(e0, e1) = e2 % 190.52/30.61 | % 190.52/30.61 | BETA: splitting (11) gives: % 190.52/30.61 | % 190.52/30.61 | Case 1: % 190.52/30.61 | | % 190.52/30.61 | | (30) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) % 190.52/30.61 | | = e1) % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (3), (14), (20), (26), (28), (30) are inconsistent by sub-proof % 190.52/30.61 | | #478. % 190.52/30.61 | | % 190.52/30.61 | Case 2: % 190.52/30.61 | | % 190.52/30.61 | | (31) (all_252_22 = e1 & op(e0, e2) = e1) | (all_252_23 = e1 & op(e0, e1) % 190.52/30.61 | | = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.52/30.61 | | % 190.52/30.61 | | BETA: splitting (31) gives: % 190.52/30.61 | | % 190.52/30.61 | | Case 1: % 190.52/30.61 | | | % 190.52/30.61 | | | (32) all_252_22 = e1 & op(e0, e2) = e1 % 190.52/30.61 | | | % 190.52/30.61 | | | ALPHA: (32) implies: % 190.52/30.61 | | | (33) all_252_22 = e1 % 190.52/30.61 | | | % 190.52/30.61 | | | BETA: splitting (17) gives: % 190.52/30.61 | | | % 190.52/30.61 | | | Case 1: % 190.52/30.61 | | | | % 190.52/30.61 | | | | (34) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, % 190.52/30.61 | | | | e2) = e0) % 190.52/30.61 | | | | % 190.52/30.61 | | | | REF_CLOSE: (3), (8), (13), (15), (23), (34) are inconsistent by % 190.52/30.61 | | | | sub-proof #546. % 190.52/30.61 | | | | % 190.52/30.61 | | | Case 2: % 190.52/30.61 | | | | % 190.52/30.61 | | | | (35) (all_252_8 = e0 & op(e2, e2) = e0) | (all_252_14 = e0 & op(e1, % 190.52/30.61 | | | | e2) = e0) | (all_252_22 = e0 & op(e0, e2) = e0) % 190.52/30.61 | | | | % 190.52/30.61 | | | | BETA: splitting (35) gives: % 190.52/30.61 | | | | % 190.52/30.61 | | | | Case 1: % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | (36) all_252_8 = e0 & op(e2, e2) = e0 % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | ALPHA: (36) implies: % 190.52/30.61 | | | | | (37) op(e2, e2) = e0 % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | GROUND_INST: instantiating (3) with all_20_2, e2, e1, e0, simplifying % 190.52/30.61 | | | | | with (10), (29) gives: % 190.52/30.61 | | | | | (38) all_20_2 = e2 % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | REF_CLOSE: (2), (3), (7), (9), (16), (37), (38) are inconsistent by % 190.52/30.61 | | | | | sub-proof #476. % 190.52/30.61 | | | | | % 190.52/30.61 | | | | Case 2: % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | (39) (all_252_14 = e0 & op(e1, e2) = e0) | (all_252_22 = e0 & % 190.52/30.61 | | | | | op(e0, e2) = e0) % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | BETA: splitting (39) gives: % 190.52/30.61 | | | | | % 190.52/30.61 | | | | | Case 1: % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | (40) all_252_14 = e0 & op(e1, e2) = e0 % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | ALPHA: (40) implies: % 190.52/30.61 | | | | | | (41) op(e1, e2) = e0 % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | REF_CLOSE: (3), (6), (22), (41) are inconsistent by sub-proof #545. % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | Case 2: % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | (42) all_252_22 = e0 & op(e0, e2) = e0 % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | ALPHA: (42) implies: % 190.52/30.61 | | | | | | (43) all_252_22 = e0 % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | COMBINE_EQS: (33), (43) imply: % 190.52/30.61 | | | | | | (44) e1 = e0 % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | SIMP: (44) implies: % 190.52/30.61 | | | | | | (45) e1 = e0 % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | REDUCE: (19), (45) imply: % 190.52/30.61 | | | | | | (46) $false % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | | CLOSE: (46) is inconsistent. % 190.52/30.61 | | | | | | % 190.52/30.61 | | | | | End of split % 190.52/30.61 | | | | | % 190.52/30.61 | | | | End of split % 190.52/30.61 | | | | % 190.52/30.61 | | | End of split % 190.52/30.61 | | | % 190.52/30.61 | | Case 2: % 190.52/30.61 | | | % 190.52/30.61 | | | (47) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, % 190.52/30.61 | | | e0) = e1) % 190.52/30.61 | | | % 190.52/30.61 | | | REF_CLOSE: (3), (4), (9), (10), (24), (29), (47) are inconsistent by % 190.52/30.61 | | | sub-proof #473. % 190.52/30.61 | | | % 190.52/30.61 | | End of split % 190.52/30.61 | | % 190.52/30.61 | End of split % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #473 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) ~ (e2 = e1) % 190.52/30.61 (3) op(e0, e1) = e2 % 190.52/30.61 (4) op(e0, e0) = all_244_24 % 190.52/30.61 (5) (all_252_23 = e1 & op(e0, e1) = e1) | (all_252_24 = e1 & op(e0, e0) = e1) % 190.52/30.61 (6) op(e0, e1) = all_20_2 % 190.52/30.61 (7) ~ (all_244_24 = e1) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | BETA: splitting (5) gives: % 190.52/30.61 | % 190.52/30.61 | Case 1: % 190.52/30.61 | | % 190.52/30.61 | | (8) all_252_23 = e1 & op(e0, e1) = e1 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (8) implies: % 190.52/30.61 | | (9) op(e0, e1) = e1 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (2), (3), (6), (9) are inconsistent by sub-proof #475. % 190.52/30.61 | | % 190.52/30.61 | Case 2: % 190.52/30.61 | | % 190.52/30.61 | | (10) all_252_24 = e1 & op(e0, e0) = e1 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (10) implies: % 190.52/30.61 | | (11) op(e0, e0) = e1 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (4), (7), (11) are inconsistent by sub-proof #474. % 190.52/30.61 | | % 190.52/30.61 | End of split % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #474 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e0, e0) = all_244_24 % 190.52/30.61 (3) op(e0, e0) = e1 % 190.52/30.61 (4) ~ (all_244_24 = e1) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_244_24, e1, e0, e0, simplifying with % 190.52/30.61 | (2), (3) gives: % 190.52/30.61 | (5) all_244_24 = e1 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #475 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) ~ (e2 = e1) % 190.52/30.61 (3) op(e0, e1) = e2 % 190.52/30.61 (4) op(e0, e1) = all_20_2 % 190.52/30.61 (5) op(e0, e1) = e1 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_20_2, e1, e1, e0, simplifying with % 190.52/30.61 | (4), (5) gives: % 190.52/30.61 | (6) all_20_2 = e1 % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_20_2, e2, e1, e0, simplifying with % 190.52/30.61 | (3), (4) gives: % 190.52/30.61 | (7) all_20_2 = e2 % 190.52/30.61 | % 190.52/30.61 | COMBINE_EQS: (6), (7) imply: % 190.52/30.61 | (8) e2 = e1 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (2), (8) imply: % 190.52/30.61 | (9) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (9) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #476 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) op(e2, e2) = all_244_8 % 190.52/30.61 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (3) ~ (all_244_24 = all_20_2) % 190.52/30.61 (4) op(e0, e0) = all_244_24 % 190.52/30.61 (5) all_20_2 = e2 % 190.52/30.61 (6) op(e2, e2) = e0 % 190.52/30.61 (7) op(all_244_8, all_244_8) = e2 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (2) with all_244_8, e0, e2, e2, simplifying with % 190.52/30.61 | (1), (6) gives: % 190.52/30.61 | (8) all_244_8 = e0 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (3), (5) imply: % 190.52/30.61 | (9) ~ (all_244_24 = e2) % 190.52/30.61 | % 190.52/30.61 | REDUCE: (7), (8) imply: % 190.52/30.61 | (10) op(e0, e0) = e2 % 190.52/30.61 | % 190.52/30.61 | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #477. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #477 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e0, e0) = all_244_24 % 190.52/30.61 (3) op(e0, e0) = e2 % 190.52/30.61 (4) ~ (all_244_24 = e2) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_244_24, e2, e0, e0, simplifying with % 190.52/30.61 | (2), (3) gives: % 190.52/30.61 | (5) all_244_24 = e2 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #478 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) (all_252_20 = e1 & op(e0, e4) = e1) | (all_252_21 = e1 & op(e0, e3) = e1) % 190.52/30.61 (3) op(e0, e3) = all_22_2 % 190.52/30.61 (4) ~ (all_22_2 = e1) % 190.52/30.61 (5) ~ (all_12_2 = e1) % 190.52/30.61 (6) op(e0, e4) = all_12_2 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | BETA: splitting (2) gives: % 190.52/30.61 | % 190.52/30.61 | Case 1: % 190.52/30.61 | | % 190.52/30.61 | | (7) all_252_20 = e1 & op(e0, e4) = e1 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (7) implies: % 190.52/30.61 | | (8) op(e0, e4) = e1 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #530. % 190.52/30.61 | | % 190.52/30.61 | Case 2: % 190.52/30.61 | | % 190.52/30.61 | | (9) all_252_21 = e1 & op(e0, e3) = e1 % 190.52/30.61 | | % 190.52/30.61 | | ALPHA: (9) implies: % 190.52/30.61 | | (10) op(e0, e3) = e1 % 190.52/30.61 | | % 190.52/30.61 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #479. % 190.52/30.61 | | % 190.52/30.61 | End of split % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #479 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (2) op(e0, e3) = all_22_2 % 190.52/30.61 (3) op(e0, e3) = e1 % 190.52/30.61 (4) ~ (all_22_2 = e1) % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | GROUND_INST: instantiating (1) with all_22_2, e1, e3, e0, simplifying with % 190.52/30.61 | (2), (3) gives: % 190.52/30.61 | (5) all_22_2 = e1 % 190.52/30.61 | % 190.52/30.61 | REDUCE: (4), (5) imply: % 190.52/30.61 | (6) $false % 190.52/30.61 | % 190.52/30.61 | CLOSE: (6) is inconsistent. % 190.52/30.61 | % 190.52/30.61 End of proof % 190.52/30.61 % 190.52/30.61 Sub-proof #480 shows that the following formulas are inconsistent: % 190.52/30.61 ---------------------------------------------------------------- % 190.52/30.61 (1) ~ (all_244_24 = e3) % 190.52/30.61 (2) ~ (all_84_2 = all_22_2) % 190.52/30.61 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.61 (4) ~ (all_236_2 = e3) | (op(e3, e4) = all_236_1 & $i(all_236_1) & ( ~ % 190.52/30.61 (all_236_1 = e1) | ( ~ (all_236_0 = e2) & op(e4, e1) = all_236_0 & % 190.52/30.61 $i(all_236_0)))) % 190.52/30.61 (5) op(e0, e2) = all_28_2 % 190.52/30.61 (6) op(e4, e3) = all_84_2 % 190.52/30.61 (7) ~ (all_82_2 = e3) | (op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 190.52/30.61 (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, e1) = all_82_0 & % 190.52/30.61 $i(all_82_0)))) % 190.52/30.61 (8) ~ (all_20_2 = e3) % 190.52/30.61 (9) op(e0, e0) = all_244_24 % 190.52/30.61 (10) op(e0, e1) = all_20_2 % 190.52/30.61 (11) op(e0, all_28_2) = e2 % 190.52/30.61 (12) op(e0, e3) = all_22_2 % 190.52/30.61 (13) op(e3, all_48_2) = e0 % 190.52/30.61 (14) all_236_2 = e3 % 190.52/30.61 (15) ~ (all_22_2 = e2) % 190.52/30.61 (16) op(all_22_2, all_48_2) = e3 % 190.52/30.61 (17) all_82_2 = all_28_2 % 190.52/30.61 (18) op(e0, e4) = all_12_2 % 190.52/30.61 (19) ~ (all_12_2 = e3) % 190.52/30.61 (20) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 190.52/30.61 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.52/30.61 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.52/30.61 (21) op(e4, e3) = e0 % 190.52/30.61 % 190.52/30.61 Begin of proof % 190.52/30.61 | % 190.52/30.61 | BETA: splitting (4) gives: % 190.52/30.61 | % 190.52/30.61 | Case 1: % 190.52/30.61 | | % 190.52/30.61 | | (22) ~ (all_236_2 = e3) % 190.52/30.61 | | % 190.52/30.61 | | REDUCE: (14), (22) imply: % 190.52/30.61 | | (23) $false % 190.52/30.61 | | % 190.52/30.61 | | CLOSE: (23) is inconsistent. % 190.52/30.61 | | % 190.52/30.61 | Case 2: % 190.52/30.61 | | % 190.52/30.62 | | % 190.52/30.62 | | GROUND_INST: instantiating (3) with all_84_2, e0, e3, e4, simplifying with % 190.52/30.62 | | (6), (21) gives: % 190.52/30.62 | | (24) all_84_2 = e0 % 190.52/30.62 | | % 190.52/30.62 | | REDUCE: (2), (24) imply: % 190.52/30.62 | | (25) ~ (all_22_2 = e0) % 190.52/30.62 | | % 190.52/30.62 | | SIMP: (25) implies: % 190.52/30.62 | | (26) ~ (all_22_2 = e0) % 190.52/30.62 | | % 190.52/30.62 | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (13), (15), (16), % 190.52/30.62 | | (17), (18), (19), (20), (26) are inconsistent by sub-proof #481. % 190.52/30.62 | | % 190.52/30.62 | End of split % 190.52/30.62 | % 190.52/30.62 End of proof % 190.52/30.62 % 190.52/30.62 Sub-proof #481 shows that the following formulas are inconsistent: % 190.52/30.62 ---------------------------------------------------------------- % 190.52/30.62 (1) ~ (all_244_24 = e3) % 190.52/30.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.62 (3) op(e0, e2) = all_28_2 % 190.52/30.62 (4) ~ (all_22_2 = e0) % 190.52/30.62 (5) ~ (all_82_2 = e3) | (op(e3, e0) = all_82_1 & $i(all_82_1) & ( ~ % 190.52/30.62 (all_82_1 = e1) | ( ~ (all_82_0 = e4) & op(e0, e1) = all_82_0 & % 190.52/30.62 $i(all_82_0)))) % 190.52/30.62 (6) ~ (all_20_2 = e3) % 190.52/30.62 (7) op(e0, e0) = all_244_24 % 190.52/30.62 (8) op(e0, e1) = all_20_2 % 190.52/30.62 (9) op(e0, all_28_2) = e2 % 190.52/30.62 (10) op(e0, e3) = all_22_2 % 190.52/30.62 (11) op(e3, all_48_2) = e0 % 190.52/30.62 (12) ~ (all_22_2 = e2) % 190.52/30.62 (13) op(all_22_2, all_48_2) = e3 % 190.52/30.62 (14) all_82_2 = all_28_2 % 190.52/30.62 (15) op(e0, e4) = all_12_2 % 190.52/30.62 (16) ~ (all_12_2 = e3) % 190.52/30.62 (17) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, e3) = % 190.52/30.62 e3) | (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.52/30.62 e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.52/30.62 % 190.52/30.62 Begin of proof % 190.52/30.62 | % 190.52/30.62 | BETA: splitting (5) gives: % 190.52/30.62 | % 190.52/30.62 | Case 1: % 190.52/30.62 | | % 190.52/30.62 | | (18) ~ (all_82_2 = e3) % 190.52/30.62 | | % 190.52/30.62 | | REDUCE: (14), (18) imply: % 190.52/30.62 | | (19) ~ (all_28_2 = e3) % 190.52/30.62 | | % 190.52/30.62 | | BETA: splitting (17) gives: % 190.52/30.62 | | % 190.52/30.62 | | Case 1: % 190.52/30.62 | | | % 190.52/30.62 | | | (20) (all_252_20 = e3 & op(e0, e4) = e3) | (all_252_21 = e3 & op(e0, % 190.52/30.62 | | | e3) = e3) % 190.52/30.62 | | | % 190.52/30.62 | | | BETA: splitting (20) gives: % 190.52/30.62 | | | % 190.52/30.62 | | | Case 1: % 190.52/30.62 | | | | % 190.52/30.62 | | | | (21) all_252_20 = e3 & op(e0, e4) = e3 % 190.52/30.62 | | | | % 190.52/30.62 | | | | ALPHA: (21) implies: % 190.52/30.62 | | | | (22) op(e0, e4) = e3 % 190.52/30.62 | | | | % 190.52/30.62 | | | | REF_CLOSE: (2), (15), (16), (22) are inconsistent by sub-proof #512. % 190.52/30.62 | | | | % 190.52/30.62 | | | Case 2: % 190.52/30.62 | | | | % 190.52/30.62 | | | | (23) all_252_21 = e3 & op(e0, e3) = e3 % 190.52/30.62 | | | | % 190.52/30.62 | | | | REF_CLOSE: (2), (4), (10), (11), (13), (23) are inconsistent by % 190.52/30.62 | | | | sub-proof #482. % 190.52/30.62 | | | | % 190.52/30.62 | | | End of split % 190.52/30.62 | | | % 190.52/30.62 | | Case 2: % 190.52/30.62 | | | % 190.52/30.62 | | | (24) (all_252_22 = e3 & op(e0, e2) = e3) | (all_252_23 = e3 & op(e0, % 190.52/30.62 | | | e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.52/30.62 | | | % 190.52/30.62 | | | BETA: splitting (24) gives: % 190.52/30.62 | | | % 190.52/30.62 | | | Case 1: % 190.52/30.62 | | | | % 190.52/30.62 | | | | (25) all_252_22 = e3 & op(e0, e2) = e3 % 190.52/30.62 | | | | % 190.52/30.62 | | | | REF_CLOSE: (2), (3), (19), (25) are inconsistent by sub-proof #509. % 190.52/30.62 | | | | % 190.52/30.62 | | | Case 2: % 190.52/30.62 | | | | % 190.52/30.62 | | | | (26) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, % 190.52/30.62 | | | | e0) = e3) % 190.52/30.62 | | | | % 190.52/30.62 | | | | REF_CLOSE: (1), (2), (6), (7), (8), (26) are inconsistent by sub-proof % 190.52/30.62 | | | | #506. % 190.52/30.62 | | | | % 190.52/30.62 | | | End of split % 190.52/30.62 | | | % 190.52/30.62 | | End of split % 190.52/30.62 | | % 190.52/30.62 | Case 2: % 190.52/30.62 | | % 190.52/30.62 | | (27) all_82_2 = e3 % 190.52/30.62 | | % 190.52/30.62 | | COMBINE_EQS: (14), (27) imply: % 190.52/30.62 | | (28) all_28_2 = e3 % 190.52/30.62 | | % 190.52/30.62 | | REDUCE: (9), (28) imply: % 190.52/30.62 | | (29) op(e0, e3) = e2 % 190.52/30.62 | | % 190.52/30.62 | | REF_CLOSE: (2), (10), (12), (29) are inconsistent by sub-proof #543. % 190.52/30.62 | | % 190.52/30.62 | End of split % 190.52/30.62 | % 190.52/30.62 End of proof % 190.52/30.62 % 190.52/30.62 Sub-proof #482 shows that the following formulas are inconsistent: % 190.52/30.62 ---------------------------------------------------------------- % 190.52/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.62 (2) ~ (all_22_2 = e0) % 190.52/30.62 (3) op(e0, e3) = all_22_2 % 190.52/30.62 (4) op(e3, all_48_2) = e0 % 190.52/30.62 (5) op(all_22_2, all_48_2) = e3 % 190.52/30.62 (6) all_252_21 = e3 & op(e0, e3) = e3 % 190.52/30.62 % 190.52/30.62 Begin of proof % 190.52/30.62 | % 190.52/30.62 | ALPHA: (6) implies: % 190.52/30.62 | (7) op(e0, e3) = e3 % 190.52/30.62 | % 190.52/30.62 | GROUND_INST: instantiating (1) with all_22_2, e3, e3, e0, simplifying with % 190.52/30.62 | (3), (7) gives: % 190.52/30.62 | (8) all_22_2 = e3 % 190.52/30.62 | % 190.52/30.62 | REDUCE: (2), (8) imply: % 190.52/30.62 | (9) ~ (e3 = e0) % 190.52/30.62 | % 190.52/30.62 | REF_CLOSE: (1), (4), (5), (8), (9) are inconsistent by sub-proof #510. % 190.52/30.62 | % 190.52/30.62 End of proof % 190.52/30.62 % 190.52/30.62 Sub-proof #483 shows that the following formulas are inconsistent: % 190.52/30.62 ---------------------------------------------------------------- % 190.52/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.62 (2) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | % 190.52/30.62 all_250_20 = e0 % 190.52/30.62 (3) all_250_20 = all_12_2 % 190.52/30.62 (4) op(e1, e4) = e0 % 190.52/30.62 (5) ~ (all_12_2 = e2) % 190.52/30.62 (6) op(all_12_2, all_30_2) = e4 % 190.52/30.62 (7) all_232_2 = e4 % 190.52/30.62 (8) ~ (all_16_2 = all_12_2) % 190.52/30.62 (9) op(e1, e4) = all_16_2 % 190.52/30.62 (10) op(e4, all_30_2) = e0 % 190.52/30.62 (11) ~ (all_232_2 = e4) | (op(e4, e1) = all_232_1 & $i(all_232_1) & ( ~ % 190.52/30.62 (all_232_1 = e3) | ( ~ (all_232_0 = e2) & op(e1, e3) = all_232_0 & % 190.52/30.62 $i(all_232_0)))) % 190.52/30.62 (12) ~ (all_12_2 = e1) % 190.52/30.62 (13) ~ (all_12_2 = e3) % 190.52/30.62 % 190.52/30.62 Begin of proof % 190.52/30.62 | % 190.52/30.62 | BETA: splitting (11) gives: % 190.52/30.62 | % 190.52/30.62 | Case 1: % 190.52/30.62 | | % 190.52/30.62 | | (14) ~ (all_232_2 = e4) % 190.52/30.62 | | % 190.52/30.62 | | REDUCE: (7), (14) imply: % 190.52/30.62 | | (15) $false % 190.52/30.62 | | % 190.52/30.62 | | CLOSE: (15) is inconsistent. % 190.52/30.62 | | % 190.52/30.62 | Case 2: % 190.52/30.62 | | % 190.52/30.62 | | % 190.52/30.62 | | GROUND_INST: instantiating (1) with all_16_2, e0, e4, e1, simplifying with % 190.52/30.62 | | (4), (9) gives: % 190.52/30.62 | | (16) all_16_2 = e0 % 190.52/30.62 | | % 190.52/30.62 | | REDUCE: (8), (16) imply: % 190.52/30.62 | | (17) ~ (all_12_2 = e0) % 190.52/30.62 | | % 190.52/30.62 | | REF_CLOSE: (1), (2), (3), (5), (6), (10), (12), (13), (17) are inconsistent % 190.52/30.62 | | by sub-proof #503. % 190.52/30.62 | | % 190.52/30.62 | End of split % 190.52/30.62 | % 190.52/30.62 End of proof % 190.52/30.62 % 190.52/30.62 Sub-proof #484 shows that the following formulas are inconsistent: % 190.52/30.62 ---------------------------------------------------------------- % 190.52/30.62 (1) ~ (all_28_2 = e1) % 190.52/30.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.62 (3) ~ (all_20_2 = e4) % 190.52/30.62 (4) op(e0, e2) = all_28_2 % 190.52/30.62 (5) op(e1, all_34_2) = e0 % 190.52/30.62 (6) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 190.52/30.62 all_250_23 = e0 % 190.52/30.62 (7) all_58_2 = all_20_2 % 190.52/30.62 (8) ~ (all_20_2 = e3) % 190.52/30.62 (9) op(e0, all_20_2) = e1 % 190.52/30.62 (10) ~ (all_20_2 = e0) % 190.52/30.62 (11) op(all_20_2, all_34_2) = e1 % 190.52/30.62 (12) all_250_23 = all_20_2 % 190.52/30.62 (13) ~ (all_58_2 = e2) | (op(e2, e0) = all_58_1 & $i(all_58_1) & ( ~ % 190.52/30.62 (all_58_1 = e3) | ( ~ (all_58_0 = e4) & op(e0, e3) = all_58_0 & % 190.52/30.62 $i(all_58_0)))) % 190.52/30.62 % 190.52/30.62 Begin of proof % 190.52/30.62 | % 190.52/30.62 | BETA: splitting (13) gives: % 190.52/30.62 | % 190.52/30.62 | Case 1: % 190.52/30.62 | | % 190.52/30.62 | | (14) ~ (all_58_2 = e2) % 190.52/30.62 | | % 190.52/30.62 | | REDUCE: (7), (14) imply: % 190.52/30.62 | | (15) ~ (all_20_2 = e2) % 190.52/30.62 | | % 190.52/30.62 | | REF_CLOSE: (2), (3), (5), (6), (8), (10), (11), (12), (15) are inconsistent % 190.52/30.62 | | by sub-proof #485. % 190.52/30.62 | | % 190.52/30.62 | Case 2: % 190.52/30.62 | | % 190.52/30.62 | | (16) all_58_2 = e2 % 190.52/30.62 | | % 190.52/30.62 | | REF_CLOSE: (1), (2), (4), (7), (9), (16) are inconsistent by sub-proof #501. % 190.52/30.62 | | % 190.52/30.62 | End of split % 190.52/30.62 | % 190.52/30.62 End of proof % 190.52/30.62 % 190.52/30.62 Sub-proof #485 shows that the following formulas are inconsistent: % 190.52/30.62 ---------------------------------------------------------------- % 190.52/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.52/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.52/30.62 (2) ~ (all_20_2 = e4) % 190.52/30.62 (3) op(e1, all_34_2) = e0 % 190.52/30.62 (4) all_250_23 = e4 | all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | % 190.52/30.62 all_250_23 = e0 % 190.52/30.62 (5) ~ (all_20_2 = e3) % 190.52/30.62 (6) ~ (all_20_2 = e0) % 190.52/30.62 (7) ~ (all_20_2 = e2) % 190.52/30.62 (8) op(all_20_2, all_34_2) = e1 % 190.52/30.62 (9) all_250_23 = all_20_2 % 190.52/30.62 % 190.52/30.62 Begin of proof % 190.52/30.62 | % 190.52/30.62 | BETA: splitting (4) gives: % 190.52/30.62 | % 190.52/30.62 | Case 1: % 190.52/30.62 | | % 190.52/30.62 | | (10) all_250_23 = e4 % 190.52/30.62 | | % 190.52/30.62 | | REF_CLOSE: (2), (9), (10) are inconsistent by sub-proof #489. % 190.52/30.62 | | % 190.52/30.62 | Case 2: % 190.52/30.62 | | % 190.52/30.62 | | (11) all_250_23 = e3 | all_250_23 = e2 | all_250_23 = e1 | all_250_23 = % 190.52/30.62 | | e0 % 190.52/30.62 | | % 190.52/30.62 | | BETA: splitting (11) gives: % 190.52/30.62 | | % 190.52/30.62 | | Case 1: % 190.52/30.62 | | | % 190.52/30.62 | | | (12) all_250_23 = e3 % 190.52/30.62 | | | % 190.52/30.62 | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #488. % 190.52/30.62 | | | % 190.52/30.62 | | Case 2: % 190.52/30.62 | | | % 190.52/30.62 | | | (13) all_250_23 = e2 | all_250_23 = e1 | all_250_23 = e0 % 190.52/30.62 | | | % 190.52/30.62 | | | BETA: splitting (13) gives: % 190.52/30.62 | | | % 190.52/30.62 | | | Case 1: % 190.52/30.62 | | | | % 190.52/30.62 | | | | (14) all_250_23 = e2 % 190.52/30.62 | | | | % 190.52/30.62 | | | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #487. % 190.52/30.62 | | | | % 190.52/30.62 | | | Case 2: % 190.52/30.62 | | | | % 190.52/30.62 | | | | (15) all_250_23 = e1 | all_250_23 = e0 % 190.52/30.62 | | | | % 190.52/30.62 | | | | BETA: splitting (15) gives: % 190.52/30.62 | | | | % 190.52/30.62 | | | | Case 1: % 190.52/30.62 | | | | | % 190.52/30.62 | | | | | (16) all_250_23 = e1 % 190.52/30.62 | | | | | % 190.52/30.62 | | | | | COMBINE_EQS: (9), (16) imply: % 190.59/30.62 | | | | | (17) all_20_2 = e1 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | SIMP: (17) implies: % 190.59/30.62 | | | | | (18) all_20_2 = e1 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REDUCE: (6), (18) imply: % 190.59/30.62 | | | | | (19) ~ (e1 = e0) % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REDUCE: (8), (18) imply: % 190.59/30.62 | | | | | (20) op(e1, all_34_2) = e1 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | GROUND_INST: instantiating (1) with e0, e1, all_34_2, e1, simplifying % 190.59/30.62 | | | | | with (3), (20) gives: % 190.59/30.62 | | | | | (21) e1 = e0 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REDUCE: (19), (21) imply: % 190.59/30.62 | | | | | (22) $false % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | CLOSE: (22) is inconsistent. % 190.59/30.62 | | | | | % 190.59/30.62 | | | | Case 2: % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | (23) all_250_23 = e0 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REF_CLOSE: (6), (9), (23) are inconsistent by sub-proof #486. % 190.59/30.62 | | | | | % 190.59/30.62 | | | | End of split % 190.59/30.62 | | | | % 190.59/30.62 | | | End of split % 190.59/30.62 | | | % 190.59/30.62 | | End of split % 190.59/30.62 | | % 190.59/30.62 | End of split % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #486 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) all_250_23 = all_20_2 % 190.59/30.62 (2) all_250_23 = e0 % 190.59/30.62 (3) ~ (all_20_2 = e0) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | COMBINE_EQS: (1), (2) imply: % 190.59/30.62 | (4) all_20_2 = e0 % 190.59/30.62 | % 190.59/30.62 | SIMP: (4) implies: % 190.59/30.62 | (5) all_20_2 = e0 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (3), (5) imply: % 190.59/30.62 | (6) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (6) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #487 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) all_250_23 = all_20_2 % 190.59/30.62 (2) all_250_23 = e2 % 190.59/30.62 (3) ~ (all_20_2 = e2) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | COMBINE_EQS: (1), (2) imply: % 190.59/30.62 | (4) all_20_2 = e2 % 190.59/30.62 | % 190.59/30.62 | SIMP: (4) implies: % 190.59/30.62 | (5) all_20_2 = e2 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (3), (5) imply: % 190.59/30.62 | (6) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (6) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #488 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) all_250_23 = all_20_2 % 190.59/30.62 (2) all_250_23 = e3 % 190.59/30.62 (3) ~ (all_20_2 = e3) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | COMBINE_EQS: (1), (2) imply: % 190.59/30.62 | (4) all_20_2 = e3 % 190.59/30.62 | % 190.59/30.62 | SIMP: (4) implies: % 190.59/30.62 | (5) all_20_2 = e3 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (3), (5) imply: % 190.59/30.62 | (6) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (6) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #489 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) all_250_23 = all_20_2 % 190.59/30.62 (2) all_250_23 = e4 % 190.59/30.62 (3) ~ (all_20_2 = e4) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | COMBINE_EQS: (1), (2) imply: % 190.59/30.62 | (4) all_20_2 = e4 % 190.59/30.62 | % 190.59/30.62 | SIMP: (4) implies: % 190.59/30.62 | (5) all_20_2 = e4 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (3), (5) imply: % 190.59/30.62 | (6) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (6) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #490 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.62 (2) op(e2, e2) = all_244_8 % 190.59/30.62 (3) op(e2, e2) = e1 % 190.59/30.62 (4) ~ (all_244_8 = e1) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | GROUND_INST: instantiating (1) with all_244_8, e1, e2, e2, simplifying with % 190.59/30.62 | (2), (3) gives: % 190.59/30.62 | (5) all_244_8 = e1 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (4), (5) imply: % 190.59/30.62 | (6) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (6) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #491 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.62 (2) ~ (all_174_2 = e3) | (op(e3, e2) = all_174_1 & $i(all_174_1) & ( ~ % 190.59/30.62 (all_174_1 = e1) | ( ~ (all_174_0 = e4) & op(e2, e1) = all_174_0 & % 190.59/30.62 $i(all_174_0)))) % 190.59/30.62 (3) all_174_2 = all_40_2 % 190.59/30.62 (4) op(e2, e3) = all_10_2 % 190.59/30.62 (5) ~ (all_20_2 = e3) % 190.59/30.62 (6) op(e0, e1) = all_20_2 % 190.59/30.62 (7) op(all_10_2, e1) = e3 % 190.59/30.62 (8) op(e2, all_40_2) = e0 % 190.59/30.62 (9) all_40_2 = e3 % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | COMBINE_EQS: (3), (9) imply: % 190.59/30.62 | (10) all_174_2 = e3 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (8), (9) imply: % 190.59/30.62 | (11) op(e2, e3) = e0 % 190.59/30.62 | % 190.59/30.62 | BETA: splitting (2) gives: % 190.59/30.62 | % 190.59/30.62 | Case 1: % 190.59/30.62 | | % 190.59/30.62 | | (12) ~ (all_174_2 = e3) % 190.59/30.62 | | % 190.59/30.62 | | REDUCE: (10), (12) imply: % 190.59/30.62 | | (13) $false % 190.59/30.62 | | % 190.59/30.62 | | CLOSE: (13) is inconsistent. % 190.59/30.62 | | % 190.59/30.62 | Case 2: % 190.59/30.62 | | % 190.59/30.62 | | % 190.59/30.62 | | GROUND_INST: instantiating (1) with all_10_2, e0, e3, e2, simplifying with % 190.59/30.62 | | (4), (11) gives: % 190.59/30.62 | | (14) all_10_2 = e0 % 190.59/30.62 | | % 190.59/30.62 | | REDUCE: (7), (14) imply: % 190.59/30.62 | | (15) op(e0, e1) = e3 % 190.59/30.62 | | % 190.59/30.62 | | REF_CLOSE: (1), (5), (6), (15) are inconsistent by sub-proof #508. % 190.59/30.62 | | % 190.59/30.62 | End of split % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #492 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) op(e2, e2) = all_244_8 % 190.59/30.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.62 (3) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 190.59/30.62 (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 190.59/30.62 $i(all_102_0)))) % 190.59/30.62 (4) op(e3, e3) = all_244_3 % 190.59/30.62 (5) ~ (all_84_2 = e2) | (op(e2, e4) = all_84_1 & $i(all_84_1) & ( ~ % 190.59/30.62 (all_84_1 = e1) | ( ~ (all_84_0 = e0) & op(e4, e1) = all_84_0 & % 190.59/30.62 $i(all_84_0)))) % 190.59/30.62 (6) op(e1, e3) = all_62_2 % 190.59/30.62 (7) ~ (all_244_3 = e2) % 190.59/30.62 (8) op(e2, e3) = all_10_2 % 190.59/30.62 (9) op(e4, e3) = all_84_2 % 190.59/30.62 (10) ~ (all_214_2 = e3) | (op(e3, e4) = all_214_1 & $i(all_214_1) & ( ~ % 190.59/30.62 (all_214_1 = e1) | ( ~ (all_214_0 = e0) & op(e4, e1) = all_214_0 & % 190.59/30.62 $i(all_214_0)))) % 190.59/30.62 (11) ~ (all_10_2 = e1) % 190.59/30.62 (12) op(e4, all_84_2) = e3 % 190.59/30.62 (13) op(e0, e3) = all_22_2 % 190.59/30.62 (14) all_214_2 = all_6_2 % 190.59/30.62 (15) ~ (all_10_2 = e4) % 190.59/30.62 (16) op(all_10_2, e1) = e3 % 190.59/30.62 (17) op(all_10_2, all_8_2) = e3 % 190.59/30.62 (18) ~ (all_40_2 = e3) % 190.59/30.62 (19) ~ (all_80_2 = e3) | (op(e3, e4) = all_80_1 & $i(all_80_1) & ( ~ % 190.59/30.62 (all_80_1 = e0) | ( ~ (all_80_0 = e1) & op(e4, e0) = all_80_0 & % 190.59/30.62 $i(all_80_0)))) % 190.59/30.62 (20) ~ (all_22_2 = e2) % 190.59/30.62 (21) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, e3) = e2) % 190.59/30.62 | (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, e3) = % 190.59/30.62 e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.59/30.62 (22) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | % 190.59/30.62 all_250_11 = e0 % 190.59/30.62 (23) op(e2, all_10_2) = e3 % 190.59/30.62 (24) op(e4, all_6_2) = e2 % 190.59/30.62 (25) op(e2, e0) = all_40_2 % 190.59/30.62 (26) ~ (all_84_2 = all_10_2) % 190.59/30.62 (27) ~ (all_62_2 = e2) % 190.59/30.62 (28) all_102_2 = all_10_2 % 190.59/30.62 (29) all_80_2 = all_6_2 % 190.59/30.62 (30) op(e3, all_8_2) = e2 % 190.59/30.62 (31) op(e4, e2) = all_6_2 % 190.59/30.62 (32) op(e2, e1) = all_38_2 % 190.59/30.62 (33) all_250_11 = all_10_2 % 190.59/30.62 (34) ~ (all_244_8 = all_38_2) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | BETA: splitting (19) gives: % 190.59/30.62 | % 190.59/30.62 | Case 1: % 190.59/30.62 | | % 190.59/30.62 | | (35) ~ (all_80_2 = e3) % 190.59/30.62 | | % 190.59/30.62 | | REDUCE: (29), (35) imply: % 190.59/30.62 | | (36) ~ (all_6_2 = e3) % 190.59/30.62 | | % 190.59/30.62 | | BETA: splitting (5) gives: % 190.59/30.62 | | % 190.59/30.62 | | Case 1: % 190.59/30.62 | | | % 190.59/30.62 | | | (37) ~ (all_84_2 = e2) % 190.59/30.62 | | | % 190.59/30.62 | | | BETA: splitting (21) gives: % 190.59/30.62 | | | % 190.59/30.62 | | | Case 1: % 190.59/30.62 | | | | % 190.59/30.62 | | | | (38) (all_252_1 = e2 & op(e4, e3) = e2) | (all_252_3 = e2 & op(e3, % 190.59/30.62 | | | | e3) = e2) % 190.59/30.62 | | | | % 190.59/30.62 | | | | BETA: splitting (38) gives: % 190.59/30.62 | | | | % 190.59/30.62 | | | | Case 1: % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | (39) all_252_1 = e2 & op(e4, e3) = e2 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REF_CLOSE: (2), (9), (37), (39) are inconsistent by sub-proof #523. % 190.59/30.62 | | | | | % 190.59/30.62 | | | | Case 2: % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | (40) all_252_3 = e2 & op(e3, e3) = e2 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REF_CLOSE: (2), (4), (7), (40) are inconsistent by sub-proof #496. % 190.59/30.62 | | | | | % 190.59/30.62 | | | | End of split % 190.59/30.62 | | | | % 190.59/30.62 | | | Case 2: % 190.59/30.62 | | | | % 190.59/30.62 | | | | (41) (all_252_7 = e2 & op(e2, e3) = e2) | (all_252_13 = e2 & op(e1, % 190.59/30.62 | | | | e3) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.59/30.62 | | | | % 190.59/30.62 | | | | BETA: splitting (41) gives: % 190.59/30.62 | | | | % 190.59/30.62 | | | | Case 1: % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | (42) all_252_7 = e2 & op(e2, e3) = e2 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | ALPHA: (42) implies: % 190.59/30.62 | | | | | (43) op(e2, e3) = e2 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | GROUND_INST: instantiating (2) with all_10_2, e2, e3, e2, simplifying % 190.59/30.62 | | | | | with (8), (43) gives: % 190.59/30.62 | | | | | (44) all_10_2 = e2 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REDUCE: (16), (44) imply: % 190.59/30.62 | | | | | (45) op(e2, e1) = e3 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REDUCE: (23), (44) imply: % 190.59/30.62 | | | | | (46) op(e2, e2) = e3 % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | REF_CLOSE: (1), (2), (32), (34), (45), (46) are inconsistent by % 190.59/30.62 | | | | | sub-proof #495. % 190.59/30.62 | | | | | % 190.59/30.62 | | | | Case 2: % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | (47) (all_252_13 = e2 & op(e1, e3) = e2) | (all_252_21 = e2 & % 190.59/30.62 | | | | | op(e0, e3) = e2) % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | BETA: splitting (47) gives: % 190.59/30.62 | | | | | % 190.59/30.62 | | | | | Case 1: % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | | (48) all_252_13 = e2 & op(e1, e3) = e2 % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | | ALPHA: (48) implies: % 190.59/30.62 | | | | | | (49) op(e1, e3) = e2 % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | | REF_CLOSE: (2), (6), (27), (49) are inconsistent by sub-proof #572. % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | Case 2: % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | | (50) all_252_21 = e2 & op(e0, e3) = e2 % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | | ALPHA: (50) implies: % 190.59/30.62 | | | | | | (51) op(e0, e3) = e2 % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | | REF_CLOSE: (2), (13), (20), (51) are inconsistent by sub-proof #543. % 190.59/30.62 | | | | | | % 190.59/30.62 | | | | | End of split % 190.59/30.62 | | | | | % 190.59/30.62 | | | | End of split % 190.59/30.62 | | | | % 190.59/30.62 | | | End of split % 190.59/30.62 | | | % 190.59/30.62 | | Case 2: % 190.59/30.62 | | | % 190.59/30.62 | | | (52) all_84_2 = e2 % 190.59/30.62 | | | % 190.59/30.62 | | | REDUCE: (12), (52) imply: % 190.59/30.62 | | | (53) op(e4, e2) = e3 % 190.59/30.62 | | | % 190.59/30.62 | | | REF_CLOSE: (2), (31), (36), (53) are inconsistent by sub-proof #494. % 190.59/30.62 | | | % 190.59/30.62 | | End of split % 190.59/30.62 | | % 190.59/30.62 | Case 2: % 190.59/30.62 | | % 190.59/30.62 | | (54) all_80_2 = e3 % 190.59/30.62 | | % 190.59/30.62 | | COMBINE_EQS: (29), (54) imply: % 190.59/30.62 | | (55) all_6_2 = e3 % 190.59/30.62 | | % 190.59/30.62 | | SIMP: (55) implies: % 190.59/30.62 | | (56) all_6_2 = e3 % 190.59/30.62 | | % 190.59/30.62 | | REF_CLOSE: (2), (3), (9), (10), (11), (14), (15), (17), (18), (22), (23), % 190.59/30.62 | | (24), (25), (26), (28), (30), (33), (56) are inconsistent by % 190.59/30.62 | | sub-proof #493. % 190.59/30.62 | | % 190.59/30.62 | End of split % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #493 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.62 (2) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 190.59/30.62 (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 190.59/30.62 $i(all_102_0)))) % 190.59/30.62 (3) op(e4, e3) = all_84_2 % 190.59/30.62 (4) ~ (all_214_2 = e3) | (op(e3, e4) = all_214_1 & $i(all_214_1) & ( ~ % 190.59/30.62 (all_214_1 = e1) | ( ~ (all_214_0 = e0) & op(e4, e1) = all_214_0 & % 190.59/30.62 $i(all_214_0)))) % 190.59/30.62 (5) ~ (all_10_2 = e1) % 190.59/30.62 (6) all_214_2 = all_6_2 % 190.59/30.62 (7) ~ (all_10_2 = e4) % 190.59/30.62 (8) op(all_10_2, all_8_2) = e3 % 190.59/30.62 (9) ~ (all_40_2 = e3) % 190.59/30.62 (10) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | % 190.59/30.62 all_250_11 = e0 % 190.59/30.62 (11) op(e2, all_10_2) = e3 % 190.59/30.62 (12) op(e4, all_6_2) = e2 % 190.59/30.62 (13) op(e2, e0) = all_40_2 % 190.59/30.62 (14) ~ (all_84_2 = all_10_2) % 190.59/30.62 (15) all_102_2 = all_10_2 % 190.59/30.62 (16) all_6_2 = e3 % 190.59/30.62 (17) op(e3, all_8_2) = e2 % 190.59/30.62 (18) all_250_11 = all_10_2 % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | COMBINE_EQS: (6), (16) imply: % 190.59/30.62 | (19) all_214_2 = e3 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (12), (16) imply: % 190.59/30.62 | (20) op(e4, e3) = e2 % 190.59/30.62 | % 190.59/30.62 | BETA: splitting (4) gives: % 190.59/30.62 | % 190.59/30.62 | Case 1: % 190.59/30.62 | | % 190.59/30.62 | | (21) ~ (all_214_2 = e3) % 190.59/30.62 | | % 190.59/30.62 | | REDUCE: (19), (21) imply: % 190.59/30.62 | | (22) $false % 190.59/30.62 | | % 190.59/30.62 | | CLOSE: (22) is inconsistent. % 190.59/30.62 | | % 190.59/30.62 | Case 2: % 190.59/30.62 | | % 190.59/30.62 | | % 190.59/30.62 | | GROUND_INST: instantiating (1) with all_84_2, e2, e3, e4, simplifying with % 190.59/30.62 | | (3), (20) gives: % 190.59/30.62 | | (23) all_84_2 = e2 % 190.59/30.62 | | % 190.59/30.62 | | REDUCE: (14), (23) imply: % 190.59/30.62 | | (24) ~ (all_10_2 = e2) % 190.59/30.62 | | % 190.59/30.62 | | SIMP: (24) implies: % 190.59/30.62 | | (25) ~ (all_10_2 = e2) % 190.59/30.62 | | % 190.59/30.62 | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (11), (13), (15), (17), (18), % 190.59/30.62 | | (25) are inconsistent by sub-proof #565. % 190.59/30.62 | | % 190.59/30.62 | End of split % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #494 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.62 (2) op(e4, e2) = all_6_2 % 190.59/30.62 (3) op(e4, e2) = e3 % 190.59/30.62 (4) ~ (all_6_2 = e3) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | GROUND_INST: instantiating (1) with all_6_2, e3, e2, e4, simplifying with (2), % 190.59/30.62 | (3) gives: % 190.59/30.62 | (5) all_6_2 = e3 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (4), (5) imply: % 190.59/30.62 | (6) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (6) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #495 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) op(e2, e2) = all_244_8 % 190.59/30.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.62 (3) op(e2, e1) = e3 % 190.59/30.62 (4) op(e2, e2) = e3 % 190.59/30.62 (5) op(e2, e1) = all_38_2 % 190.59/30.62 (6) ~ (all_244_8 = all_38_2) % 190.59/30.62 % 190.59/30.62 Begin of proof % 190.59/30.62 | % 190.59/30.62 | GROUND_INST: instantiating (2) with all_38_2, e3, e1, e2, simplifying with % 190.59/30.62 | (3), (5) gives: % 190.59/30.62 | (7) all_38_2 = e3 % 190.59/30.62 | % 190.59/30.62 | GROUND_INST: instantiating (2) with all_244_8, e3, e2, e2, simplifying with % 190.59/30.62 | (1), (4) gives: % 190.59/30.62 | (8) all_244_8 = e3 % 190.59/30.62 | % 190.59/30.62 | REDUCE: (6), (7), (8) imply: % 190.59/30.62 | (9) $false % 190.59/30.62 | % 190.59/30.62 | CLOSE: (9) is inconsistent. % 190.59/30.62 | % 190.59/30.62 End of proof % 190.59/30.62 % 190.59/30.62 Sub-proof #496 shows that the following formulas are inconsistent: % 190.59/30.62 ---------------------------------------------------------------- % 190.59/30.62 (1) all_252_3 = e2 & op(e3, e3) = e2 % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) op(e3, e3) = all_244_3 % 190.59/30.63 (4) ~ (all_244_3 = e2) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | ALPHA: (1) implies: % 190.59/30.63 | (5) op(e3, e3) = e2 % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (2) with all_244_3, e2, e3, e3, simplifying with % 190.59/30.63 | (3), (5) gives: % 190.59/30.63 | (6) all_244_3 = e2 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (6) imply: % 190.59/30.63 | (7) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (7) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #497 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(all_48_2, all_22_2) = e0 % 190.59/30.63 (3) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 190.59/30.63 (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 190.59/30.63 $i(all_102_0)))) % 190.59/30.63 (4) ~ (all_36_2 = e0) % 190.59/30.63 (5) op(e3, e1) = all_36_2 % 190.59/30.63 (6) all_76_2 = all_40_2 % 190.59/30.63 (7) all_78_2 = all_10_2 % 190.59/30.63 (8) ~ (all_78_2 = e4) | (op(e4, e2) = all_78_1 & $i(all_78_1) & ( ~ % 190.59/30.63 (all_78_1 = e1) | ( ~ (all_78_0 = e0) & op(e2, e1) = all_78_0 & % 190.59/30.63 $i(all_78_0)))) % 190.59/30.63 (9) ~ (all_200_2 = e1) | (op(e1, e3) = all_200_1 & $i(all_200_1) & ( ~ % 190.59/30.63 (all_200_1 = e2) | ( ~ (all_200_0 = e4) & op(e3, e2) = all_200_0 & % 190.59/30.63 $i(all_200_0)))) % 190.59/30.63 (10) all_200_2 = all_48_2 % 190.59/30.63 (11) ~ (all_10_2 = e1) % 190.59/30.63 (12) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | % 190.59/30.63 all_250_9 = e0 % 190.59/30.63 (13) ~ (all_76_2 = e3) | (op(e3, e2) = all_76_1 & $i(all_76_1) & ( ~ % 190.59/30.63 (all_76_1 = e4) | ( ~ (all_76_0 = e1) & op(e2, e4) = all_76_0 & % 190.59/30.63 $i(all_76_0)))) % 190.59/30.63 (14) op(e0, all_22_2) = e3 % 190.59/30.63 (15) op(e4, e4) = all_244_0 % 190.59/30.63 (16) op(e4, all_10_2) = e2 % 190.59/30.63 (17) all_250_9 = all_48_2 % 190.59/30.63 (18) ~ (all_244_0 = e2) % 190.59/30.63 (19) op(e3, all_48_2) = e0 % 190.59/30.63 (20) op(all_10_2, all_8_2) = e3 % 190.59/30.63 (21) ~ (all_48_2 = e4) % 190.59/30.63 (22) ~ (all_48_2 = all_40_2) % 190.59/30.63 (23) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | % 190.59/30.63 all_250_11 = e0 % 190.59/30.63 (24) ~ (all_10_2 = e2) % 190.59/30.63 (25) op(e2, all_10_2) = e3 % 190.59/30.63 (26) op(e2, e0) = all_40_2 % 190.59/30.63 (27) all_102_2 = all_10_2 % 190.59/30.63 (28) op(e3, all_8_2) = e2 % 190.59/30.63 (29) ~ (all_48_2 = e2) % 190.59/30.63 (30) all_250_11 = all_10_2 % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (9) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (31) ~ (all_200_2 = e1) % 190.59/30.63 | | % 190.59/30.63 | | REDUCE: (10), (31) imply: % 190.59/30.63 | | (32) ~ (all_48_2 = e1) % 190.59/30.63 | | % 190.59/30.63 | | BETA: splitting (13) gives: % 190.59/30.63 | | % 190.59/30.63 | | Case 1: % 190.59/30.63 | | | % 190.59/30.63 | | | (33) ~ (all_76_2 = e3) % 190.59/30.63 | | | % 190.59/30.63 | | | REDUCE: (6), (33) imply: % 190.59/30.63 | | | (34) ~ (all_40_2 = e3) % 190.59/30.63 | | | % 190.59/30.63 | | | BETA: splitting (8) gives: % 190.59/30.63 | | | % 190.59/30.63 | | | Case 1: % 190.59/30.63 | | | | % 190.59/30.63 | | | | (35) ~ (all_78_2 = e4) % 190.59/30.63 | | | | % 190.59/30.63 | | | | REDUCE: (7), (35) imply: % 190.59/30.63 | | | | (36) ~ (all_10_2 = e4) % 190.59/30.63 | | | | % 190.59/30.63 | | | | REF_CLOSE: (1), (3), (11), (20), (23), (24), (25), (26), (27), (28), % 190.59/30.63 | | | | (30), (34), (36) are inconsistent by sub-proof #565. % 190.59/30.63 | | | | % 190.59/30.63 | | | Case 2: % 190.59/30.63 | | | | % 190.59/30.63 | | | | (37) all_78_2 = e4 % 190.59/30.63 | | | | % 190.59/30.63 | | | | COMBINE_EQS: (7), (37) imply: % 190.59/30.63 | | | | (38) all_10_2 = e4 % 190.59/30.63 | | | | % 190.59/30.63 | | | | SIMP: (38) implies: % 190.59/30.63 | | | | (39) all_10_2 = e4 % 190.59/30.63 | | | | % 190.59/30.63 | | | | REDUCE: (16), (39) imply: % 190.59/30.63 | | | | (40) op(e4, e4) = e2 % 190.59/30.63 | | | | % 190.59/30.63 | | | | REF_CLOSE: (1), (15), (18), (40) are inconsistent by sub-proof #500. % 190.59/30.63 | | | | % 190.59/30.63 | | | End of split % 190.59/30.63 | | | % 190.59/30.63 | | Case 2: % 190.59/30.63 | | | % 190.59/30.63 | | | (41) all_76_2 = e3 % 190.59/30.63 | | | % 190.59/30.63 | | | COMBINE_EQS: (6), (41) imply: % 190.59/30.63 | | | (42) all_40_2 = e3 % 190.59/30.63 | | | % 190.59/30.63 | | | SIMP: (42) implies: % 190.59/30.63 | | | (43) all_40_2 = e3 % 190.59/30.63 | | | % 190.59/30.63 | | | REDUCE: (22), (43) imply: % 190.59/30.63 | | | (44) ~ (all_48_2 = e3) % 190.59/30.63 | | | % 190.59/30.63 | | | REF_CLOSE: (1), (2), (12), (14), (17), (21), (29), (32), (44) are % 190.59/30.63 | | | inconsistent by sub-proof #499. % 190.59/30.63 | | | % 190.59/30.63 | | End of split % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (45) all_200_2 = e1 % 190.59/30.63 | | % 190.59/30.63 | | COMBINE_EQS: (10), (45) imply: % 190.59/30.63 | | (46) all_48_2 = e1 % 190.59/30.63 | | % 190.59/30.63 | | REDUCE: (19), (46) imply: % 190.59/30.63 | | (47) op(e3, e1) = e0 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (1), (4), (5), (47) are inconsistent by sub-proof #498. % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #498 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e3, e1) = all_36_2 % 190.59/30.63 (3) op(e3, e1) = e0 % 190.59/30.63 (4) ~ (all_36_2 = e0) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_36_2, e0, e1, e3, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_36_2 = e0 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #499 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(all_48_2, all_22_2) = e0 % 190.59/30.63 (3) all_250_9 = e4 | all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | % 190.59/30.63 all_250_9 = e0 % 190.59/30.63 (4) op(e0, all_22_2) = e3 % 190.59/30.63 (5) all_250_9 = all_48_2 % 190.59/30.63 (6) ~ (all_48_2 = e4) % 190.59/30.63 (7) ~ (all_48_2 = e1) % 190.59/30.63 (8) ~ (all_48_2 = e3) % 190.59/30.63 (9) ~ (all_48_2 = e2) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (3) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (10) all_250_9 = e4 % 190.59/30.63 | | % 190.59/30.63 | | COMBINE_EQS: (5), (10) imply: % 190.59/30.63 | | (11) all_48_2 = e4 % 190.59/30.63 | | % 190.59/30.63 | | SIMP: (11) implies: % 190.59/30.63 | | (12) all_48_2 = e4 % 190.59/30.63 | | % 190.59/30.63 | | REDUCE: (6), (12) imply: % 190.59/30.63 | | (13) $false % 190.59/30.63 | | % 190.59/30.63 | | CLOSE: (13) is inconsistent. % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (14) all_250_9 = e3 | all_250_9 = e2 | all_250_9 = e1 | all_250_9 = e0 % 190.59/30.63 | | % 190.59/30.63 | | BETA: splitting (14) gives: % 190.59/30.63 | | % 190.59/30.63 | | Case 1: % 190.59/30.63 | | | % 190.59/30.63 | | | (15) all_250_9 = e3 % 190.59/30.63 | | | % 190.59/30.63 | | | COMBINE_EQS: (5), (15) imply: % 190.59/30.63 | | | (16) all_48_2 = e3 % 190.59/30.63 | | | % 190.59/30.63 | | | SIMP: (16) implies: % 190.59/30.63 | | | (17) all_48_2 = e3 % 190.59/30.63 | | | % 190.59/30.63 | | | REDUCE: (8), (17) imply: % 190.59/30.63 | | | (18) $false % 190.59/30.63 | | | % 190.59/30.63 | | | CLOSE: (18) is inconsistent. % 190.59/30.63 | | | % 190.59/30.63 | | Case 2: % 190.59/30.63 | | | % 190.59/30.63 | | | (19) ~ (all_250_9 = e3) % 190.59/30.63 | | | (20) all_250_9 = e2 | all_250_9 = e1 | all_250_9 = e0 % 190.59/30.63 | | | % 190.59/30.63 | | | BETA: splitting (20) gives: % 190.59/30.63 | | | % 190.59/30.63 | | | Case 1: % 190.59/30.63 | | | | % 190.59/30.63 | | | | (21) all_250_9 = e2 % 190.59/30.63 | | | | % 190.59/30.63 | | | | COMBINE_EQS: (5), (21) imply: % 190.59/30.63 | | | | (22) all_48_2 = e2 % 190.59/30.63 | | | | % 190.59/30.63 | | | | SIMP: (22) implies: % 190.59/30.63 | | | | (23) all_48_2 = e2 % 190.59/30.63 | | | | % 190.59/30.63 | | | | REDUCE: (9), (23) imply: % 190.59/30.63 | | | | (24) $false % 190.59/30.63 | | | | % 190.59/30.63 | | | | CLOSE: (24) is inconsistent. % 190.59/30.63 | | | | % 190.59/30.63 | | | Case 2: % 190.59/30.63 | | | | % 190.59/30.63 | | | | (25) all_250_9 = e1 | all_250_9 = e0 % 190.59/30.63 | | | | % 190.59/30.63 | | | | BETA: splitting (25) gives: % 190.59/30.63 | | | | % 190.59/30.63 | | | | Case 1: % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | (26) all_250_9 = e1 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | COMBINE_EQS: (5), (26) imply: % 190.59/30.63 | | | | | (27) all_48_2 = e1 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | SIMP: (27) implies: % 190.59/30.63 | | | | | (28) all_48_2 = e1 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | REDUCE: (7), (28) imply: % 190.59/30.63 | | | | | (29) $false % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | CLOSE: (29) is inconsistent. % 190.59/30.63 | | | | | % 190.59/30.63 | | | | Case 2: % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | (30) all_250_9 = e0 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | COMBINE_EQS: (5), (30) imply: % 190.59/30.63 | | | | | (31) all_48_2 = e0 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | SIMP: (31) implies: % 190.59/30.63 | | | | | (32) all_48_2 = e0 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | REDUCE: (8), (32) imply: % 190.59/30.63 | | | | | (33) ~ (e3 = e0) % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | SIMP: (33) implies: % 190.59/30.63 | | | | | (34) ~ (e3 = e0) % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | REDUCE: (2), (32) imply: % 190.59/30.63 | | | | | (35) op(e0, all_22_2) = e0 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | GROUND_INST: instantiating (1) with e3, e0, all_22_2, e0, simplifying % 190.59/30.63 | | | | | with (4), (35) gives: % 190.59/30.63 | | | | | (36) e3 = e0 % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | REDUCE: (34), (36) imply: % 190.59/30.63 | | | | | (37) $false % 190.59/30.63 | | | | | % 190.59/30.63 | | | | | CLOSE: (37) is inconsistent. % 190.59/30.63 | | | | | % 190.59/30.63 | | | | End of split % 190.59/30.63 | | | | % 190.59/30.63 | | | End of split % 190.59/30.63 | | | % 190.59/30.63 | | End of split % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #500 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e4, e4) = all_244_0 % 190.59/30.63 (3) op(e4, e4) = e2 % 190.59/30.63 (4) ~ (all_244_0 = e2) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_244_0, e2, e4, e4, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_244_0 = e2 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #501 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ~ (all_28_2 = e1) % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) op(e0, e2) = all_28_2 % 190.59/30.63 (4) all_58_2 = e2 % 190.59/30.63 (5) all_58_2 = all_20_2 % 190.59/30.63 (6) op(e0, all_20_2) = e1 % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | COMBINE_EQS: (4), (5) imply: % 190.59/30.63 | (7) all_20_2 = e2 % 190.59/30.63 | % 190.59/30.63 | SIMP: (7) implies: % 190.59/30.63 | (8) all_20_2 = e2 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (6), (8) imply: % 190.59/30.63 | (9) op(e0, e2) = e1 % 190.59/30.63 | % 190.59/30.63 | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #502. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #502 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e0, e2) = all_28_2 % 190.59/30.63 (3) op(e0, e2) = e1 % 190.59/30.63 (4) ~ (all_28_2 = e1) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_28_2, e1, e2, e0, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_28_2 = e1 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #503 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) all_250_20 = e4 | all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | % 190.59/30.63 all_250_20 = e0 % 190.59/30.63 (3) ~ (all_12_2 = e0) % 190.59/30.63 (4) all_250_20 = all_12_2 % 190.59/30.63 (5) ~ (all_12_2 = e2) % 190.59/30.63 (6) op(all_12_2, all_30_2) = e4 % 190.59/30.63 (7) op(e4, all_30_2) = e0 % 190.59/30.63 (8) ~ (all_12_2 = e1) % 190.59/30.63 (9) ~ (all_12_2 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | SIMP: (3) implies: % 190.59/30.63 | (10) ~ (all_12_2 = e0) % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (2) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (11) all_250_20 = e4 % 190.59/30.63 | | % 190.59/30.63 | | COMBINE_EQS: (4), (11) imply: % 190.59/30.63 | | (12) all_12_2 = e4 % 190.59/30.63 | | % 190.59/30.63 | | SIMP: (12) implies: % 190.59/30.63 | | (13) all_12_2 = e4 % 190.59/30.63 | | % 190.59/30.63 | | REDUCE: (10), (13) imply: % 190.59/30.63 | | (14) ~ (e4 = e0) % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (1), (6), (7), (13), (14) are inconsistent by sub-proof #505. % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (15) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 = % 190.59/30.63 | | e0 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (4), (5), (8), (9), (10), (15) are inconsistent by sub-proof % 190.59/30.63 | | #504. % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #504 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) all_250_20 = all_12_2 % 190.59/30.63 (2) ~ (all_12_2 = e2) % 190.59/30.63 (3) ~ (all_12_2 = e1) % 190.59/30.63 (4) all_250_20 = e3 | all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0 % 190.59/30.63 (5) ~ (all_12_2 = e3) % 190.59/30.63 (6) ~ (all_12_2 = e0) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (4) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (7) all_250_20 = e3 % 190.59/30.63 | | % 190.59/30.63 | | COMBINE_EQS: (1), (7) imply: % 190.59/30.63 | | (8) all_12_2 = e3 % 190.59/30.63 | | % 190.59/30.63 | | REDUCE: (5), (8) imply: % 190.59/30.63 | | (9) $false % 190.59/30.63 | | % 190.59/30.63 | | CLOSE: (9) is inconsistent. % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (10) all_250_20 = e2 | all_250_20 = e1 | all_250_20 = e0 % 190.59/30.63 | | % 190.59/30.63 | | BETA: splitting (10) gives: % 190.59/30.63 | | % 190.59/30.63 | | Case 1: % 190.59/30.63 | | | % 190.59/30.63 | | | (11) all_250_20 = e2 % 190.59/30.63 | | | % 190.59/30.63 | | | COMBINE_EQS: (1), (11) imply: % 190.59/30.63 | | | (12) all_12_2 = e2 % 190.59/30.63 | | | % 190.59/30.63 | | | REDUCE: (2), (12) imply: % 190.59/30.63 | | | (13) $false % 190.59/30.63 | | | % 190.59/30.63 | | | CLOSE: (13) is inconsistent. % 190.59/30.63 | | | % 190.59/30.63 | | Case 2: % 190.59/30.63 | | | % 190.59/30.63 | | | (14) all_250_20 = e1 | all_250_20 = e0 % 190.59/30.63 | | | % 190.59/30.63 | | | BETA: splitting (14) gives: % 190.59/30.63 | | | % 190.59/30.63 | | | Case 1: % 190.59/30.63 | | | | % 190.59/30.63 | | | | (15) all_250_20 = e1 % 190.59/30.63 | | | | % 190.59/30.63 | | | | COMBINE_EQS: (1), (15) imply: % 190.59/30.63 | | | | (16) all_12_2 = e1 % 190.59/30.63 | | | | % 190.59/30.63 | | | | REDUCE: (3), (16) imply: % 190.59/30.63 | | | | (17) $false % 190.59/30.63 | | | | % 190.59/30.63 | | | | CLOSE: (17) is inconsistent. % 190.59/30.63 | | | | % 190.59/30.63 | | | Case 2: % 190.59/30.63 | | | | % 190.59/30.63 | | | | (18) all_250_20 = e0 % 190.59/30.63 | | | | % 190.59/30.63 | | | | COMBINE_EQS: (1), (18) imply: % 190.59/30.63 | | | | (19) all_12_2 = e0 % 190.59/30.63 | | | | % 190.59/30.63 | | | | REDUCE: (6), (19) imply: % 190.59/30.63 | | | | (20) $false % 190.59/30.63 | | | | % 190.59/30.63 | | | | CLOSE: (20) is inconsistent. % 190.59/30.63 | | | | % 190.59/30.63 | | | End of split % 190.59/30.63 | | | % 190.59/30.63 | | End of split % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #505 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) ~ (e4 = e0) % 190.59/30.63 (3) all_12_2 = e4 % 190.59/30.63 (4) op(all_12_2, all_30_2) = e4 % 190.59/30.63 (5) op(e4, all_30_2) = e0 % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | REDUCE: (3), (4) imply: % 190.59/30.63 | (6) op(e4, all_30_2) = e4 % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with e0, e4, all_30_2, e4, simplifying with % 190.59/30.63 | (5), (6) gives: % 190.59/30.63 | (7) e4 = e0 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (2), (7) imply: % 190.59/30.63 | (8) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (8) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #506 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ~ (all_244_24 = e3) % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) ~ (all_20_2 = e3) % 190.59/30.63 (4) (all_252_23 = e3 & op(e0, e1) = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.59/30.63 (5) op(e0, e0) = all_244_24 % 190.59/30.63 (6) op(e0, e1) = all_20_2 % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (4) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (7) all_252_23 = e3 & op(e0, e1) = e3 % 190.59/30.63 | | % 190.59/30.63 | | ALPHA: (7) implies: % 190.59/30.63 | | (8) op(e0, e1) = e3 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #508. % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (9) all_252_24 = e3 & op(e0, e0) = e3 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #507. % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #507 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) all_252_24 = e3 & op(e0, e0) = e3 % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) op(e0, e0) = all_244_24 % 190.59/30.63 (4) ~ (all_244_24 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | ALPHA: (1) implies: % 190.59/30.63 | (5) op(e0, e0) = e3 % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (2) with all_244_24, e3, e0, e0, simplifying with % 190.59/30.63 | (3), (5) gives: % 190.59/30.63 | (6) all_244_24 = e3 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (6) imply: % 190.59/30.63 | (7) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (7) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #508 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e0, e1) = all_20_2 % 190.59/30.63 (3) op(e0, e1) = e3 % 190.59/30.63 (4) ~ (all_20_2 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_20_2, e3, e1, e0, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_20_2 = e3 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #509 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) all_252_22 = e3 & op(e0, e2) = e3 % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) op(e0, e2) = all_28_2 % 190.59/30.63 (4) ~ (all_28_2 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | ALPHA: (1) implies: % 190.59/30.63 | (5) op(e0, e2) = e3 % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (2) with all_28_2, e3, e2, e0, simplifying with % 190.59/30.63 | (3), (5) gives: % 190.59/30.63 | (6) all_28_2 = e3 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (6) imply: % 190.59/30.63 | (7) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (7) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #510 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) all_22_2 = e3 % 190.59/30.63 (3) ~ (e3 = e0) % 190.59/30.63 (4) op(e3, all_48_2) = e0 % 190.59/30.63 (5) op(all_22_2, all_48_2) = e3 % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | REDUCE: (2), (5) imply: % 190.59/30.63 | (6) op(e3, all_48_2) = e3 % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with e0, e3, all_48_2, e3, simplifying with % 190.59/30.63 | (4), (6) gives: % 190.59/30.63 | (7) e3 = e0 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (3), (7) imply: % 190.59/30.63 | (8) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (8) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #511 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) (all_252_12 = e3 & op(e1, e4) = e3) | (all_252_20 = e3 & op(e0, e4) = e3) % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) ~ (all_16_2 = e3) % 190.59/30.63 (4) op(e1, e4) = all_16_2 % 190.59/30.63 (5) op(e0, e4) = all_12_2 % 190.59/30.63 (6) ~ (all_12_2 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (1) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (7) all_252_12 = e3 & op(e1, e4) = e3 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #513. % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (8) all_252_20 = e3 & op(e0, e4) = e3 % 190.59/30.63 | | % 190.59/30.63 | | ALPHA: (8) implies: % 190.59/30.63 | | (9) op(e0, e4) = e3 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #512. % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #512 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e0, e4) = all_12_2 % 190.59/30.63 (3) op(e0, e4) = e3 % 190.59/30.63 (4) ~ (all_12_2 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_12_2, e3, e4, e0, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_12_2 = e3 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #513 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) all_252_12 = e3 & op(e1, e4) = e3 % 190.59/30.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (3) op(e1, e4) = all_16_2 % 190.59/30.63 (4) ~ (all_16_2 = e3) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | ALPHA: (1) implies: % 190.59/30.63 | (5) op(e1, e4) = e3 % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (2) with all_16_2, e3, e4, e1, simplifying with % 190.59/30.63 | (3), (5) gives: % 190.59/30.63 | (6) all_16_2 = e3 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (6) imply: % 190.59/30.63 | (7) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (7) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #514 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e1, e1) = all_244_15 % 190.59/30.63 (3) op(e0, e1) = all_20_2 % 190.59/30.63 (4) ~ (all_20_2 = e2) % 190.59/30.63 (5) (all_252_15 = e2 & op(e1, e1) = e2) | (all_252_23 = e2 & op(e0, e1) = e2) % 190.59/30.63 (6) ~ (all_244_15 = e2) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | BETA: splitting (5) gives: % 190.59/30.63 | % 190.59/30.63 | Case 1: % 190.59/30.63 | | % 190.59/30.63 | | (7) all_252_15 = e2 & op(e1, e1) = e2 % 190.59/30.63 | | % 190.59/30.63 | | ALPHA: (7) implies: % 190.59/30.63 | | (8) op(e1, e1) = e2 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #515. % 190.59/30.63 | | % 190.59/30.63 | Case 2: % 190.59/30.63 | | % 190.59/30.63 | | (9) all_252_23 = e2 & op(e0, e1) = e2 % 190.59/30.63 | | % 190.59/30.63 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #540. % 190.59/30.63 | | % 190.59/30.63 | End of split % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #515 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e1, e1) = all_244_15 % 190.59/30.63 (3) op(e1, e1) = e2 % 190.59/30.63 (4) ~ (all_244_15 = e2) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_244_15, e2, e1, e1, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_244_15 = e2 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #516 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.63 (2) op(e2, e0) = all_40_2 % 190.59/30.63 (3) op(e2, e0) = e1 % 190.59/30.63 (4) ~ (all_40_2 = e1) % 190.59/30.63 % 190.59/30.63 Begin of proof % 190.59/30.63 | % 190.59/30.63 | GROUND_INST: instantiating (1) with all_40_2, e1, e0, e2, simplifying with % 190.59/30.63 | (2), (3) gives: % 190.59/30.63 | (5) all_40_2 = e1 % 190.59/30.63 | % 190.59/30.63 | REDUCE: (4), (5) imply: % 190.59/30.63 | (6) $false % 190.59/30.63 | % 190.59/30.63 | CLOSE: (6) is inconsistent. % 190.59/30.63 | % 190.59/30.63 End of proof % 190.59/30.63 % 190.59/30.63 Sub-proof #517 shows that the following formulas are inconsistent: % 190.59/30.63 ---------------------------------------------------------------- % 190.59/30.63 (1) all_252_11 = e1 & op(e2, e1) = e1 % 190.59/30.63 (2) all_252_11 = e2 % 190.59/30.64 (3) ~ (e2 = e1) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (4) all_252_11 = e1 % 190.59/30.64 | % 190.59/30.64 | COMBINE_EQS: (2), (4) imply: % 190.59/30.64 | (5) e2 = e1 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (3), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #518 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_23 = e4 & op(e0, e1) = e4 % 190.59/30.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (3) op(e0, e1) = all_20_2 % 190.59/30.64 (4) ~ (all_20_2 = e4) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (5) op(e0, e1) = e4 % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (2) with all_20_2, e4, e1, e0, simplifying with % 190.59/30.64 | (3), (5) gives: % 190.59/30.64 | (6) all_20_2 = e4 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (6) imply: % 190.59/30.64 | (7) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (7) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #519 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_21 = e4 & op(e0, e3) = e4 % 190.59/30.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (3) op(e0, e3) = all_22_2 % 190.59/30.64 (4) ~ (all_22_2 = e4) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (5) op(e0, e3) = e4 % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (2) with all_22_2, e4, e3, e0, simplifying with % 190.59/30.64 | (3), (5) gives: % 190.59/30.64 | (6) all_22_2 = e4 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (6) imply: % 190.59/30.64 | (7) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (7) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #520 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e0, e2) = e4 % 190.59/30.64 (3) op(e0, e2) = e0 % 190.59/30.64 (4) ~ (e4 = e0) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with e4, e0, e2, e0, simplifying with (2), (3) % 190.59/30.64 | gives: % 190.59/30.64 | (5) e4 = e0 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #521 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e3, e2) = all_8_2 % 190.59/30.64 (3) op(e3, e2) = e4 % 190.59/30.64 (4) ~ (all_8_2 = e4) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with all_8_2, e4, e2, e3, simplifying with (2), % 190.59/30.64 | (3) gives: % 190.59/30.64 | (5) all_8_2 = e4 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #522 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_24 = e4 & op(e0, e0) = e4 % 190.59/30.64 (2) all_252_24 = e2 % 190.59/30.64 (3) ~ (e4 = e2) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (4) all_252_24 = e4 % 190.59/30.64 | % 190.59/30.64 | COMBINE_EQS: (2), (4) imply: % 190.59/30.64 | (5) e4 = e2 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (3), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #523 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_1 = e2 & op(e4, e3) = e2 % 190.59/30.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (3) op(e4, e3) = all_84_2 % 190.59/30.64 (4) ~ (all_84_2 = e2) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (5) op(e4, e3) = e2 % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (2) with all_84_2, e2, e3, e4, simplifying with % 190.59/30.64 | (3), (5) gives: % 190.59/30.64 | (6) all_84_2 = e2 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (6) imply: % 190.59/30.64 | (7) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (7) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #524 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_24 = e1 & op(e0, e0) = e1 % 190.59/30.64 (2) all_252_24 = e2 % 190.59/30.64 (3) ~ (e2 = e1) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (4) all_252_24 = e1 % 190.59/30.64 | % 190.59/30.64 | COMBINE_EQS: (2), (4) imply: % 190.59/30.64 | (5) e2 = e1 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (3), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #525 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_20 = e4 % 190.59/30.64 (2) all_252_20 = e0 % 190.59/30.64 (3) ~ (e4 = e0) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | COMBINE_EQS: (1), (2) imply: % 190.59/30.64 | (4) e4 = e0 % 190.59/30.64 | % 190.59/30.64 | SIMP: (4) implies: % 190.59/30.64 | (5) e4 = e0 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (3), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #526 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_19 = e1 % 190.59/30.64 (2) all_252_19 = e0 % 190.59/30.64 (3) ~ (e1 = e0) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | COMBINE_EQS: (1), (2) imply: % 190.59/30.64 | (4) e1 = e0 % 190.59/30.64 | % 190.59/30.64 | SIMP: (4) implies: % 190.59/30.64 | (5) e1 = e0 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (3), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #527 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e1, e0) = e4 % 190.59/30.64 (3) op(e1, e0) = e1 % 190.59/30.64 (4) ~ (e4 = e1) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with e1, e4, e0, e1, simplifying with (2), (3) % 190.59/30.64 | gives: % 190.59/30.64 | (5) e4 = e1 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #528 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e1, e2) = e4 % 190.59/30.64 (3) op(e1, e2) = e3 % 190.59/30.64 (4) ~ (e4 = e3) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with e4, e3, e2, e1, simplifying with (2), (3) % 190.59/30.64 | gives: % 190.59/30.64 | (5) e4 = e3 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #529 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e1, e3) = e4 % 190.59/30.64 (3) op(e1, e3) = e2 % 190.59/30.64 (4) ~ (e4 = e2) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with e4, e2, e3, e1, simplifying with (2), (3) % 190.59/30.64 | gives: % 190.59/30.64 | (5) e4 = e2 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #530 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e0, e4) = all_12_2 % 190.59/30.64 (3) op(e0, e4) = e1 % 190.59/30.64 (4) ~ (all_12_2 = e1) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with all_12_2, e1, e4, e0, simplifying with % 190.59/30.64 | (2), (3) gives: % 190.59/30.64 | (5) all_12_2 = e1 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (5) imply: % 190.59/30.64 | (6) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (6) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #531 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) ~ (all_16_2 = e0) % 190.59/30.64 (3) op(e1, e3) = e2 % 190.59/30.64 (4) op(e1, e4) = all_16_2 % 190.59/30.64 (5) (all_252_12 = e0 & op(e1, e4) = e0) | (all_252_13 = e0 & op(e1, e3) = e0) % 190.59/30.64 (6) ~ (e2 = e0) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | BETA: splitting (5) gives: % 190.59/30.64 | % 190.59/30.64 | Case 1: % 190.59/30.64 | | % 190.59/30.64 | | (7) all_252_12 = e0 & op(e1, e4) = e0 % 190.59/30.64 | | % 190.59/30.64 | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #532. % 190.59/30.64 | | % 190.59/30.64 | Case 2: % 190.59/30.64 | | % 190.59/30.64 | | (8) all_252_13 = e0 & op(e1, e3) = e0 % 190.59/30.64 | | % 190.59/30.64 | | ALPHA: (8) implies: % 190.59/30.64 | | (9) op(e1, e3) = e0 % 190.59/30.64 | | % 190.59/30.64 | | GROUND_INST: instantiating (1) with e0, e2, e3, e1, simplifying with (3), % 190.59/30.64 | | (9) gives: % 190.59/30.64 | | (10) e2 = e0 % 190.59/30.64 | | % 190.59/30.64 | | REDUCE: (6), (10) imply: % 190.59/30.64 | | (11) $false % 190.59/30.64 | | % 190.59/30.64 | | CLOSE: (11) is inconsistent. % 190.59/30.64 | | % 190.59/30.64 | End of split % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #532 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_12 = e0 & op(e1, e4) = e0 % 190.59/30.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (3) op(e1, e4) = all_16_2 % 190.59/30.64 (4) ~ (all_16_2 = e0) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (5) op(e1, e4) = e0 % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (2) with all_16_2, e0, e4, e1, simplifying with % 190.59/30.64 | (3), (5) gives: % 190.59/30.64 | (6) all_16_2 = e0 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (4), (6) imply: % 190.59/30.64 | (7) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (7) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #533 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) op(e2, e0) = all_40_2 % 190.59/30.64 (3) ~ (e1 = e0) % 190.59/30.64 (4) op(e2, e0) = e0 % 190.59/30.64 (5) op(e2, e0) = e1 % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with all_40_2, e0, e0, e2, simplifying with % 190.59/30.64 | (2), (4) gives: % 190.59/30.64 | (6) all_40_2 = e0 % 190.59/30.64 | % 190.59/30.64 | GROUND_INST: instantiating (1) with all_40_2, e1, e0, e2, simplifying with % 190.59/30.64 | (2), (5) gives: % 190.59/30.64 | (7) all_40_2 = e1 % 190.59/30.64 | % 190.59/30.64 | COMBINE_EQS: (6), (7) imply: % 190.59/30.64 | (8) e1 = e0 % 190.59/30.64 | % 190.59/30.64 | REDUCE: (3), (8) imply: % 190.59/30.64 | (9) $false % 190.59/30.64 | % 190.59/30.64 | CLOSE: (9) is inconsistent. % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #534 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) ~ (all_30_2 = e3) % 190.59/30.64 (3) op(e4, e0) = all_30_2 % 190.59/30.64 (4) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) = e3) % 190.59/30.64 | (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) = % 190.59/30.64 e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.59/30.64 (5) all_252_24 = e2 % 190.59/30.64 (6) ~ (all_40_2 = e3) % 190.59/30.64 (7) ~ (e3 = e2) % 190.59/30.64 (8) op(e2, e0) = all_40_2 % 190.59/30.64 (9) ~ (e3 = e1) % 190.59/30.64 (10) op(e1, e0) = all_34_2 % 190.59/30.64 (11) ~ (all_34_2 = e3) % 190.59/30.64 (12) all_252_17 = e1 % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | BETA: splitting (4) gives: % 190.59/30.64 | % 190.59/30.64 | Case 1: % 190.59/30.64 | | % 190.59/30.64 | | (13) (all_252_16 = e3 & op(e4, e0) = e3) | (all_252_17 = e3 & op(e3, e0) % 190.59/30.64 | | = e3) % 190.59/30.64 | | % 190.59/30.64 | | BETA: splitting (13) gives: % 190.59/30.64 | | % 190.59/30.64 | | Case 1: % 190.59/30.64 | | | % 190.59/30.64 | | | (14) all_252_16 = e3 & op(e4, e0) = e3 % 190.59/30.64 | | | % 190.59/30.64 | | | ALPHA: (14) implies: % 190.59/30.64 | | | (15) op(e4, e0) = e3 % 190.59/30.64 | | | % 190.59/30.64 | | | REF_CLOSE: (1), (2), (3), (15) are inconsistent by sub-proof #539. % 190.59/30.64 | | | % 190.59/30.64 | | Case 2: % 190.59/30.64 | | | % 190.59/30.64 | | | (16) all_252_17 = e3 & op(e3, e0) = e3 % 190.59/30.64 | | | % 190.59/30.64 | | | REF_CLOSE: (9), (12), (16) are inconsistent by sub-proof #537. % 190.59/30.64 | | | % 190.59/30.64 | | End of split % 190.59/30.64 | | % 190.59/30.64 | Case 2: % 190.59/30.64 | | % 190.59/30.64 | | (17) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) % 190.59/30.64 | | = e3) | (all_252_24 = e3 & op(e0, e0) = e3) % 190.59/30.64 | | % 190.59/30.64 | | REF_CLOSE: (1), (5), (6), (7), (8), (10), (11), (17) are inconsistent by % 190.59/30.64 | | sub-proof #535. % 190.59/30.64 | | % 190.59/30.64 | End of split % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #535 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (2) (all_252_18 = e3 & op(e2, e0) = e3) | (all_252_19 = e3 & op(e1, e0) = e3) % 190.59/30.64 | (all_252_24 = e3 & op(e0, e0) = e3) % 190.59/30.64 (3) all_252_24 = e2 % 190.59/30.64 (4) ~ (all_40_2 = e3) % 190.59/30.64 (5) ~ (e3 = e2) % 190.59/30.64 (6) op(e2, e0) = all_40_2 % 190.59/30.64 (7) op(e1, e0) = all_34_2 % 190.59/30.64 (8) ~ (all_34_2 = e3) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | BETA: splitting (2) gives: % 190.59/30.64 | % 190.59/30.64 | Case 1: % 190.59/30.64 | | % 190.59/30.64 | | (9) all_252_18 = e3 & op(e2, e0) = e3 % 190.59/30.64 | | % 190.59/30.64 | | ALPHA: (9) implies: % 190.59/30.64 | | (10) op(e2, e0) = e3 % 190.59/30.64 | | % 190.59/30.64 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #566. % 190.59/30.64 | | % 190.59/30.64 | Case 2: % 190.59/30.64 | | % 190.59/30.64 | | (11) (all_252_19 = e3 & op(e1, e0) = e3) | (all_252_24 = e3 & op(e0, e0) % 190.59/30.64 | | = e3) % 190.59/30.64 | | % 190.59/30.64 | | BETA: splitting (11) gives: % 190.59/30.64 | | % 190.59/30.64 | | Case 1: % 190.59/30.64 | | | % 190.59/30.64 | | | (12) all_252_19 = e3 & op(e1, e0) = e3 % 190.59/30.64 | | | % 190.59/30.64 | | | REF_CLOSE: (1), (7), (8), (12) are inconsistent by sub-proof #536. % 190.59/30.64 | | | % 190.59/30.64 | | Case 2: % 190.59/30.64 | | | % 190.59/30.64 | | | (13) all_252_24 = e3 & op(e0, e0) = e3 % 190.59/30.64 | | | % 190.59/30.64 | | | ALPHA: (13) implies: % 190.59/30.64 | | | (14) all_252_24 = e3 % 190.59/30.64 | | | % 190.59/30.64 | | | COMBINE_EQS: (3), (14) imply: % 190.59/30.64 | | | (15) e3 = e2 % 190.59/30.64 | | | % 190.59/30.64 | | | REDUCE: (5), (15) imply: % 190.59/30.64 | | | (16) $false % 190.59/30.64 | | | % 190.59/30.64 | | | CLOSE: (16) is inconsistent. % 190.59/30.64 | | | % 190.59/30.64 | | End of split % 190.59/30.64 | | % 190.59/30.64 | End of split % 190.59/30.64 | % 190.59/30.64 End of proof % 190.59/30.64 % 190.59/30.64 Sub-proof #536 shows that the following formulas are inconsistent: % 190.59/30.64 ---------------------------------------------------------------- % 190.59/30.64 (1) all_252_19 = e3 & op(e1, e0) = e3 % 190.59/30.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.59/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.59/30.64 (3) op(e1, e0) = all_34_2 % 190.59/30.64 (4) ~ (all_34_2 = e3) % 190.59/30.64 % 190.59/30.64 Begin of proof % 190.59/30.64 | % 190.59/30.64 | ALPHA: (1) implies: % 190.59/30.64 | (5) op(e1, e0) = e3 % 190.59/30.64 | % 190.62/30.64 | GROUND_INST: instantiating (2) with all_34_2, e3, e0, e1, simplifying with % 190.62/30.64 | (3), (5) gives: % 190.62/30.64 | (6) all_34_2 = e3 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (4), (6) imply: % 190.62/30.64 | (7) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (7) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #537 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) all_252_17 = e3 & op(e3, e0) = e3 % 190.62/30.64 (2) all_252_17 = e1 % 190.62/30.64 (3) ~ (e3 = e1) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | ALPHA: (1) implies: % 190.62/30.64 | (4) all_252_17 = e3 % 190.62/30.64 | % 190.62/30.64 | COMBINE_EQS: (2), (4) imply: % 190.62/30.64 | (5) e3 = e1 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (3), (5) imply: % 190.62/30.64 | (6) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (6) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #538 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) all_252_16 = e1 & op(e4, e0) = e1 % 190.62/30.64 (2) all_252_16 = e4 % 190.62/30.64 (3) ~ (e4 = e1) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | ALPHA: (1) implies: % 190.62/30.64 | (4) all_252_16 = e1 % 190.62/30.64 | % 190.62/30.64 | COMBINE_EQS: (2), (4) imply: % 190.62/30.64 | (5) e4 = e1 % 190.62/30.64 | % 190.62/30.64 | SIMP: (5) implies: % 190.62/30.64 | (6) e4 = e1 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (3), (6) imply: % 190.62/30.64 | (7) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (7) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #539 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (2) op(e4, e0) = all_30_2 % 190.62/30.64 (3) op(e4, e0) = e3 % 190.62/30.64 (4) ~ (all_30_2 = e3) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | GROUND_INST: instantiating (1) with all_30_2, e3, e0, e4, simplifying with % 190.62/30.64 | (2), (3) gives: % 190.62/30.64 | (5) all_30_2 = e3 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (4), (5) imply: % 190.62/30.64 | (6) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (6) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #540 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) all_252_23 = e2 & op(e0, e1) = e2 % 190.62/30.64 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (3) op(e0, e1) = all_20_2 % 190.62/30.64 (4) ~ (all_20_2 = e2) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | ALPHA: (1) implies: % 190.62/30.64 | (5) op(e0, e1) = e2 % 190.62/30.64 | % 190.62/30.64 | GROUND_INST: instantiating (2) with all_20_2, e2, e1, e0, simplifying with % 190.62/30.64 | (3), (5) gives: % 190.62/30.64 | (6) all_20_2 = e2 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (4), (6) imply: % 190.62/30.64 | (7) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (7) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #541 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) all_252_22 = e2 & op(e0, e2) = e2 % 190.62/30.64 (2) all_252_22 = e0 % 190.62/30.64 (3) ~ (e2 = e0) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | ALPHA: (1) implies: % 190.62/30.64 | (4) all_252_22 = e2 % 190.62/30.64 | % 190.62/30.64 | COMBINE_EQS: (2), (4) imply: % 190.62/30.64 | (5) e2 = e0 % 190.62/30.64 | % 190.62/30.64 | SIMP: (5) implies: % 190.62/30.64 | (6) e2 = e0 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (3), (6) imply: % 190.62/30.64 | (7) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (7) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #542 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (2) ~ (all_12_2 = e2) % 190.62/30.64 (3) op(e0, e3) = all_22_2 % 190.62/30.64 (4) ~ (all_22_2 = e2) % 190.62/30.64 (5) (all_252_20 = e2 & op(e0, e4) = e2) | (all_252_21 = e2 & op(e0, e3) = e2) % 190.62/30.64 (6) op(e0, e4) = all_12_2 % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | BETA: splitting (5) gives: % 190.62/30.64 | % 190.62/30.64 | Case 1: % 190.62/30.64 | | % 190.62/30.64 | | (7) all_252_20 = e2 & op(e0, e4) = e2 % 190.62/30.64 | | % 190.62/30.64 | | ALPHA: (7) implies: % 190.62/30.64 | | (8) op(e0, e4) = e2 % 190.62/30.64 | | % 190.62/30.64 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #544. % 190.62/30.64 | | % 190.62/30.64 | Case 2: % 190.62/30.64 | | % 190.62/30.64 | | (9) all_252_21 = e2 & op(e0, e3) = e2 % 190.62/30.64 | | % 190.62/30.64 | | ALPHA: (9) implies: % 190.62/30.64 | | (10) op(e0, e3) = e2 % 190.62/30.64 | | % 190.62/30.64 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #543. % 190.62/30.64 | | % 190.62/30.64 | End of split % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #543 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (2) op(e0, e3) = all_22_2 % 190.62/30.64 (3) op(e0, e3) = e2 % 190.62/30.64 (4) ~ (all_22_2 = e2) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | GROUND_INST: instantiating (1) with all_22_2, e2, e3, e0, simplifying with % 190.62/30.64 | (2), (3) gives: % 190.62/30.64 | (5) all_22_2 = e2 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (4), (5) imply: % 190.62/30.64 | (6) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (6) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #544 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (2) op(e0, e4) = all_12_2 % 190.62/30.64 (3) op(e0, e4) = e2 % 190.62/30.64 (4) ~ (all_12_2 = e2) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | GROUND_INST: instantiating (1) with all_12_2, e2, e4, e0, simplifying with % 190.62/30.64 | (2), (3) gives: % 190.62/30.64 | (5) all_12_2 = e2 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (4), (5) imply: % 190.62/30.64 | (6) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (6) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #545 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (2) op(e1, e2) = all_4_2 % 190.62/30.64 (3) op(e1, e2) = e0 % 190.62/30.64 (4) ~ (all_4_2 = e0) % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | GROUND_INST: instantiating (1) with all_4_2, e0, e2, e1, simplifying with (2), % 190.62/30.64 | (3) gives: % 190.62/30.64 | (5) all_4_2 = e0 % 190.62/30.64 | % 190.62/30.64 | REDUCE: (4), (5) imply: % 190.62/30.64 | (6) $false % 190.62/30.64 | % 190.62/30.64 | CLOSE: (6) is inconsistent. % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #546 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.64 (2) ~ (all_8_2 = e0) % 190.62/30.64 (3) ~ (all_6_2 = e0) % 190.62/30.64 (4) op(e3, e2) = all_8_2 % 190.62/30.64 (5) (all_252_4 = e0 & op(e4, e2) = e0) | (all_252_5 = e0 & op(e3, e2) = e0) % 190.62/30.64 (6) op(e4, e2) = all_6_2 % 190.62/30.64 % 190.62/30.64 Begin of proof % 190.62/30.64 | % 190.62/30.64 | BETA: splitting (5) gives: % 190.62/30.64 | % 190.62/30.64 | Case 1: % 190.62/30.64 | | % 190.62/30.64 | | (7) all_252_4 = e0 & op(e4, e2) = e0 % 190.62/30.64 | | % 190.62/30.64 | | ALPHA: (7) implies: % 190.62/30.64 | | (8) op(e4, e2) = e0 % 190.62/30.64 | | % 190.62/30.64 | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #548. % 190.62/30.64 | | % 190.62/30.64 | Case 2: % 190.62/30.64 | | % 190.62/30.64 | | (9) all_252_5 = e0 & op(e3, e2) = e0 % 190.62/30.64 | | % 190.62/30.64 | | ALPHA: (9) implies: % 190.62/30.64 | | (10) op(e3, e2) = e0 % 190.62/30.64 | | % 190.62/30.64 | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #547. % 190.62/30.64 | | % 190.62/30.64 | End of split % 190.62/30.64 | % 190.62/30.64 End of proof % 190.62/30.64 % 190.62/30.64 Sub-proof #547 shows that the following formulas are inconsistent: % 190.62/30.64 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e3, e2) = all_8_2 % 190.62/30.65 (3) op(e3, e2) = e0 % 190.62/30.65 (4) ~ (all_8_2 = e0) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_8_2, e0, e2, e3, simplifying with (2), % 190.62/30.65 | (3) gives: % 190.62/30.65 | (5) all_8_2 = e0 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #548 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e4, e2) = all_6_2 % 190.62/30.65 (3) op(e4, e2) = e0 % 190.62/30.65 (4) ~ (all_6_2 = e0) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_6_2, e0, e2, e4, simplifying with (2), % 190.62/30.65 | (3) gives: % 190.62/30.65 | (5) all_6_2 = e0 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #549 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e2, e1) = all_38_2 % 190.62/30.65 (3) op(e2, e1) = e0 % 190.62/30.65 (4) ~ (all_38_2 = e0) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_38_2, e0, e1, e2, simplifying with % 190.62/30.65 | (2), (3) gives: % 190.62/30.65 | (5) all_38_2 = e0 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #550 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_252_8 = e0 & op(e2, e2) = e0 % 190.62/30.65 (2) all_252_8 = e1 % 190.62/30.65 (3) ~ (e1 = e0) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | ALPHA: (1) implies: % 190.62/30.65 | (4) all_252_8 = e0 % 190.62/30.65 | % 190.62/30.65 | COMBINE_EQS: (2), (4) imply: % 190.62/30.65 | (5) e1 = e0 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (3), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #551 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) ~ (e4 = e0) % 190.62/30.65 (3) (all_252_6 = e0 & op(e2, e4) = e0) | (all_252_7 = e0 & op(e2, e3) = e0) % 190.62/30.65 (4) ~ (e3 = e0) % 190.62/30.65 (5) all_252_7 = e4 % 190.62/30.65 (6) op(e2, e4) = e3 % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (3) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (7) all_252_6 = e0 & op(e2, e4) = e0 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #552. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (8) all_252_7 = e0 & op(e2, e3) = e0 % 190.62/30.65 | | % 190.62/30.65 | | ALPHA: (8) implies: % 190.62/30.65 | | (9) all_252_7 = e0 % 190.62/30.65 | | % 190.62/30.65 | | COMBINE_EQS: (5), (9) imply: % 190.62/30.65 | | (10) e4 = e0 % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (2), (10) imply: % 190.62/30.65 | | (11) $false % 190.62/30.65 | | % 190.62/30.65 | | CLOSE: (11) is inconsistent. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #552 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_252_6 = e0 & op(e2, e4) = e0 % 190.62/30.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (3) op(e2, e4) = e3 % 190.62/30.65 (4) ~ (e3 = e0) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | ALPHA: (1) implies: % 190.62/30.65 | (5) op(e2, e4) = e0 % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (2) with e0, e3, e4, e2, simplifying with (3), (5) % 190.62/30.65 | gives: % 190.62/30.65 | (6) e3 = e0 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (6) imply: % 190.62/30.65 | (7) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (7) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #553 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) (all_252_6 = e1 & op(e2, e4) = e1) | (all_252_7 = e1 & op(e2, e3) = e1) % 190.62/30.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (3) op(e2, e3) = all_10_2 % 190.62/30.65 (4) ~ (all_10_2 = e1) % 190.62/30.65 (5) all_252_6 = e3 % 190.62/30.65 (6) ~ (e3 = e1) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (1) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (7) all_252_6 = e1 & op(e2, e4) = e1 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (5), (6), (7) are inconsistent by sub-proof #555. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (8) all_252_7 = e1 & op(e2, e3) = e1 % 190.62/30.65 | | % 190.62/30.65 | | ALPHA: (8) implies: % 190.62/30.65 | | (9) op(e2, e3) = e1 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #554. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #554 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e2, e3) = all_10_2 % 190.62/30.65 (3) op(e2, e3) = e1 % 190.62/30.65 (4) ~ (all_10_2 = e1) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_10_2, e1, e3, e2, simplifying with % 190.62/30.65 | (2), (3) gives: % 190.62/30.65 | (5) all_10_2 = e1 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #555 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_252_6 = e1 & op(e2, e4) = e1 % 190.62/30.65 (2) all_252_6 = e3 % 190.62/30.65 (3) ~ (e3 = e1) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | ALPHA: (1) implies: % 190.62/30.65 | (4) all_252_6 = e1 % 190.62/30.65 | % 190.62/30.65 | COMBINE_EQS: (2), (4) imply: % 190.62/30.65 | (5) e3 = e1 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (3), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #556 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ~ (all_26_2 = e2) % 190.62/30.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (3) op(e3, e1) = all_36_2 % 190.62/30.65 (4) ~ (all_36_2 = e2) % 190.62/30.65 (5) (all_252_9 = e2 & op(e4, e1) = e2) | (all_252_10 = e2 & op(e3, e1) = e2) % 190.62/30.65 (6) op(e4, e1) = all_26_2 % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (5) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (7) all_252_9 = e2 & op(e4, e1) = e2 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #558. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (8) all_252_10 = e2 & op(e3, e1) = e2 % 190.62/30.65 | | % 190.62/30.65 | | ALPHA: (8) implies: % 190.62/30.65 | | (9) op(e3, e1) = e2 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #557. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #557 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e3, e1) = all_36_2 % 190.62/30.65 (3) op(e3, e1) = e2 % 190.62/30.65 (4) ~ (all_36_2 = e2) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_36_2, e2, e1, e3, simplifying with % 190.62/30.65 | (2), (3) gives: % 190.62/30.65 | (5) all_36_2 = e2 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #558 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_252_9 = e2 & op(e4, e1) = e2 % 190.62/30.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (3) op(e4, e1) = all_26_2 % 190.62/30.65 (4) ~ (all_26_2 = e2) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | ALPHA: (1) implies: % 190.62/30.65 | (5) op(e4, e1) = e2 % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (2) with all_26_2, e2, e1, e4, simplifying with % 190.62/30.65 | (3), (5) gives: % 190.62/30.65 | (6) all_26_2 = e2 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (6) imply: % 190.62/30.65 | (7) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (7) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #559 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) ~ (all_244_0 = e3) % 190.62/30.65 (3) op(e3, e4) = all_100_2 % 190.62/30.65 (4) (all_252_0 = e3 & op(e4, e4) = e3) | (all_252_2 = e3 & op(e3, e4) = e3) % 190.62/30.65 (5) op(e4, e4) = all_244_0 % 190.62/30.65 (6) ~ (all_100_2 = e3) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (4) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (7) all_252_0 = e3 & op(e4, e4) = e3 % 190.62/30.65 | | % 190.62/30.65 | | ALPHA: (7) implies: % 190.62/30.65 | | (8) op(e4, e4) = e3 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #561. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (9) all_252_2 = e3 & op(e3, e4) = e3 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #560. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #560 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_252_2 = e3 & op(e3, e4) = e3 % 190.62/30.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (3) op(e3, e4) = all_100_2 % 190.62/30.65 (4) ~ (all_100_2 = e3) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | ALPHA: (1) implies: % 190.62/30.65 | (5) op(e3, e4) = e3 % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (2) with all_100_2, e3, e4, e3, simplifying with % 190.62/30.65 | (3), (5) gives: % 190.62/30.65 | (6) all_100_2 = e3 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (6) imply: % 190.62/30.65 | (7) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (7) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #561 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e4, e4) = all_244_0 % 190.62/30.65 (3) op(e4, e4) = e3 % 190.62/30.65 (4) ~ (all_244_0 = e3) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_244_0, e3, e4, e4, simplifying with % 190.62/30.65 | (2), (3) gives: % 190.62/30.65 | (5) all_244_0 = e3 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #562 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e3, e3) = all_244_3 % 190.62/30.65 (3) (all_252_1 = e4 & op(e4, e3) = e4) | (all_252_3 = e4 & op(e3, e3) = e4) % 190.62/30.65 (4) op(e4, e3) = all_84_2 % 190.62/30.65 (5) ~ (all_84_2 = e4) % 190.62/30.65 (6) ~ (all_244_3 = e4) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (3) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (7) all_252_1 = e4 & op(e4, e3) = e4 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #564. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (8) all_252_3 = e4 & op(e3, e3) = e4 % 190.62/30.65 | | % 190.62/30.65 | | ALPHA: (8) implies: % 190.62/30.65 | | (9) op(e3, e3) = e4 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #563. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #563 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e3, e3) = all_244_3 % 190.62/30.65 (3) op(e3, e3) = e4 % 190.62/30.65 (4) ~ (all_244_3 = e4) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_244_3, e4, e3, e3, simplifying with % 190.62/30.65 | (2), (3) gives: % 190.62/30.65 | (5) all_244_3 = e4 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #564 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_252_1 = e4 & op(e4, e3) = e4 % 190.62/30.65 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (3) op(e4, e3) = all_84_2 % 190.62/30.65 (4) ~ (all_84_2 = e4) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | ALPHA: (1) implies: % 190.62/30.65 | (5) op(e4, e3) = e4 % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (2) with all_84_2, e4, e3, e4, simplifying with % 190.62/30.65 | (3), (5) gives: % 190.62/30.65 | (6) all_84_2 = e4 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (6) imply: % 190.62/30.65 | (7) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (7) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #565 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) ~ (all_102_2 = e0) | (op(e0, e2) = all_102_1 & $i(all_102_1) & ( ~ % 190.62/30.65 (all_102_1 = e4) | ( ~ (all_102_0 = e1) & op(e2, e4) = all_102_0 & % 190.62/30.65 $i(all_102_0)))) % 190.62/30.65 (3) ~ (all_10_2 = e1) % 190.62/30.65 (4) ~ (all_10_2 = e4) % 190.62/30.65 (5) op(all_10_2, all_8_2) = e3 % 190.62/30.65 (6) ~ (all_40_2 = e3) % 190.62/30.65 (7) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | % 190.62/30.65 all_250_11 = e0 % 190.62/30.65 (8) ~ (all_10_2 = e2) % 190.62/30.65 (9) op(e2, all_10_2) = e3 % 190.62/30.65 (10) op(e2, e0) = all_40_2 % 190.62/30.65 (11) all_102_2 = all_10_2 % 190.62/30.65 (12) op(e3, all_8_2) = e2 % 190.62/30.65 (13) all_250_11 = all_10_2 % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (2) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (14) ~ (all_102_2 = e0) % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (11), (14) imply: % 190.62/30.65 | | (15) ~ (all_10_2 = e0) % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (12), (13), (15) are inconsistent % 190.62/30.65 | | by sub-proof #567. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (16) all_102_2 = e0 % 190.62/30.65 | | % 190.62/30.65 | | COMBINE_EQS: (11), (16) imply: % 190.62/30.65 | | (17) all_10_2 = e0 % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (9), (17) imply: % 190.62/30.65 | | (18) op(e2, e0) = e3 % 190.62/30.65 | | % 190.62/30.65 | | REF_CLOSE: (1), (6), (10), (18) are inconsistent by sub-proof #566. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #566 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) op(e2, e0) = all_40_2 % 190.62/30.65 (3) op(e2, e0) = e3 % 190.62/30.65 (4) ~ (all_40_2 = e3) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | GROUND_INST: instantiating (1) with all_40_2, e3, e0, e2, simplifying with % 190.62/30.65 | (2), (3) gives: % 190.62/30.65 | (5) all_40_2 = e3 % 190.62/30.65 | % 190.62/30.65 | REDUCE: (4), (5) imply: % 190.62/30.65 | (6) $false % 190.62/30.65 | % 190.62/30.65 | CLOSE: (6) is inconsistent. % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #567 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) ~ (all_10_2 = e1) % 190.62/30.65 (3) ~ (all_10_2 = e4) % 190.62/30.65 (4) op(all_10_2, all_8_2) = e3 % 190.62/30.65 (5) all_250_11 = e4 | all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | % 190.62/30.65 all_250_11 = e0 % 190.62/30.65 (6) ~ (all_10_2 = e2) % 190.62/30.65 (7) ~ (all_10_2 = e0) % 190.62/30.65 (8) op(e3, all_8_2) = e2 % 190.62/30.65 (9) all_250_11 = all_10_2 % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (5) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (10) all_250_11 = e4 % 190.62/30.65 | | % 190.62/30.65 | | COMBINE_EQS: (9), (10) imply: % 190.62/30.65 | | (11) all_10_2 = e4 % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (3), (11) imply: % 190.62/30.65 | | (12) $false % 190.62/30.65 | | % 190.62/30.65 | | CLOSE: (12) is inconsistent. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (13) all_250_11 = e3 | all_250_11 = e2 | all_250_11 = e1 | all_250_11 = % 190.62/30.65 | | e0 % 190.62/30.65 | | % 190.62/30.65 | | BETA: splitting (13) gives: % 190.62/30.65 | | % 190.62/30.65 | | Case 1: % 190.62/30.65 | | | % 190.62/30.65 | | | (14) all_250_11 = e3 % 190.62/30.65 | | | % 190.62/30.65 | | | COMBINE_EQS: (9), (14) imply: % 190.62/30.65 | | | (15) all_10_2 = e3 % 190.62/30.65 | | | % 190.62/30.65 | | | REDUCE: (6), (15) imply: % 190.62/30.65 | | | (16) ~ (e3 = e2) % 190.62/30.65 | | | % 190.62/30.65 | | | REDUCE: (4), (15) imply: % 190.62/30.65 | | | (17) op(e3, all_8_2) = e3 % 190.62/30.65 | | | % 190.62/30.65 | | | GROUND_INST: instantiating (1) with e2, e3, all_8_2, e3, simplifying with % 190.62/30.65 | | | (8), (17) gives: % 190.62/30.65 | | | (18) e3 = e2 % 190.62/30.65 | | | % 190.62/30.65 | | | REDUCE: (16), (18) imply: % 190.62/30.65 | | | (19) $false % 190.62/30.65 | | | % 190.62/30.65 | | | CLOSE: (19) is inconsistent. % 190.62/30.65 | | | % 190.62/30.65 | | Case 2: % 190.62/30.65 | | | % 190.62/30.65 | | | (20) all_250_11 = e2 | all_250_11 = e1 | all_250_11 = e0 % 190.62/30.65 | | | % 190.62/30.65 | | | BETA: splitting (20) gives: % 190.62/30.65 | | | % 190.62/30.65 | | | Case 1: % 190.62/30.65 | | | | % 190.62/30.65 | | | | (21) all_250_11 = e2 % 190.62/30.65 | | | | % 190.62/30.65 | | | | COMBINE_EQS: (9), (21) imply: % 190.62/30.65 | | | | (22) all_10_2 = e2 % 190.62/30.65 | | | | % 190.62/30.65 | | | | REDUCE: (6), (22) imply: % 190.62/30.65 | | | | (23) $false % 190.62/30.65 | | | | % 190.62/30.65 | | | | CLOSE: (23) is inconsistent. % 190.62/30.65 | | | | % 190.62/30.65 | | | Case 2: % 190.62/30.65 | | | | % 190.62/30.65 | | | | (24) all_250_11 = e1 | all_250_11 = e0 % 190.62/30.65 | | | | % 190.62/30.65 | | | | REF_CLOSE: (2), (7), (9), (24) are inconsistent by sub-proof #568. % 190.62/30.65 | | | | % 190.62/30.65 | | | End of split % 190.62/30.65 | | | % 190.62/30.65 | | End of split % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #568 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) all_250_11 = e1 | all_250_11 = e0 % 190.62/30.65 (2) all_250_11 = all_10_2 % 190.62/30.65 (3) ~ (all_10_2 = e1) % 190.62/30.65 (4) ~ (all_10_2 = e0) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (1) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (5) all_250_11 = e1 % 190.62/30.65 | | % 190.62/30.65 | | COMBINE_EQS: (2), (5) imply: % 190.62/30.65 | | (6) all_10_2 = e1 % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (3), (6) imply: % 190.62/30.65 | | (7) $false % 190.62/30.65 | | % 190.62/30.65 | | CLOSE: (7) is inconsistent. % 190.62/30.65 | | % 190.62/30.65 | Case 2: % 190.62/30.65 | | % 190.62/30.65 | | (8) all_250_11 = e0 % 190.62/30.65 | | % 190.62/30.65 | | COMBINE_EQS: (2), (8) imply: % 190.62/30.65 | | (9) all_10_2 = e0 % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (4), (9) imply: % 190.62/30.65 | | (10) $false % 190.62/30.65 | | % 190.62/30.65 | | CLOSE: (10) is inconsistent. % 190.62/30.65 | | % 190.62/30.65 | End of split % 190.62/30.65 | % 190.62/30.65 End of proof % 190.62/30.65 % 190.62/30.65 Sub-proof #569 shows that the following formulas are inconsistent: % 190.62/30.65 ---------------------------------------------------------------- % 190.62/30.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.65 (2) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | % 190.62/30.65 all_250_17 = e0 % 190.62/30.65 (3) ~ (all_180_2 = e4) | (op(e4, e1) = all_180_1 & $i(all_180_1) & ( ~ % 190.62/30.65 (all_180_1 = e0) | ( ~ (all_180_0 = e3) & op(e1, e0) = all_180_0 & % 190.62/30.65 $i(all_180_0)))) % 190.62/30.65 (4) ~ (all_16_2 = e2) % 190.62/30.65 (5) op(e1, e3) = all_62_2 % 190.62/30.65 (6) op(e2, all_38_2) = e1 % 190.62/30.65 (7) ~ (all_4_2 = e0) % 190.62/30.65 (8) ~ (all_16_2 = e3) % 190.62/30.65 (9) ~ (all_150_2 = e3) | (op(e3, e1) = all_150_1 & $i(all_150_1) & ( ~ % 190.62/30.65 (all_150_1 = e0) | ( ~ (all_150_0 = e4) & op(e1, e0) = all_150_0 & % 190.62/30.65 $i(all_150_0)))) % 190.62/30.65 (10) ~ (all_66_2 = e0) | (op(e0, e1) = all_66_1 & $i(all_66_1) & ( ~ % 190.62/30.65 (all_66_1 = e3) | ( ~ (all_66_0 = e2) & op(e1, e3) = all_66_0 & % 190.62/30.65 $i(all_66_0)))) % 190.62/30.65 (11) all_66_2 = all_16_2 % 190.62/30.65 (12) all_150_2 = all_4_2 % 190.62/30.65 (13) all_250_15 = all_16_2 % 190.62/30.65 (14) op(all_4_2, all_38_2) = e2 % 190.62/30.65 (15) all_250_15 = e4 | all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 | % 190.62/30.65 all_250_15 = e0 % 190.62/30.65 (16) all_250_17 = all_4_2 % 190.62/30.65 (17) op(e1, all_4_2) = e2 % 190.62/30.65 (18) op(e1, e4) = all_16_2 % 190.62/30.65 (19) op(e1, all_16_2) = e4 % 190.62/30.65 (20) ~ (all_16_2 = all_4_2) % 190.62/30.65 (21) op(e4, all_26_2) = e1 % 190.62/30.65 (22) ~ (all_62_2 = e2) % 190.62/30.65 (23) op(e1, e0) = all_34_2 % 190.62/30.65 (24) ~ (all_34_2 = e4) % 190.62/30.65 (25) all_180_2 = all_4_2 % 190.62/30.65 (26) op(all_16_2, all_26_2) = e4 % 190.62/30.65 (27) ~ (e4 = e1) % 190.62/30.65 % 190.62/30.65 Begin of proof % 190.62/30.65 | % 190.62/30.65 | BETA: splitting (10) gives: % 190.62/30.65 | % 190.62/30.65 | Case 1: % 190.62/30.65 | | % 190.62/30.65 | | (28) ~ (all_66_2 = e0) % 190.62/30.65 | | % 190.62/30.65 | | REDUCE: (11), (28) imply: % 190.62/30.65 | | (29) ~ (all_16_2 = e0) % 190.62/30.65 | | % 190.62/30.65 | | BETA: splitting (9) gives: % 190.62/30.65 | | % 190.62/30.65 | | Case 1: % 190.62/30.65 | | | % 190.62/30.65 | | | (30) ~ (all_150_2 = e3) % 190.62/30.65 | | | % 190.62/30.65 | | | REDUCE: (12), (30) imply: % 190.62/30.65 | | | (31) ~ (all_4_2 = e3) % 190.62/30.65 | | | % 190.62/30.65 | | | BETA: splitting (3) gives: % 190.62/30.65 | | | % 190.62/30.65 | | | Case 1: % 190.62/30.65 | | | | % 190.62/30.65 | | | | (32) ~ (all_180_2 = e4) % 190.62/30.65 | | | | % 190.62/30.65 | | | | REDUCE: (25), (32) imply: % 190.62/30.65 | | | | (33) ~ (all_4_2 = e4) % 190.62/30.65 | | | | % 190.62/30.65 | | | | BETA: splitting (15) gives: % 190.62/30.65 | | | | % 190.62/30.65 | | | | Case 1: % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | (34) all_250_15 = e4 % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | COMBINE_EQS: (13), (34) imply: % 190.62/30.65 | | | | | (35) all_16_2 = e4 % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | SIMP: (35) implies: % 190.62/30.65 | | | | | (36) all_16_2 = e4 % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | REDUCE: (26), (36) imply: % 190.62/30.65 | | | | | (37) op(e4, all_26_2) = e4 % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | REF_CLOSE: (1), (21), (27), (37) are inconsistent by sub-proof #579. % 190.62/30.65 | | | | | % 190.62/30.65 | | | | Case 2: % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | (38) all_250_15 = e3 | all_250_15 = e2 | all_250_15 = e1 | % 190.62/30.65 | | | | | all_250_15 = e0 % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | BETA: splitting (38) gives: % 190.62/30.65 | | | | | % 190.62/30.65 | | | | | Case 1: % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | | (39) all_250_15 = e3 % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | | REF_CLOSE: (8), (13), (39) are inconsistent by sub-proof #578. % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | Case 2: % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | | (40) all_250_15 = e2 | all_250_15 = e1 | all_250_15 = e0 % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | | BETA: splitting (40) gives: % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | | Case 1: % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | | (41) all_250_15 = e2 % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | | REF_CLOSE: (4), (13), (41) are inconsistent by sub-proof #577. % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | Case 2: % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | | (42) all_250_15 = e1 | all_250_15 = e0 % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | | BETA: splitting (42) gives: % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | | Case 1: % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | (43) all_250_15 = e1 % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | COMBINE_EQS: (13), (43) imply: % 190.62/30.65 | | | | | | | | (44) all_16_2 = e1 % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | SIMP: (44) implies: % 190.62/30.65 | | | | | | | | (45) all_16_2 = e1 % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | REDUCE: (20), (45) imply: % 190.62/30.65 | | | | | | | | (46) ~ (all_4_2 = e1) % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | SIMP: (46) implies: % 190.62/30.65 | | | | | | | | (47) ~ (all_4_2 = e1) % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | REF_CLOSE: (1), (2), (6), (7), (14), (16), (31), (33), (47) are % 190.62/30.65 | | | | | | | | inconsistent by sub-proof #575. % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | Case 2: % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | (48) all_250_15 = e0 % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | | REF_CLOSE: (13), (29), (48) are inconsistent by sub-proof #574. % 190.62/30.65 | | | | | | | | % 190.62/30.65 | | | | | | | End of split % 190.62/30.65 | | | | | | | % 190.62/30.65 | | | | | | End of split % 190.62/30.65 | | | | | | % 190.62/30.65 | | | | | End of split % 190.62/30.65 | | | | | % 190.62/30.65 | | | | End of split % 190.62/30.65 | | | | % 190.62/30.65 | | | Case 2: % 190.62/30.65 | | | | % 190.62/30.65 | | | | (49) all_180_2 = e4 % 190.62/30.65 | | | | % 190.62/30.65 | | | | COMBINE_EQS: (25), (49) imply: % 190.62/30.65 | | | | (50) all_4_2 = e4 % 190.62/30.65 | | | | % 190.62/30.65 | | | | REDUCE: (17), (50) imply: % 190.62/30.66 | | | | (51) op(e1, e4) = e2 % 190.62/30.66 | | | | % 190.62/30.66 | | | | REF_CLOSE: (1), (4), (18), (51) are inconsistent by sub-proof #573. % 190.62/30.66 | | | | % 190.62/30.66 | | | End of split % 190.62/30.66 | | | % 190.62/30.66 | | Case 2: % 190.62/30.66 | | | % 190.62/30.66 | | | (52) all_150_2 = e3 % 190.62/30.66 | | | % 190.62/30.66 | | | COMBINE_EQS: (12), (52) imply: % 190.62/30.66 | | | (53) all_4_2 = e3 % 190.62/30.66 | | | % 190.62/30.66 | | | SIMP: (53) implies: % 190.62/30.66 | | | (54) all_4_2 = e3 % 190.62/30.66 | | | % 190.62/30.66 | | | REDUCE: (17), (54) imply: % 190.62/30.66 | | | (55) op(e1, e3) = e2 % 190.62/30.66 | | | % 190.62/30.66 | | | REF_CLOSE: (1), (5), (22), (55) are inconsistent by sub-proof #572. % 190.62/30.66 | | | % 190.62/30.66 | | End of split % 190.62/30.66 | | % 190.62/30.66 | Case 2: % 190.62/30.66 | | % 190.62/30.66 | | (56) all_66_2 = e0 % 190.62/30.66 | | % 190.62/30.66 | | REF_CLOSE: (1), (11), (19), (23), (24), (56) are inconsistent by sub-proof % 190.62/30.66 | | #570. % 190.62/30.66 | | % 190.62/30.66 | End of split % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #570 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) all_66_2 = e0 % 190.62/30.66 (3) all_66_2 = all_16_2 % 190.62/30.66 (4) op(e1, all_16_2) = e4 % 190.62/30.66 (5) op(e1, e0) = all_34_2 % 190.62/30.66 (6) ~ (all_34_2 = e4) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | COMBINE_EQS: (2), (3) imply: % 190.62/30.66 | (7) all_16_2 = e0 % 190.62/30.66 | % 190.62/30.66 | SIMP: (7) implies: % 190.62/30.66 | (8) all_16_2 = e0 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (4), (8) imply: % 190.62/30.66 | (9) op(e1, e0) = e4 % 190.62/30.66 | % 190.62/30.66 | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #571. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #571 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) op(e1, e0) = all_34_2 % 190.62/30.66 (3) op(e1, e0) = e4 % 190.62/30.66 (4) ~ (all_34_2 = e4) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | GROUND_INST: instantiating (1) with all_34_2, e4, e0, e1, simplifying with % 190.62/30.66 | (2), (3) gives: % 190.62/30.66 | (5) all_34_2 = e4 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (4), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #572 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) op(e1, e3) = all_62_2 % 190.62/30.66 (3) op(e1, e3) = e2 % 190.62/30.66 (4) ~ (all_62_2 = e2) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | GROUND_INST: instantiating (1) with all_62_2, e2, e3, e1, simplifying with % 190.62/30.66 | (2), (3) gives: % 190.62/30.66 | (5) all_62_2 = e2 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (4), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #573 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) op(e1, e4) = all_16_2 % 190.62/30.66 (3) op(e1, e4) = e2 % 190.62/30.66 (4) ~ (all_16_2 = e2) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | GROUND_INST: instantiating (1) with all_16_2, e2, e4, e1, simplifying with % 190.62/30.66 | (2), (3) gives: % 190.62/30.66 | (5) all_16_2 = e2 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (4), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #574 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) all_250_15 = all_16_2 % 190.62/30.66 (2) all_250_15 = e0 % 190.62/30.66 (3) ~ (all_16_2 = e0) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | COMBINE_EQS: (1), (2) imply: % 190.62/30.66 | (4) all_16_2 = e0 % 190.62/30.66 | % 190.62/30.66 | SIMP: (4) implies: % 190.62/30.66 | (5) all_16_2 = e0 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (3), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #575 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) all_250_17 = e4 | all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | % 190.62/30.66 all_250_17 = e0 % 190.62/30.66 (3) ~ (all_4_2 = e4) % 190.62/30.66 (4) op(e2, all_38_2) = e1 % 190.62/30.66 (5) ~ (all_4_2 = e0) % 190.62/30.66 (6) ~ (all_4_2 = e1) % 190.62/30.66 (7) op(all_4_2, all_38_2) = e2 % 190.62/30.66 (8) all_250_17 = all_4_2 % 190.62/30.66 (9) ~ (all_4_2 = e3) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | BETA: splitting (2) gives: % 190.62/30.66 | % 190.62/30.66 | Case 1: % 190.62/30.66 | | % 190.62/30.66 | | (10) all_250_17 = e4 % 190.62/30.66 | | % 190.62/30.66 | | COMBINE_EQS: (8), (10) imply: % 190.62/30.66 | | (11) all_4_2 = e4 % 190.62/30.66 | | % 190.62/30.66 | | REDUCE: (3), (11) imply: % 190.62/30.66 | | (12) $false % 190.62/30.66 | | % 190.62/30.66 | | CLOSE: (12) is inconsistent. % 190.62/30.66 | | % 190.62/30.66 | Case 2: % 190.62/30.66 | | % 190.62/30.66 | | (13) all_250_17 = e3 | all_250_17 = e2 | all_250_17 = e1 | all_250_17 = % 190.62/30.66 | | e0 % 190.62/30.66 | | % 190.62/30.66 | | BETA: splitting (13) gives: % 190.62/30.66 | | % 190.62/30.66 | | Case 1: % 190.62/30.66 | | | % 190.62/30.66 | | | (14) all_250_17 = e3 % 190.62/30.66 | | | % 190.62/30.66 | | | COMBINE_EQS: (8), (14) imply: % 190.62/30.66 | | | (15) all_4_2 = e3 % 190.62/30.66 | | | % 190.62/30.66 | | | REDUCE: (9), (15) imply: % 190.62/30.66 | | | (16) $false % 190.62/30.66 | | | % 190.62/30.66 | | | CLOSE: (16) is inconsistent. % 190.62/30.66 | | | % 190.62/30.66 | | Case 2: % 190.62/30.66 | | | % 190.62/30.66 | | | (17) all_250_17 = e2 | all_250_17 = e1 | all_250_17 = e0 % 190.62/30.66 | | | % 190.62/30.66 | | | BETA: splitting (17) gives: % 190.62/30.66 | | | % 190.62/30.66 | | | Case 1: % 190.62/30.66 | | | | % 190.62/30.66 | | | | (18) all_250_17 = e2 % 190.62/30.66 | | | | % 190.62/30.66 | | | | COMBINE_EQS: (8), (18) imply: % 190.62/30.66 | | | | (19) all_4_2 = e2 % 190.62/30.66 | | | | % 190.62/30.66 | | | | REF_CLOSE: (1), (4), (6), (7), (19) are inconsistent by sub-proof #576. % 190.62/30.66 | | | | % 190.62/30.66 | | | Case 2: % 190.62/30.66 | | | | % 190.62/30.66 | | | | (20) all_250_17 = e1 | all_250_17 = e0 % 190.62/30.66 | | | | % 190.62/30.66 | | | | BETA: splitting (20) gives: % 190.62/30.66 | | | | % 190.62/30.66 | | | | Case 1: % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | (21) all_250_17 = e1 % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | COMBINE_EQS: (8), (21) imply: % 190.62/30.66 | | | | | (22) all_4_2 = e1 % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | REDUCE: (6), (22) imply: % 190.62/30.66 | | | | | (23) $false % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | CLOSE: (23) is inconsistent. % 190.62/30.66 | | | | | % 190.62/30.66 | | | | Case 2: % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | (24) all_250_17 = e0 % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | COMBINE_EQS: (8), (24) imply: % 190.62/30.66 | | | | | (25) all_4_2 = e0 % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | REDUCE: (5), (25) imply: % 190.62/30.66 | | | | | (26) $false % 190.62/30.66 | | | | | % 190.62/30.66 | | | | | CLOSE: (26) is inconsistent. % 190.62/30.66 | | | | | % 190.62/30.66 | | | | End of split % 190.62/30.66 | | | | % 190.62/30.66 | | | End of split % 190.62/30.66 | | | % 190.62/30.66 | | End of split % 190.62/30.66 | | % 190.62/30.66 | End of split % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #576 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) op(e2, all_38_2) = e1 % 190.62/30.66 (3) ~ (all_4_2 = e1) % 190.62/30.66 (4) op(all_4_2, all_38_2) = e2 % 190.62/30.66 (5) all_4_2 = e2 % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | REDUCE: (3), (5) imply: % 190.62/30.66 | (6) ~ (e2 = e1) % 190.62/30.66 | % 190.62/30.66 | REDUCE: (4), (5) imply: % 190.62/30.66 | (7) op(e2, all_38_2) = e2 % 190.62/30.66 | % 190.62/30.66 | GROUND_INST: instantiating (1) with e1, e2, all_38_2, e2, simplifying with % 190.62/30.66 | (2), (7) gives: % 190.62/30.66 | (8) e2 = e1 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (6), (8) imply: % 190.62/30.66 | (9) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (9) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #577 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) all_250_15 = all_16_2 % 190.62/30.66 (2) all_250_15 = e2 % 190.62/30.66 (3) ~ (all_16_2 = e2) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | COMBINE_EQS: (1), (2) imply: % 190.62/30.66 | (4) all_16_2 = e2 % 190.62/30.66 | % 190.62/30.66 | SIMP: (4) implies: % 190.62/30.66 | (5) all_16_2 = e2 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (3), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #578 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) all_250_15 = all_16_2 % 190.62/30.66 (2) all_250_15 = e3 % 190.62/30.66 (3) ~ (all_16_2 = e3) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | COMBINE_EQS: (1), (2) imply: % 190.62/30.66 | (4) all_16_2 = e3 % 190.62/30.66 | % 190.62/30.66 | SIMP: (4) implies: % 190.62/30.66 | (5) all_16_2 = e3 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (3), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % 190.62/30.66 Sub-proof #579 shows that the following formulas are inconsistent: % 190.62/30.66 ---------------------------------------------------------------- % 190.62/30.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 190.62/30.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0)) % 190.62/30.66 (2) op(e4, all_26_2) = e4 % 190.62/30.66 (3) op(e4, all_26_2) = e1 % 190.62/30.66 (4) ~ (e4 = e1) % 190.62/30.66 % 190.62/30.66 Begin of proof % 190.62/30.66 | % 190.62/30.66 | GROUND_INST: instantiating (1) with e1, e4, all_26_2, e4, simplifying with % 190.62/30.66 | (2), (3) gives: % 190.62/30.66 | (5) e4 = e1 % 190.62/30.66 | % 190.62/30.66 | REDUCE: (4), (5) imply: % 190.62/30.66 | (6) $false % 190.62/30.66 | % 190.62/30.66 | CLOSE: (6) is inconsistent. % 190.62/30.66 | % 190.62/30.66 End of proof % 190.62/30.66 % SZS output end Proof for theBenchmark % 190.62/30.66 % 190.62/30.66 30066ms %------------------------------------------------------------------------------